Okay, So today we’re going to be talking about measures of central tendency. Central tendency, it describes the points around which the rest of this course focus. So the three measures that we use for central tendencies are the mean, the median, and the mode. So the mean is just the arithmetic average score of all the scores in a set of scores. The median is considered the central score, or that point which divides a distribution into two equal parts with 50% of the distribution on one side of the median and 50 percent on the other. The mode is considered the typical or most frequent occurring score in a distribution of scores. Each has its own assumptions. And it is important to know these assumptions in order to know when, when is appropriate to report daring data analysis. So the mode is the most common score, as I just talked about. It can be used with variables at all three levels of measurement. It makes it very versatile. Most often used with nominal level variables. So when we want to find the mode, we count the number of times that each core occurs, and the score that occurs the most often is the mode at the variable is presented in a frequency distribution. The mode is the largest category or the one with the most frequencies. And at the variable is presented in a line chart, then the mode is the highest peak. So that would represent the, the one with the most. Okay, so here we have a couple of examples trying to find the mode. And so if we go through and count, we would see that we have two 25s where 326 is 21 at the rest of them, right? So that means that 26 is our mode. So for the next array, we would want to go through and kind of do the same. So we have three 25s, 320, sixes, and 327. So that means that this one actually has three modes. And so for the next one, we have two and then two sets and then 22 and then two. And so once we hit more than three, we would consider it to not have a mode kind of the same if it wasn’t multiple of one particular score. So we can have unimodal with just one node. We can have bimodal with two modes, or three modes would be multimodal. But then after that, it’s considered not to have a mode. So when we look at the mode for group scores, the mode for group data is defined as the midpoint of the interval containing the most frequencies. So three is the maximum number for group modes as well. So if there’s a fourth, then is considered not to have a mode. Use the mid points of the intervals as the mode. Example here, we would have to find out where our one is with the most frequencies. And so that looks like it is here with the team. And so 15 is found in the interval of 40 to 44. And so the next step would be to find the midpoint of this particular interval. And so to find the midpoint, you take the lower limit of the variable that, or if sorry, of the interval that you’re in. So the lower limit here would be 39.5. So that’s the lowest line because it could round up and 240. And then you divide the interval size by two. So five divided by two would be equal to 2.5. And so now I want to add 90 or sorry, 39.5 to 2.5 and that gives me 42. So when you have very small interval sizes, of course it’s easy to count and just see that it is 42. But that’s the way that you would go about looking at it and seeing. And so over here we have three sets of 15. And so this one would be considered to be tri modal. And you would just go through the same process and just find the midpoint for each one of these intervals. So, so when we’re looking at this, Typically have to realize that the most popular is not always the most central score. It can actually be very far away from the central tendency. So deviant scores are outliers. Score is located in one extreme or the other, can affect the mode. And so an example of this could be on a, on a quiz. And so let’s say that you have five people who made a 90 on it. And then you have by people who made a 80 on it. And then you have for people who made a 100, right? And so really you would have the 22 modes, right? But that really doesn’t an 80 and 90. And then all those hundreds doesn’t really give you exactly very much useful information at all. So you’ve really got to consider why exactly that you are reporting your data as into which one it is that you want. But also, let’s say with that same score, and you had to buy five zeros. And the zeros, we’re just because somebody had taken them yet. And so that would be extremely misleading if that was the mode. So some of the limitations of the mode. So some distribution tab, no mode. Some distribution have multiple modes. And mode of a ordinal or interval ratio level variable may not be central to the whole distribution. And so again, that’s why we use it a lot more for nominal variables even though it can be used for all three. So the median, the exact center of the distribution of scores. So essentially just the one in the middle. It can be used with variables measured at the ordinal or interval. And ratio levels cannot be used for nominal level variables. So we can’t really have the middle colors. It doesn’t make any sense. At least not numerically to have 50 percent of the site green and 50 percent about site green just doesn’t work that way of where as for the mode, right, we could say that Green had the highest frequency. So in order to find the mean, you need to put all the scores into an array. So array the cases from low to high or from high to low. It really doesn’t matter as long as you put them in order, you locate the middle case. So if n is odd, the median score in the middle case. If n is even, and the median is the average of the scores of the two middle cases. And so here we have a couple of arrays that we can use for district nutrition. And so here when we’re looking for the one in the middle. So we’ll, we have three cases. That would mean that 15 would be our median. So here we have a even number. So that means that the two in the middle we have to add together and then we divide by two. And so that would give us immediate 16. And so here though, is where the median could also be helpful and maybe a little bit more resistant to outliers. Because still here, even though we have a 100 instead of a 19, the median is still 16. And so here it’s 15 and 35. And then here we’d have to do 15 plus 15 divided by 2 is 13. So that is pretty much it. It’s really pretty easy to be able to find out which one that is. It gets a little bit more difficult if we’re needing to find the median for group data. So the formula for finding the median for group data is the lower limit plus frequencies needed in the interval divided by frequencies found in the interval times the interval size. Okay? And so this is where having a cumulative frequency comes in handy. And so the first thing that I want to do is find out where exactly the sinner score is. And so to do that, I would take my a 111 and divide it by two. And so that would give me 55.5. And so I want to go up through here and find out how close I can get to 55.5 without going over. And so it looks like I can get to 51. Alright, so how many more do I need in order to hit my pity by 0.5? So 55.5 minus one gives me 4.5. So that would be my frequencies needed out the next interval. And so if I go up to the next interval, it looks like I find nine frequencies, so that’s my frequencies pound. And so I want to use the lower limit of the interval from which I am going to be borrowing some of these frequencies from. So that would be a 139.5. And so I would just go through and fill it in. So a 139.5 plus 4.5 divided by nine times five. And so my essentially my median would be essentially a 142, would be our closest guess. And so that is how we would figure out where the median is by just finding out what these numbers are and then doing the math. So pretty simple. So one of the things about median is that it assumes that data can be measured at the ordinal or scale or higher. So again, it can’t be like we’ve already talked about, used for actual, for nominal data is still. So this is a pretty stable measure of central tendency in the sense that it divides the scores in half. So it is the center of the data. So we don’t have to look at just the 50 percent. Sometimes it will tell us more to look at maybe descent tiles or desk styles or quartiles. So 50 percent is the desk style, but it’s also the second quartile. And so this, this gives us a little bit more information. So if you have ever taken an exam and you scored in the 75th percentile, that means that you scored better than 75% of all the other people who took that particular exam. And so if we’re wanting to look at near 30 percent, 33 percent, then that would be the 33rd Gentile. And so it’s very, some work easy way to look at it as like with our coins. It’s like $0.01. It’s 1%. A dime, 10, $0.10 quarter, 25 cents. So that’s kind of an easier way to help you remember it. And so like if I wanted to find the 75th percentile or the third quartile for the dataset that we just had, then instead divided by 2. Or if I wanted to multiply, I would multiply it by 0.5, which will be the same equivalent. So here I would just take the 111 and multiply it by 0.75. And so the 75th percentile for that data set that we were just looking at is 83.2. And then from there we would just use a formula to plug in and find where exactly that particular score would be. So the mean is very simply, the average score. Requires variables measured at the interval ratio level. But it’s often used with the ordinal level variables. Really shouldn’t do that. It’s really bad practice to do this because it violates a couple of assumptions, but some people do. Well. And when you get to the other classes, we’ll talk more about how to handle that. But for the most part, it really just needs to be used for interval ratio. Because it doesn’t essentially you can’t have a 4.5 agreement or a level of agreement. So it doesn’t make sense to use at the ordinal level variable. So cannot be used for nominal level variables at all. Definitely can’t be 0.5 green. And so kind of the same reason that you really should not use it at the ordinal level either because you can’t be 0.5 agreeable. So the mean or arithmetic average is by far the most commonly used measure of central tendency. So the formula for the mean is just the x bar. That’s the symbol here, equals the mean. And so you have your sum symbol here, and you have this symbol for scores. So when you see this, this just means the sum of the scores. And then n is the number of cases that you have. So some of the characteristics of the mean, the mean balances out all of the scores in a distribution. So all scores cancel out around the mean. So if we was to take each individual score and minus it from the mean, and then some that together it should always equals 0. And we’ll talk more about that in the next chapter’s lecture video. The mean is the point of minimised variation of the scores. So the least squares principle. So again, that has to do a lot more with it. Levels of variants. And so again, we’ll talk more about that next lecture video. The mean is affected by all scores. So all scores are used in the calculation of the mean. And so this makes it very difficult because when you have extreme scores and it really throws off the demand and the main can actually be very misleading. And so a lot of times you would want to look at your outliers and maybe report both means or report the median. And I mean, we’re just kinda talk about it in some way so that you’re not misleading your audience when you do have a skewed mean. So a strength of the mean is that the mean is used at the available information from the variable. So it uses all of the information. Some of the weaknesses though, is that it is affected by every score. So our high scores and low scores or outliers, do you affect it? If there are some very high or very low scores? So what we’re talking about here would be a skewed distribution, then the mean can be very misleading, like I just talked about. Here, is kind of an example. And so all you do is, you know, this fancy formula let me into really is that you add up all the numbers that you have here. And so if we totaled them together, we would have 695. And then I have 21 scores. And so I take the 695 and I divide it by 21. And that would give me a mean of 33.1. And so when I’m talking about it being sensitive to outliers, Let’s say that instead of the 60, we had 600. And so that would be a very far extreme from where our data actually is. That if we want to have a 600 instead of 60, that would change our mean, 258.8. And so 58.8 would be nowhere near our central of this particular data set. And so a lot of times the median is the most appropriate when there are extreme outliers like because in that case than the median will be centered, more central to where the rest of the cases are. So the mean for group data is simply the sum of the frequencies times and then points divided by n. And so we find the midpoints for each of our intervals. And then we multiply that by the number of frequencies. So here we have 8 times 8, which gives us 464. So you keep going down through. And once you find that Then you divide by n. And so in this particular case, N equals 100, 15. And so you would, if we added amount together, then we would have books like my numbers are off a little bit. Canada up to 404,615 divided by 15. And then that would give us 40, 0.1. And so, and so this, ignore this right here. This right here should, or you want to go to. And so that’s really pretty simple. I mean, it’s a lot of work. But again, don’t let like all these fancy equations that you off. But I think that’s where a lot of people get intimidated about stats. But if you break it down into, you just take this and you multiply it by that. And then you add all this together and divide by that, then truly not that hard. You just have to pay attention to detail. All right? And so means medians and skew. When a distribution has API very high or low scores, the mean will be pulled in the direction of the extreme scores. For a positive skew, the mean will be greater than the median. And for a negative score and the mean will be less than the median. And so that is essentially how you can tell the difference between the two. So some people say if the tails to the left or to the right, that then that gets complicated as unto, you know, which lacked what right. And so positive and negative is just a direction. But the best way to be able to tell which way it’s skewed. It, It’s positive than the mean will be greater than the median. And if it’s negative, the me, an OB less than when an interval ratio level variable has a pronounced skew. The media and maybe the most trustworthy measure of central tendencies. And so that’s pretty much sums up what we’re talking about with making sure that we know why we’re reporting them. And some of the assumptions behind in order to make sure that we don’t report something that doesn’t make sense. And so we would end up with what are those studies that says that the average household has 2.3 kids, um, because you can’t really have 0.3 of my kids. So that’s make sure that you know, all these assumptions so that you don’t end up saying something like that, right? And that pretty much covers central tendency.
For this video, we are going to be talking about measures of variability or dispersion. That the concept of dispersion, it refers to the variety, diversity, or amount of variation among scores. The greater the dispersion of a variable, the greater the range of scores and the greater the differences between scores. When we’re looking at measuring variability, we have to consider the different types of data that we have. And also why it is that we are trying to measure the variability. And so the ones that we’re going to be talking about in this lecture are the ICU UV range, a deviation score or average deviation, variance and standard deviation. So if we have nominal data, then the one that we have to use is Miller and scholars index a qualitative variation. Range can be used for a number different types of variables. So this is the distance between over which particular proportions of scores are spread. Deviation score. It’s a distance of scores from the mean of their distribution. Variance is the sum of the squared deviation scores divided by n. And then our standard deviation is the square root of the variance. And the standard deviation is important because it’s the one that we use for decision-making about if something is significant or not. So very important part of understanding statistics. Okay, so here we’re going to talk about I QV first. And so this particular is the formula I QV equals observed heterogeneity divided by maximum heterogeneity the times a 100. And so essentially to be able to find out how many of these observed and maximums that you need. You would use this particular formula, k times k minus one divided by two. And so here we have an example of nominal data and which we have different types of grapes. And so we have date rape, rate bag, close friend, by a family acquaintance, by a stranger, and by a relative. And so in order to find out our level of variance between these, we need to find out the observed and the expected. And so if there is nothing going on, if there was no types influences on the outside as to what leads to these different types of grapes, then we would expect for all of them to be even all to be 200. And so that would be our maximum heterogeneity, right? And so in this particular case, we would look at the number of products. And so here we have 12345 cases. Then we multiply it by that same number minus 1, so 5 plus 4. And then we would divide it by two. So that gives us 10. So we would have 10 different sets of products. And so what that’s talking about here is for our observed, our first product would be 200 times 100. And then we would add that score to 200 times 200. And then we would add that score to 200 times 350 and then 200 times 150. And then we would go down to the next one. And we would have a 100 times 200100 times 350 and a 100 times a 150. And so going ahead and knowing how many products you should have, right? So product, this means how many times you’re going to be multiplying something by. And that kinda lets us go ahead and lay out the equation and know exactly what it’s supposed to be expected. And so since the base is the same. Then you can actually just go ahead and we know that it’s going to be 10 products. So you could just take 200 times 200 and raise it to the tenth, which would give us 400 thousand. So that’s pretty easy to do on this side. But essentially to know that we do a 10, right? So this is one, this is two, this is three, this is four. This is 567. This is eight, this is nine, this is 10. And so it just helps keep everything straight. And then you add all those together. And said If we did that, then we would end up with 382,500 divided by 400 thousand. And so that gives us 0.9562. And then we multiply that by a 100 in order to get it into a percentage. And so that would be 95.62. And so that tells us that there is a, a decent amount of diversity, but it’s really not that far along because like Syria we have here that are 200 even and the a 150 is close. And so that tells us that essentially there’s not a whole lot of dispersion there between observed and expected. Okay, so the range, range indicates the distance between the highest and lowest scores of a distribution. Range is often indicated with an r equals high score minus lowest score. It is a quick and easy indication. Variability. It can be used with ordinal or interval ratio data. And the reason that, again, that we can’t use the range from a nominal variable is that it just wouldn’t make sense that you would have a measurable distance between pigs and cows are between apples and oranges. So it can only be used for the higher levels of measurement. So here we have an example of an array that we’re going to talk about the range for. And so we would indicate and find our highest and our lowest. So again, by putting them in array, that helps us to find that information. And so our lowest is 20 and our highest is 49. And so the range, so distance over which 100% of the scores in a distribution is spread would be 49 minus 20. So that would give us 29. So some textbooks would say that you, that you should use the lower limits and upper limits. And so again, it depends on the textbook, so always pay attention to that. So like if back when I was where you guys were at, I would actually hacked they take 49.5 and subtract it from night team 0.5 and so my range would be 30. So it really depends. And again, you’ve had a look at what your textbooks wanting and what your teachers wanting. So this follow the textbooks guidance on that one. So here we can also find our interquartile range. And so we’ll go back to this slide here just a second. So the interquartile range is a type of range measurement. It considers only the middle 50 percent of cases of a distribution. It avoid some of the problems of the range by focusing on just the middle 50 percent of the scores. It is limited because the inner quartile range is based only on to scores. Yeah, it felt to yield any information from all of the other scores. So you’re cutting off 50% of the scores. And so if we went back here and we wanted to find where our information would be, then I would need to locate my first third quartile. So the first one. So it would be our fifth case. So 1234. Five, so 28 is our first quartile. And then the last 5, 1, 2, 3, 4, 5. Though, that would be the start of the fourth. So I want the end of the third. And so this would give me 44 minus 28, which would give me a intake or inter-quartile range of 16, which is very different from the 2009 that we got before. So this when there really wouldn’t be any need to do that because we don’t have extreme outliers on either side. So that would be kind of misleading in order to use that type of range for this particular distribution. So again, you’ve got to look at what your data looks like and to determine what you should report. So kind of the same whenever we’re wanting to find the range for group data, then we would just take the lowest from whichever said it is that we have so the 115 and 179. And so essentially the range would be 179 minus 1. That teen or if you’re doing old school like I was raised to do when some 9.5 minus 1.514. So again, follow the textbook and do whichever way the textbook tells you to do. All right? And so here, the 175 minus 14.5.75.5 minus 1414.5 equals 61. So this is a very unstable measure because it is very sensitive to deviant scores. So it’s a poor choice if you have outliers. And so we can also find the interquartile range or group data as well, kind of like we talked about with the last video. So this is actually the same chart that we’re going to be looking at from, from that. And so here, if we were doing the halfway, would take it by five. So this is exactly what we went through with our last equation. And so go through that and we would just change it up a little bit. Where if we wanted to find the first third quartiles, then we would have to take the 111 and multiply it by point T5. And so that would give us the 27.5. And then we would take this and multiply the a 111 by 0.75 to give us the third quartile. And then based on that information, we would find the median score for each of those. So weird. Yeah, Essentially you’d have to go figure out which one it is and you’d have to go through and follow the exact same steps. And so if I wanted to find where 27.5 would be, I would go as close as I can get without going over. So there is 26. So I would need to borrow from this particular interval right here. So my lower than that would be my 129.5. And I at 26. So 27.5 minus 26 would be what, 1.5. So that is the number that I need. But I ended up finding 15. I only needed 1.5. And so that’s why I would have to take and put my frequency needed and divide it by my frequency found times 5. And so remember when you’re doing these equations that we have to go by order of operations. So again, that’s why this, you gotta make sure Follow-up order of operations. Okay, so for this formula, remember. At this right here, then this right here is to multiply. It’s not the parentheses. And so it’s essentially meaning that we need to multiply the frequency needed divided by the frequency spans times the interval. And so in order to do that, we would take the 1.5, which is what we found, and the 15, and we multiply it by five. And so anytime you multiply a fraction by the, by a whole number, you would put one as being the number below. That would be the divider. And so that is essentially why this bill ends up as nine because nine times one is nine. And then I’m sorry, nine times. Yeah. And then five times the top number. And so here we would end up with is point 1 times 5, which gives us 0.5 if we were trying to find the 25th percentile. And so our actual first quartile would be a 130. So we would actually just use this first one right here. And so then we would go up and then we’ll find the third quartile, and then we would subtract the two. And that’s pretty much how you would find. The range for group data. Though, limitations of the range, range is based on only two scores. So this is distorted by a typically high or low score. So very similar to the mean. No information about variables between high and low scores. And so you don’t really know how many are things going man finds. And so it really doesn’t give us a good look at the data within itself. So when we look at the average deviation, the average deviation variation of scores from the mean of the distribution is essentially on average, how far is a distribution off? So this little symbol right here just means that it is the deviation score. And of course the sum you guys have already seen. And then this, the sidebars here means the absolute value of those. And then n is the sample size that you take each score and subtract it from the mean to get the deviation score. So here our mean is 29. And so, but say that this was a basketball player and he, he or she normally scored 29 points per game. And so for this particular game, they shy that are scored 23 points, which is six less than their average. And here 30. So that would be one more than average, and 31 would be two more, and so on and so forth. And so we did this over the course of five games, right? 12345. And so we would take the absolute value. So we would want to turn all of these and the positives. That’s all that means is we will get rid of the negatives and added altogether. So if we added everything, then we would end up with 40 divided by five and our average deviation would be eight. And so essentially, what that means is if we were going to maybe bet on this particular person, then we would do it with their average mine and it’s essentially plus or minus 8. And then we would be pretty often as N2 where they’re probably going to fall. So really as far as that’s concerned, this kinda goes along with like bedding and trying to figure out like what’s a safe bet and what’s not. So, you know, you never know for sure, but this gives you a decent idea of what to expect from a particular player on any given day. So this goes into where you can check and make sure that you didn’t make any mistakes by like we were talking about the last video. Is that the mean was calculated correctly. The sum of all the deviation scores will always equal 0. So here we have 17 minus 14, right? Which gives us 3 plus 2 is 5, plus 1 is 6, minus 6 is 0. So we didn’t make any mistakes here. That’s just the way of going back and double checking yourself. The standard deviation calculation. So to solve, we have to subtract the mean from each score. Then we have to square the deviations. And then we sum the squared deviations. And we divide the sum of the squared deviations by n, and then we find the square root of those results. And so the first steps up until the Find the square roots is actually finding the variance first, right? And then, so S squared is variance. And then just plain old S is your standard deviation. So here, so variance is the sum of the squared deviation scores divided by n. And standard deviation is just the square root at those. And so here we were able to, we have our numbers. So let’s say that we were looking at days missed for 11 kids. And so this person or maybe pays attended. So this person intended 20 days and this person intended 30 days. Let’s say it’s 30. So this one had perfect attendance. And so on average, how did the group do? And so we would take our total number of days and we would divide it by the number of students that we had. And so that would give us 275 divided by 11. Or maybe you would make more sense to use the example course because it does the test scores. And so it could really be whatever it is that you want it to be. But anyway, if you add all of those scores together, you’re going to get to 175. And we have 11 kids, so 275 divided by 11 gives us 25. And so from each of the scores, we’re going to subtract 25. And so that gives us our deviation score. And so if you add all these up, we get 0. So that means that we did it correctly. And then the next thing we want to do is to square the deviation scores, though, right? So here we have the sum of the difference between, so the sum of the deviation scores squared. That means that I have to square all the deviation scores, right? Because remember again, that you have to follow order of operations and this particular case, then this is parentheses, so it is done first and then exponents, right? Please excuse. And then adding would be last as far as that. And then dividing. So we take all this and then we’ll divide it by that bit. Gotta go through this first. And so essentially, we, if we were to take all of these squared and we would get to a 110. We added everything together. And so a 110 divided by 11 would give us 10. So our variance is 10. And then in order to get the square root, that variance, then we would take the square root of 10, which is 3.16. And so that is pretty much how you calculate for their deviation. And we could do it for grouped that your books not going to. So I’m just going to go ahead and stop the lecture here.
For this video, we are going to be going over Module 2. And so Marshall to you is all about measures of central tendency and dispersion. And so here you had your lecture videos on Chapters 3 and 4. And here’s some basic information about how to use SPSS and here’s the PowerPoints that I used for the video presentations. And so for the quiz, There’s going to be 10 questions from Chapter 3 and 10 questions from Chapter 4 are very similar to the way it was set up Module 1. Right? And so the discussion board, essentially all of these, if you read the chapters and you watch the videos, you will have no problem answering any of these questions here. Pretty straightforward. For assignment one. So in the videos and the readings and everything, you will learn how to calculate the mean, the median, the mode, the range and standard deviation, and the third quartile. And so remember back from module one, where I talk about in the lecture video of putting things that are in disarray an array. And so that’s going to be very important in order to be able to find the median, the mode, and the range for each of these three years. So don’t forget to do that. Otherwise, it’s going to be a lot harder for you to be able to figure out what is the range and puts the mode and the median. So all of those should be pretty standard. Then SPSS part though. So that’s apart. That may not be quite as easy. And so I’m going to go over how to do that particular assignment. And so I am at home, so I have logged in via the V lab. And so to get here, all I did was google UN GB lab and entered in my username and password. And then the software center, you can go ahead and download it. And it will remember your profile. So once you download it, you don’t have to keep downloading it from the software center each time. You’ll just have to go search for it if it’s not pinned already for you. All right, so here I have kind of started with your first task. So your first task is to create a SPSS file for the data above, and then answer the following questions based on the data set. All right, and so we have respondents. And so I went ahead and gave them their ID numbers. So here all I had to do was type then each of these. And so if you have a nominal variable, we have to still put that into mathematics. So here’s the way that you would go about it. So I would just type and the one and then protists that and then add and that will click it over into this area right here. And then two Catholic add and keep going until you got all the way up to four. Kinda the same for males and females. Again, it’s a nominal variables though. You want to change over, though the number of partners a person has as a interval ratio or in SPSS, they treat them the same. So it is a scale variable. And so in your dataset, only one that you will have, that is ordinal will be legalization of marijuana. So that’s the only one that you’re going to list. Those are ordinal. And so in order to do this here, but say if I want to create a new variable, I would just do age. Okay? And so for age, I just want one decimal. We’re not doing point whatever. Let’s go ahead and move that down. And age we are going to put as a scale variable. And then I go through and I look at the list over here. So our first respond, it looks like page at freshman was 18. And then the next one was 20 and then 21. And then a TM band looks like our fifth one has started a little later in life at 25. So that’s just how you go about adding variables into your dataset. So one of the things is UNED it as like spaces or special characters. So I kinda had to go a little bit creative with how you label these things. So if you wanted to put ID here service by me, you could that try and make sure that you know exactly what you need to make it easy enough to read, thank easier for me to be able to grade. So keeping with as close as what’s up there is probably the easiest thing for me to be able to grade though, to make extra sure that I know you did it right. I would probably use those same lines. So here, the next is after you get all of your information and so on. We did for the first five, just so that I can have enough data to show you how to do each of these. Your first task is to create a frequency distribution for the following variables. So religion, gender, and race. All right, and so to do that, we’ll go up to Analyze and then Descriptive Statistics and Frequencies. And so I already have gender here. So I also want to do religion and race. So I need to add religion and rapes. And, okay. And that gives me my frequency distributions for religion, race, and gender. And so here, we don’t really mean the inset this point, so don’t worry about that. That will actually probably come back to this here in just a minute. So the next question is what percentage of females are Catholic? And so to be able to look at that, we will go to analyze descriptives and then cross tabs. And so I want the mouth right? You are Catholic, which means I need to look at religion. And so you can go ahead and put the percentages if you want. It’ll look at my percentages first. And so this is very cluttered. But you can find out. So we are wanting to know what percent of females are Catholic, though we were to look at are females. And percent within our gender is thirty-three point three. And so essentially, a third of all the females are Catholic. And so we only have three, and we don’t have any that were nine and a Jew, Catholic and Protestant. So I went out to three. Well, it says that 33 percent and then say you would do for the both white and male, then you would have to look at the total line in order to be able to figure that one out. So if I wanted to say, oh, wow, I took the total was both female and Catholic. Then I would go down to female and want to look at the total. And here acts like we did not have any Mel’s, you were Catholic, so that would give us 20% of the population would be both female and Catholic. So now we’re cooking out of five, right? And so we have one out of five. And that’s where we get our 20 percent at. And so make sure that you’re looking at the total. So for me a lot of times, it’s easier to not have all of this and to just go and look at it. So we’ll go back to the cross tabs. And this time I’m going to take away the percentages and run it again. And so to me it’s a lot easier to just look at this and say that. You know, one out of three females, so a third, so thirty-three point three percent are Protestant or Catholic, either way, any of them, there’s going to be 33 percent. And then so if I wanted. So females who were though males and females who were Protestant as a whole, like so then that would be the two over five. So that would be 40%. So that is, It’s really up to you, however you think it is to most easily read the chart to me, the simple ones better, but some people like to be able to look at is that the key is though, which total you look at Connect. That can make a huge difference because that could be the difference between right and wrong answer as if you look at the total. So to me, that’s why I think MY simple totals are so much easier. Also for the proportion, when asked for a proportion of males to females. Then you also might want to look at the simple our chart, because this is all in percentages. So if you report percentages, then you’re going to get that question wrong. So I need to leave it and proportions. All right, and then the next few questions are about the central tendencies. And so here we have. First one is what is the best representation? Give level and count of the central tendency for religion and why. Okay? And so what go up here? And we’re going to look at and analyze descriptives, frequencies, stats, I want, I mean, median and mode. Okay? This time I just want to look at religion. Okay? And so here, even though I have selected for the mean, median and mode, it didn’t give me anything. Because you can’t really be essentially 1.5 Catholic or if he was to put these in an order. Right. The order does it really matter any at all? And so you’re not going to have a central one. And so the only one that would make sense would be the mode, which is 2 here. And so that would be very important to talk about the fact that that it just wouldn’t make sense to have a center one because there is no order to them, a rhyme or reason. And what makes sense to have an average, because then you would end up with 0 something. And so you now, on average, a person is of a certain, certain religion and this doesn’t make any sense. So you would do the mode, and so you would talk about that. And so we’ll have different numbers. And so an example of one where it would show and where does that make any sense? By just looking at the char would be if we did it for gender. Oh, sorry. I need help. I’m going to cancel this. That’s okay. I do have a model there and okay. Alright. And so here, it does give us a mean, a median and mode. And so mean this can’t really be 1.6 of male or female. You’re kind of one there unless other is an option that still, it’s a nominal variable, so you wouldn’t be 0.6 other either. And so the median is showing that it is a two. So. That you would have to translate, right? Remember what you saved as 12, so there’s five. And so we have TP mouth though, it would be 2, 2, 3, 3, 3. Which in this case, my workout that this though, you know, one of your choices with not essentially to write your choices are male or female? As to which one is the most, right? Okay, so I just gave it to you. You should do the mode. Clearly the mode to you’d have to know the conversion of. So just looking over here and looking at the frequencies, the mode is female. And so therefore, again, you’d talk about fact that it’s nominal and it just doesn’t make sense to report the others because of just the fact that white boy the coding. So if the mode was two, and here we’re talking about males versus females than people would have no clue what you’re talking about. In this case though too, does translate and TIF female. So bay, The same. Females have the most, and females are in the media. And so you could report both because they are both the same. But again, that’s up to you as long as you answer why you reported both. But make sure that you do not report the mean, because that makes no sense whatsoever for a nominal variable. And the rest of them are pretty much exactly like that. So you would pick like number of partners and y. So let’s go up here and we analyze Descriptive frequencies. And this time I want number part nerves. And there we go. Maybe go ahead, put some in there too. Oh, it’s sometimes good to have your totals as well. All right. And so here, our choices were between 0 to six and 10. So you’ll have a wider variety to work with. That here, this is a scale variable. So you could use the mean or the median or the mode. So for this one though, it looks like it may be a little bit skewed because, you know, right here where the 246 and this ten, That’s quite a bit higher than the rest of them. And so that might be bringing it up just a little bit. And so the average being higher than the mean would mean that are soluble. Mean being higher than the median, right? Means that it is key in the positive direction. And so in this case here, you might want to report the mode, but it’s also the media as well to you. So, but depending on what you end up with, at the very end, just talk about outliers and things like that and how it could affect this and this. Compare the three numbers and see which one you think would be most appropriate. Because in theory, you could report any of those for your scaled. It’s not like the nominal where you’re more limited. And so what you do that then just write up a little narrative about what you found. And so for the prejudiced with the freshmen and then prejudice for the seniors, just talk a little bit about the central tendencies. How they’ve changed, that they go up or did they go down? Things along those lines. And so we’re not going to talk about significant or not. Just talk about if it, if there does look like there was a change and talk about just the central tendencies. And so that is pretty much all you really need to do. So make sure that you keep this set of data that you fix neglect because we’re going to come back through this for a lot of or activities. So that pretty much covers Module 2. Let me know if you have any questions. Thanks.
Measures of central tendency
Central tendency
Describe points around which the rest of the scores focus
Three measures
Mean
Median
Mode
Mode is considered the typical or more frequently occurring score in a distribution of score.
Median is considered the central score, or that point which divides a distribution into two equal parts, with 50% of the distribution on one side of the median and 50% on the other side.
Mean is the arithmetic average score of all scores in a set of scores.
Each has it’s own assumptions– it is important to know these assumptions in order to know when one is appropriate to report during data analysis.
2
Mode
The most common score
Can be used with variables at all three levels of measurement
Most often used with nominal level variables
Finding the Mode
Count the number of times each score occurred
The score that occurs most often is the mode
If the variable is presented in a frequency distribution, the mode is the largest category
If the variable is presented in a line chart, the mode is the highest peak
The mode
22, 23, 25, 25, 26, 26, 26, 27, 27, 28, 29, 30, 31, 32, 33, 35
22, 23, 25, 25, 25, 26, 26, 26, 27, 27, 27, 28, 29, 30, 31, 33
22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 28, 29, 30, 35, 35
Can have multiple modes, but no more than 3
4
Mode for grouped data
Sample of convicted murderers &
Sentence received
Years sentences
f
55-59
11
50-54
7
45-49
10
40-44
15
35-39
10
30-34
9
25-29
5
20-24
3
N=70
Sample of convicted murderers &
Sentence received
Years sentences
f
50-54
15
45-49
10
40-44
15
35-39
10
30-34
7
25-29
15
20-24
5
N=77
The mode for grouped data is defined as the midpoint of the interval containing the most frequencies. 3 is the maximum number for grouped modes as well. 4 there is no mode
Use the midpoint of the interval as the mode year
Example: the interval 40-44 has the highest amount of murders so this interval midpoint is our mode (42 years). 5/2= 2.5; 39.5 + 2.5= 42
One mode= unimodal
Two modes= bimodal
Three modes= multimodal
Nominal level or higher
Most popular is not always the most central score. Can be very far away from the central tendency
Deviant scores or outliers– scores located in one extreme or another (small or large)
5
Limitations of Mode
Some distributions have no mode
Some distributions have multiple modes
The mode of an ordinal or interval-ratio level variable may not be central to the whole distribution
Median
Exact center of distribution of scores
The score of the middle case
Can be used with variables measured at the ordinal or interval-ratio levels
Cannot be used for nominal level variables
Finding the Median
Array the cases from low to high (or from high to low)
Locate the middle case
If N is odd: the median is the score of the middle case
If N is even: the median is the average of the scores of the two middle cases
The median
12, 15, 17
12, 15, 17, 19
12, 15, 17, 100
9, 12, 15, 17, 100
10, 35, 39, 43, 55, 220, 320, 480, 2,000,000
9, 12, 13, 15, 15, 15, 15, 15, 15, 17, 19, 20
Point that divides a distribution of scores into two equal parts.
In an array of an uneven number of scores, the central score becomes the median.
When there is an even number we can find a median, but this number is a theoretical point dividing a distribution
15
16
16
15
55
15
9
Median for grouped data
Mdn=+(fn/ff) (i)
Satisfaction Score
Interval
f
cf
175-179
4
111
170-174
6
107
165-169
3
101
160164
13
98
155-159
8
85
150-154
7
77
145-149
10
70
140-144
9
60
135-139
10
51
130-134
15
41
125-129
11
26
120-124
10
15
115-119
5
5
N=111
LL= lower limit of the interval containing the number of frequencies we need to divide the total number of scores into two equal parts.
fn= the frequencies we need in the interval
ff= the frequencies found in the interval
I = the interval size
N/2= 111/2= 55.5
We must find the point with 55.5 scores on one side and 55.5 scores on the other side.
51 is a close are we can get to 55.5
Mdn=139.5+ 4.5/9 X 5
=139.5+22.5/9
=139.5 + 2.5
=142
Assumes data that can be measured at the ordinal scare or higher.
More stable measure of central tendency in the sense that it divides the scores in half.
10
Centiles, deciles, & quartiles
Centiles– divide distributions of scores into 1 % units
Deciles– divide distributions of scores into 10% units
Quartiles– divide distributions of scores into 25% units
50%= 5th decile and the 2nd quartile
75 centile is the point leaving 75% of all scores below it and 25% of scores above it
33 centile is the point leaving 33% of all scores below it and 67% of scores above it.
75% of scores form the 111 in the last chart we take (.75)(111)= 83.2 and from there we need to use the formula from last slide and plug in the amounts.
11
Mean
The average score
Requires variables measured at the interval-ratio level but is often used with ordinal-level variables
Cannot be used for nominal-level variables
The mean or arithmetic average, is by far the most commonly used measure of central tendency
Characteristics of the Mean
The mean “balances” out all of the scores in a distribution; all scores “cancel out” around the mean.
The mean is the point of minimized variation of the scores, “least squares principle”
The mean is affected by all scores; all scores are used in the calculation of the mean.
Strength – The mean uses all the available information from the variable
Weaknesses
The mean is affected by every score
If there are some very high or low scores (as with skewed distributions), the mean may be misleading
The Mean:
=
18, 19, 19, 20, 21, 21, 22, 25, 29, 32, 35, 37, 37, 38, 41, 41, 41, 43, 47, 49, 60
= the sum of the scores
N= the number of scores
695/21= 33.1
Replace the 60 with 600. What does the mean become?
(58.8)
Median is most appropriate when there are extreme scores or outliers.
15
Number of IPV incidents from women with PTSD
Intervals
f
MP
(f)(MP)
57-59
8
58
464
54-56
9
55
495
51-53
3
52
156
48-50
10
49
490
45-47
10
46
460
42-44
8
43
344
39-41
11
40
440
36-38
19
37
703
33-35
12
34
408
30-32
7
31
217
27-29
3
28
84
24-26
8
25
200
21-23
7
22
154
N=115
(N)(MP)=4,618
16
The mean for grouped data
=
=
Number of IPV incidents from women with PTSD
Intervals
f
MP
(f)(MP)
57-59
8
58
464
54-56
9
55
495
51-53
3
52
156
48-50
10
49
490
45-47
10
46
460
42-44
8
43
344
39-41
11
40
440
36-38
19
37
703
33-35
12
34
408
30-32
7
31
217
27-29
3
28
84
24-26
8
25
200
21-23
7
22
154
N=115
(N)(MP)=4,618
MP= interval midpoints
=
= = 40.1
17
Means, Medians, and Skew
When a distribution has a few very high or low scores, the mean will be pulled in the direction of the extreme scores
For a positive skew, the mean will be greater than the median
For a negative skew, the mean will be less than the median
When an interval-ratio level variable has a pronounced skew, the median may be the more trustworthy measure of central tendency
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IBM SPSS Statistics Base V27
IBM
Note
Before using this information and the product it supports, read the information in “Notices” on page
197.
Product Information
This edition applies to version 27, release 0, modification 0 of IBM® SPSS® Statistics and to all subsequent releases and
modifications until otherwise indicated in new editions.
© Copyright International Business Machines Corporation .
US Government Users Restricted Rights – Use, duplication or disclosure restricted by GSA ADP Schedule Contract with
IBM Corp.
Contents
Chapter 1. Core features…………………………………………………………………………….1
Power Analysis…………………………………………………………………………………………………………………………… 1
Means……………………………………………………………………………………………………………………………………2
Proportions…………………………………………………………………………………………………………………………. 12
Correlations………………………………………………………………………………………………………………………… 21
Regression………………………………………………………………………………………………………………………….. 28
Codebook………………………………………………………………………………………………………………………………… 31
Codebook Output Tab………………………………………………………………………………………………………….. 31
Codebook Statistics Tab………………………………………………………………………………………………………. 33
Frequencies………………………………………………………………………………………………………………………………33
Frequencies Statistics………………………………………………………………………………………………………….. 34
Frequencies Charts……………………………………………………………………………………………………………… 35
Frequencies Format…………………………………………………………………………………………………………….. 35
Descriptives………………………………………………………………………………………………………………………………36
Descriptives Options……………………………………………………………………………………………………………. 36
DESCRIPTIVES Command Additional Features………………………………………………………………………. 37
Explore……………………………………………………………………………………………………………………………………. 37
Explore Statistics………………………………………………………………………………………………………………….38
Explore Plots………………………………………………………………………………………………………………………..38
Explore Options…………………………………………………………………………………………………………………… 39
EXAMINE Command Additional Features………………………………………………………………………………. 39
Crosstabs………………………………………………………………………………………………………………………………… 40
Crosstabs layers………………………………………………………………………………………………………………….. 40
Crosstabs clustered bar charts……………………………………………………………………………………………… 41
Crosstabs displaying layer variables in table layers………………………………………………………………….41
Crosstabs statistics……………………………………………………………………………………………………………… 41
Crosstabs cell display………………………………………………………………………………………………………….. 43
Crosstabs table format………………………………………………………………………………………………………….44
Summarize………………………………………………………………………………………………………………………………. 44
Summarize Options……………………………………………………………………………………………………………… 44
Summarize Statistics…………………………………………………………………………………………………………….45
Means……………………………………………………………………………………………………………………………………… 46
Means Options……………………………………………………………………………………………………………………..47
OLAP Cubes………………………………………………………………………………………………………………………………48
OLAP Cubes Statistics………………………………………………………………………………………………………….. 49
OLAP Cubes Differences………………………………………………………………………………………………………. 50
OLAP Cubes Title………………………………………………………………………………………………………………….50
Proportions……………………………………………………………………………………………………………………………….50
Proportions introduction………………………………………………………………………………………………………. 50
One-Sample Proportions……………………………………………………………………………………………………….51
Paired-Samples Proportions………………………………………………………………………………………………….53
Independent-Samples Proportions……………………………………………………………………………………….. 56
T Tests……………………………………………………………………………………………………………………………………..58
T Tests……………………………………………………………………………………………………………………………….. 58
Independent-Samples T Test……………………………………………………………………………………………….. 59
Paired-Samples T Test…………………………………………………………………………………………………………. 60
One-Sample T Test……………………………………………………………………………………………………………….62
T TEST Command Additional Features…………………………………………………………………………………… 63
One-Way ANOVA……………………………………………………………………………………………………………………….63
One-Way ANOVA Contrasts………………………………………………………………………………………………….. 64
One-Way ANOVA Post Hoc Tests……………………………………………………………………………………………64
iii
One-Way ANOVA Options…………………………………………………………………………………………………….. 66
ONEWAY Command Additional Features……………………………………………………………………………….. 67
GLM Univariate Analysis……………………………………………………………………………………………………………. 67
GLM Model…………………………………………………………………………………………………………………………..68
GLM Contrasts…………………………………………………………………………………………………………………….. 70
GLM Profile Plots…………………………………………………………………………………………………………………. 70
GLM Post Hoc Comparisons…………………………………………………………………………………………………..72
GLM Save……………………………………………………………………………………………………………………………. 75
GLM Estimated Marginal Means……………………………………………………………………………………………..76
GLM Options……………………………………………………………………………………………………………………….. 76
UNIANOVA Command Additional Features……………………………………………………………………………..77
Bivariate Correlations……………………………………………………………………………………………………………….. 78
Bivariate Correlations Options………………………………………………………………………………………………. 79
Bivariate Correlations Confidence Interval…………………………………………………………………………….. 79
CORRELATIONS and NONPAR CORR Command Additional Features…………………………………………80
Partial Correlations…………………………………………………………………………………………………………………… 80
Partial Correlations Options…………………………………………………………………………………………………..81
PARTIAL CORR Command Additional Features………………………………………………………………………. 81
Distances………………………………………………………………………………………………………………………………….81
Distances Dissimilarity Measures………………………………………………………………………………………….. 82
Distances Similarity Measures……………………………………………………………………………………………….82
PROXIMITIES Command Additional Features………………………………………………………………………… 83
Linear models……………………………………………………………………………………………………………………………83
To obtain a linear model………………………………………………………………………………………………………..83
Objectives ………………………………………………………………………………………………………………………….. 83
Basics …………………………………………………………………………………………………………………………………84
Model Selection ………………………………………………………………………………………………………………….. 84
Ensembles …………………………………………………………………………………………………………………………. 85
Advanced …………………………………………………………………………………………………………………………… 86
Model Options ……………………………………………………………………………………………………………………..86
Model Summary …………………………………………………………………………………………………………………..86
Automatic Data Preparation ………………………………………………………………………………………………….86
Predictor Importance ………………………………………………………………………………………………………….. 86
Predicted By Observed …………………………………………………………………………………………………………87
Residuals …………………………………………………………………………………………………………………………… 87
Outliers ……………………………………………………………………………………………………………………………… 87
Effects ……………………………………………………………………………………………………………………………….. 87
Coefficients …………………………………………………………………………………………………………………………88
Estimated Means ………………………………………………………………………………………………………………… 88
Model Building Summary …………………………………………………………………………………………………….. 88
Linear Regression…………………………………………………………………………………………………………………….. 89
Linear Regression Variable Selection Methods……………………………………………………………………….. 89
Linear Regression Set Rule…………………………………………………………………………………………………… 90
Linear Regression Plots…………………………………………………………………………………………………………90
Linear Regression: Saving New Variables………………………………………………………………………………..91
Linear Regression Statistics…………………………………………………………………………………………………..92
Linear Regression Options……………………………………………………………………………………………………. 93
REGRESSION Command Additional Features…………………………………………………………………………. 93
Ordinal Regression ……………………………………………………………………………………………………………………93
Ordinal Regression Options………………………………………………………………………………………………….. 94
Ordinal Regression Output…………………………………………………………………………………………………….95
Ordinal Regression Location Model……………………………………………………………………………………….. 95
Ordinal Regression Scale Model……………………………………………………………………………………………. 96
PLUM Command Additional Features……………………………………………………………………………………..97
Curve Estimation……………………………………………………………………………………………………………………….97
Curve Estimation Models……………………………………………………………………………………………………… 98
Curve Estimation Save…………………………………………………………………………………………………………..98
Partial Least Squares Regression………………………………………………………………………………………………..99
iv
Model ………………………………………………………………………………………………………………………………. 100
Options ……………………………………………………………………………………………………………………………. 101
Nearest Neighbor Analysis………………………………………………………………………………………………………. 101
Neighbors ………………………………………………………………………………………………………………………… 103
Features ……………………………………………………………………………………………………………………………103
Partitions …………………………………………………………………………………………………………………………. 104
Save ………………………………………………………………………………………………………………………………… 105
Output ………………………………………………………………………………………………………………………………105
Options ……………………………………………………………………………………………………………………………. 105
Model View ………………………………………………………………………………………………………………………. 105
Discriminant Analysis……………………………………………………………………………………………………………… 108
Discriminant Analysis Define Range……………………………………………………………………………………..109
Discriminant Analysis Select Cases………………………………………………………………………………………109
Discriminant Analysis Statistics……………………………………………………………………………………………109
Discriminant Analysis Stepwise Method………………………………………………………………………………. 110
Discriminant Analysis Classification……………………………………………………………………………………..110
Discriminant Analysis Save………………………………………………………………………………………………….111
DISCRIMINANT Command Additional Features…………………………………………………………………….111
Factor Analysis ……………………………………………………………………………………………………………………….112
Factor Analysis Select Cases………………………………………………………………………………………………. 112
Factor Analysis Descriptives………………………………………………………………………………………………..113
Factor Analysis Extraction………………………………………………………………………………………………….. 113
Factor Analysis Rotation…………………………………………………………………………………………………….. 114
Factor Analysis Scores……………………………………………………………………………………………………….. 114
Factor Analysis Options……………………………………………………………………………………………………… 115
FACTOR Command Additional Features………………………………………………………………………………..115
Choosing a Procedure for Clustering………………………………………………………………………………………….115
TwoStep Cluster Analysis…………………………………………………………………………………………………………116
TwoStep Cluster Analysis Options………………………………………………………………………………………..117
TwoStep Cluster Analysis Output…………………………………………………………………………………………118
The Cluster Viewer…………………………………………………………………………………………………………….. 118
Hierarchical Cluster Analysis ……………………………………………………………………………………………………123
Hierarchical Cluster Analysis Method……………………………………………………………………………………123
Hierarchical Cluster Analysis Statistics…………………………………………………………………………………124
Hierarchical Cluster Analysis Plots……………………………………………………………………………………….124
Hierarchical Cluster Analysis Save New Variables………………………………………………………………….124
CLUSTER Command Syntax Additional Features……………………………………………………………………124
K-Means Cluster Analysis ………………………………………………………………………………………………………..124
K-Means Cluster Analysis Efficiency……………………………………………………………………………………. 125
K-Means Cluster Analysis Iterate…………………………………………………………………………………………125
K-Means Cluster Analysis Save…………………………………………………………………………………………… 126
K-Means Cluster Analysis Options………………………………………………………………………………………. 126
QUICK CLUSTER Command Additional Features……………………………………………………………………126
Nonparametric Tests………………………………………………………………………………………………………………. 127
One-Sample Nonparametric Tests………………………………………………………………………………………. 127
Independent-Samples Nonparametric Tests……………………………………………………………………….. 130
Related-Samples Nonparametric Tests……………………………………………………………………………….. 133
Model View……………………………………………………………………………………………………………………….. 135
NPTESTS command additional features………………………………………………………………………………. 139
Legacy Dialogs …………………………………………………………………………………………………………………..139
Multiple Response Analysis…………………………………………………………………………………………………….. 149
Multiple Response Analysis………………………………………………………………………………………………… 149
Multiple Response Define Sets…………………………………………………………………………………………….150
Multiple Response Frequencies………………………………………………………………………………………….. 151
Multiple Response Crosstabs……………………………………………………………………………………………… 151
Reporting Results…………………………………………………………………………………………………………………… 153
Reporting Results……………………………………………………………………………………………………………….153
Report Summaries in Rows………………………………………………………………………………………………….153
v
Report Summaries in Columns……………………………………………………………………………………………. 155
REPORT Command Additional Features………………………………………………………………………………. 157
Reliability Analysis…………………………………………………………………………………………………………………..157
Reliability Analysis: Statistics……………………………………………………………………………………………… 158
RELIABILITY Command Additional Features…………………………………………………………………………161
Weighted Kappa………………………………………………………………………………………………………………………161
Weighted Kappa: Criteria……………………………………………………………………………………………………. 162
Weighted Kappa: Print……………………………………………………………………………………………………….. 162
Multidimensional Scaling …………………………………………………………………………………………………………163
Multidimensional Scaling Shape of Data………………………………………………………………………………. 163
Multidimensional Scaling Create Measure……………………………………………………………………………. 164
Multidimensional Scaling Model…………………………………………………………………………………………..164
Multidimensional Scaling Options……………………………………………………………………………………….. 164
ALSCAL Command Additional Features……………………………………………………………………………….. 165
Ratio Statistics……………………………………………………………………………………………………………………….. 165
Ratio Statistics………………………………………………………………………………………………………………….. 165
ROC Analysis ………………………………………………………………………………………………………………………….166
ROC Analysis: Options……………………………………………………………………………………………………….. 167
ROC Analysis: Display………………………………………………………………………………………………………… 168
ROC Analysis: Define Groups (string)…………………………………………………………………………………… 169
ROC Analysis: Define Groups (numeric)……………………………………………………………………………….. 169
ROC Curves …………………………………………………………………………………………………………………………… 169
ROC Curve Options……………………………………………………………………………………………………………..170
Simulation……………………………………………………………………………………………………………………………… 170
To design a simulation based on a model file……………………………………………………………………….. 171
To design a simulation based on custom equations……………………………………………………………….171
To design a simulation without a predictive model……………………………………………………………….. 172
To run a simulation from a simulation plan……………………………………………………………………………172
Simulation Builder………………………………………………………………………………………………………………173
Run Simulation dialog………………………………………………………………………………………………………… 183
Working with chart output from Simulation………………………………………………………………………….. 185
Geospatial Modeling………………………………………………………………………………………………………………..186
Selecting Maps …………………………………………………………………………………………………………………. 187
Data Sources ……………………………………………………………………………………………………………………. 189
Geospatial Association Rules …………………………………………………………………………………………….. 190
Spatial Temporal Prediction ………………………………………………………………………………………………. 193
Finish ………………………………………………………………………………………………………………………………. 196
Notices………………………………………………………………………………………………..197
Trademarks…………………………………………………………………………………………………………………………….198
Index…………………………………………………………………………………………………. 199
vi
Chapter 1. Core features
The following core features are included in IBM SPSS Statistics Base Edition.
Power Analysis
Power analysis plays a pivotal role in a study plan, design, and conduction. The calculation of power is
usually before any sample data have been collected, except possibly from a small pilot study. The precise
estimation of the power may tell investigators how likely it is that a statistically significant difference will
be detected based on a finite sample size under a true alternative hypothesis. If the power is too low,
there is little chance of detecting a significant difference, and non-significant results are likely even if real
differences truly exist.
IBM SPSS Statistics provides the following Power Analysis procedures:
One Sample T-Test
In one-sample analysis, the observed data are collected as a single random sample. It is assumed
that the sample data independently and identically follow a normal distribution with a fixed mean and
variance, and draws statistical inference about the mean parameter.
Paired Sample T-Test
In paired-sample analysis, the observed data contain two paired and correlated samples, and each
case has two measurements. It is assumed that the data in each sample independently and
identically follow a normal distribution with a fixed mean and variance, and draws statistical inference
about the difference of the two means.
Independent Sample T-Test
In independent-sample analysis, the observed data contain two independent samples. It is assumed
that the data in each sample independently and identically follow a normal distribution with a fixed
mean and variance, and draws statistical inference about the difference of the two means.
One-way ANOVA
Analysis of variance (ANOVA) is a statistical method of estimating the means of several populations
which are often assumed to be normally distributed. The One-way ANOVA, a common type of ANOVA,
is an extension of the two-sample t-test.
Example. The power of a hypothesis test to detect a correct alternative hypothesis is the probability that
the test will reject the test hypothesis. Since the probability of a type II error is the probability of
accepting the null hypothesis when the alternative hypothesis is true, the power can be expressed as (1-
probability of a type II error), which is the probability of rejecting the null hypothesis when the alternative
hypothesis is true.
Statistics and plots. One-sided test, two-sided test, significance level, Type I error rate, test
assumptions, population standard deviation, population mean under testing, hypothesized value, two-
dimensional power by sample size, two-dimensional power by effect size, three-dimensional power by
sample size, three-dimensional power by effect size, rotation degrees, group pairs, Pearson product-
moment correlation coefficient, mean difference, plot range of the effect size, pooled population standard
deviation, contrasts and pairwise differences, contrast coefficients, contrast test, BONFERRONI, SIDAK,
LSD, power by total sample size, two-dimensional power by pooled standard deviation, three-dimensional
power by total sample, three-dimensional power by total sample size, pooled standard deviation,
Student’s t-distribution, non-central t-distribution,
Power Analysis data considerations
Data
In one-sample analysis, the observed data are collected as a single random sample.
In paired-sample analysis, the observed data contain two paired and correlated samples, and each
case has two measurements.
In independent-sample analysis, the observed data contain two independent samples.
Analysis of variance (ANOVA) is a statistical method of estimating the means of several populations
which are often assumed to be normally distributed.
Assumptions
In one-sample analysis, it is assumed that the sample data independently and identically follow a
normal distribution with a fixed mean and variance, and draws statistical inference about the mean
parameter.
In paired-sample analysis, it is assumed that the data in each sample independently and identically
follow a normal distribution with a fixed mean and variance, and draws statistical inference about the
difference of the two means.
In independent-sample analysis, it is assumed that the data in each sample independently and
identically follow a normal distribution with a fixed mean and variance, and draws statistical inference
about the difference of the two means.
In one-way ANOVA, the statistical method of estimating the means of several populations are often
assumed to be normally distributed.
Obtaining a Power Analysis
1. From the menus choose:
Analyze > Power Analysis > Compare Means > One-Sample T-Test, or Paired-Sample T-Test, or
Independent-Sample T-Test, or One-way ANOVA
2. Define the required test assumptions.
3. Click OK.
Means
The following statistics features are included in IBM SPSS Statistics Base Edition.
Power Analysis of One-Sample T Test
This feature requires IBM SPSS Statistics Base Edition.
Power analysis plays a pivotal role in a study plan, design, and conduction. The calculation of power is
usually before any sample data have been collected, except possibly from a small pilot study. The precise
estimation of the power may tell investigators how likely it is that a statistically significant difference will
be detected based on a finite sample size under a true alternative hypothesis. If the power is too low,
there is little chance of detecting a significant difference, and non-significant results are likely even if real
differences truly exist.
In one-sample analysis, the observed data are collected as a single random sample. It is assumed that
the sample data independently and identically follow a normal distribution with a fixed mean and
variance, and draws statistical inference about the mean parameter.
1. From the menus choose:
Analyze > Power Analysis > Means > One-Sample T Test
2. Select a test assumption setting (Estimate sample size or Estimate power).
3. When selecting Estimate power, enter an appropriate Sample size for power estimation value. The
value must be an integer greater than 1. When selecting Estimate sample size, enter an appropriate
Power for sample size estimation value. The value must be a single value between 0 and 1.
4. Enter a value that specifies the population mean under testing in the Population mean field. The value
must be a single numeric.
5. Optionally, enter a value that specifies the null hypothesis value to be tested in the Null value field.
The value must be a single numeric.
6. Enter a Population standard deviation value. The value must be a single numeric greater than 0.
7. Select whether the test is one or two-sided.
2 IBM SPSS Statistics Base V27
Nondirectional (two-sided) analysis
When selected, a two-sided test is used. This is the default setting.
Directional (one-sided) analysis
When selected, power is computed for a one-sided test.
8. Optionally, specify the significance level of the Type I error rate for the test in the Significance level
field. The value must be a single double value between 0 and 1. The default value is 0.05.
9. You can optionally click Plot to specify “Power Analysis of One-Sample T Test: Plot” on page 3
settings (chart output, two-dimensional plot settings, three-dimensional plot settings, and tooltips).
Note: Plot is available only when Estimate power is selected as the test assumption.
Power Analysis of One-Sample T Test: Plot
You can control the plots that are output to illustrate the two and three-dimensional power by sample/
effect size charts. You can also control the display of tool tips and the vertical/horizontal rotation degrees
for three-dimensional charts.
Two-Dimensional Plot
Power estimation versus sample size
When enabled, this optional setting provides options for controlling the two-dimensional power by
sample size chart. The setting is disabled by default.
Range of sample size
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range of the sample size
is used.
Lower bound
Controls the lower bound for the two-dimensional power by sample size chart. The value
must be greater than 1, and cannot be greater than the Upper bound value.
Upper bound
Controls the upper bound for the two-dimensional power by sample size chart. The value
must be greater than the Lower bound value and cannot be greater than 5000.
Power estimation versus effect size
By default, this optional setting is disabled. When enabled, the chart displays in the output. When
no integer values are specified for the Lower bound or Upper bound fields, the default plot range
of the effect size used.
Range of effect size
When selected, the lower and upper bound options are available.
Lower bound
Controls the lower bound for the two-dimensional power by effect size chart. The value
must be greater than, or equal to, -5.0 and cannot be greater than the Upper bound value.
Upper bound
Controls the upper bound for the two-dimensional power by effect size chart. The value
must be greater than the Lower bound value and cannot be greater than 5.0.
Three-Dimensional Plot
Power estimation versus
Provides options for controlling the three-dimensional power by sample size (x-axis) and effect
size (y-axis) chart, the vertical/horizontal rotation settings, and the user specified plot range of
sample/effect size. This setting is disabled by default.
Effect size on x-axis and sample size on y-axis
The optional setting controls the three-dimensional power by sample size (x-axis) and effect
size (y-axis) chart. By default, the chart is suppressed. When specified, the chart displays.
Chapter 1. Core features 3
Effect size on y-axis and sample size on x-axis
The optional setting controls the three-dimensional power by sample size (y-axis) and effect
size (x-axis) chart. By default, the chart is suppressed. When specified, the chart displays.
Vertical rotation
The optional setting sets the vertical rotation degrees (clockwise from the left) for the three-
dimensional chart. You can use the mouse to rotate the chart vertically. The setting takes
effect when the three-dimensional plot is requested. The value must be a single integer value
less than or equal to 359. The default value is 10.
Horizontal rotation
The optional setting sets the horizontal rotation degrees (clockwise from the front) for the
three-dimensional chart. You can use the mouse to rotate the chart horizontally. The setting
takes effect when the three-dimensional plot is requested. The value must be a single integer
value less than or equal to 359. The default value is 325.
Range of sample size
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range of the sample size
is used.
Lower bound
Controls the lower bound for the three-dimensional power by sample size chart. The value
must be greater than 1, and cannot be greater than the Upper bound value.
Upper bound
Controls the upper bound for the three-dimensional power by sample size chart. The value
must be greater than the Lower bound value and cannot be greater than 5000.
Range of effect size
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range of the effect size
is used.
Lower bound
Controls the lower bound for the three-dimensional power by effect size chart. The value
must be greater than, or equal to, -5.0 and cannot be greater than the Upper bound value.
Upper bound
Controls the upper bound for the three-dimensional power by effect size chart. The value
must be greater than the Lower bound value and cannot be greater than 5.0.
Power Analysis of Paired-Samples T Test
This feature requires IBM SPSS Statistics Base Edition.
Power analysis plays a pivotal role in a study plan, design, and conduction. The calculation of power is
usually before any sample data have been collected, except possibly from a small pilot study. The precise
estimation of the power may tell investigators how likely it is that a statistically significant difference will
be detected based on a finite sample size under a true alternative hypothesis. If the power is too low,
there is little chance of detecting a significant difference, and non-significant results are likely even if real
differences truly exist.
In paired-samples analysis, the observed data contain two paired and correlated samples, and each case
has two measurements. It is assumed that the data in each sample independently and identically follow a
normal distribution with a fixed mean and variance, and draws statistical inference about the difference of
the two means.
1. From the menus choose:
Analyze > Power Analysis > Means > Paired-Samples T Test
2. Select a test assumption setting (Estimate sample size or Estimate power).
3. When selecting Estimate power, enter an appropriate Sample size for power estimation value. The
value must be an integer greater than 1. When selecting Estimate sample size, enter an appropriate
Power for sample size estimation value. The value must be a single value between 0 and 1.
4 IBM SPSS Statistics Base V27
4. When a single population mean is required, enter a Population mean difference value. When single
value is specified, it denotes the population mean difference μd.
Note: The value cannot be 0 when Estimate sample size is selected.
5. When multiple population means are required for the specified group pairs, enter values for
Population mean for group 1 and Population mean for group 2. When multiple values are specified,
they denote the population mean difference μ1 and μ2.
Note: The two values cannot be the same when Estimate sample size is selected.
6. When a single population mean is specified, enter the Population standard deviation for mean
difference value. When a single value is specified, it denotes the population standard deviation of the
group difference σd. The value must be a single numeric greater than 0.
7. When multiple population means are specified, enter the Population standard deviation for group 1
and Population standard deviation for group 2 values. When multiple values are specified, they
denote the population standard deviation of the group difference σ1 and σ2. The values must be a
single numerics greater than 0.
8. Optionally, enter a value that specifies the Pearson product-moment correlation coefficient ρ. The
value must be a single numeric value between -1 and 1. The value cannot be 0.
Note: When a single Population standard deviation for mean difference value is specified, this
setting is ignored. Otherwise, the values for Population standard deviation for group 1 and
Population standard deviation for group 2 are used to compute σd.
9. Select whether the test is one or two-sided.
Nondirectional (two-sided) analysis
When selected, a two-sided test is used. This is the default setting.
Directional (one-sided) analysis
When selected, power is computed for a one-sided test.
10. Optionally, specify the significance level of the Type I error rate for the test in the Significance level
field. The value must be a single double value between 0 and 1. The default value is 0.05.
11. You can optionally click Plot to specify “Power Analysis of Paired-Samples T Test: Plot” on page 5
settings (chart output, two-dimensional plot settings, three-dimensional plot settings, and tooltips).
Note: Plot is available only when Estimate power is selected as the test assumption.
Power Analysis of Paired-Samples T Test: Plot
You can control the plots that are output to illustrate the two and three-dimensional power by sample/
effect size charts. You can also control the display of tool tips and the vertical/horizontal rotation degrees
for three-dimensional charts.
Two-Dimensional Plot
Power estimation versus sample size
When enabled, this optional setting provides options for controlling the two-dimensional power by
sample size chart. The setting is disabled by default.
Range of sample size
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range of the sample size
is used.
Lower bound
Controls the lower bound for the two-dimensional power by sample size chart. The value
must be greater than 1, and cannot be greater than the Upper bound value.
Upper bound
Controls the upper bound for the two-dimensional power by sample size chart. The value
must be greater than the Lower bound value and cannot be greater than 5000.
Chapter 1. Core features 5
Power estimation versus effect size
By default, this optional setting is disabled. When enabled, the chart displays in the output. When
no integer values are specified for the Lower bound or Upper bound fields, the default plot range
of the effect size used.
Range of effect size
When selected, the lower and upper bound options are available.
Lower bound
Controls the lower bound for the two-dimensional power by effect size chart. The value
must be greater than, or equal to, -5.0 and cannot be greater than the Upper bound value.
Upper bound
Controls the upper bound for the two-dimensional power by effect size chart. The value
must be greater than the Lower bound value and cannot be greater than 5.0.
Three-Dimensional Plot
Power estimation versus
Provides options for controlling the three-dimensional power by sample size (x-axis) and effect
size (y-axis) chart, the vertical/horizontal rotation settings, and the user specified plot range of
sample/effect size. This setting is disabled by default.
Effect size on x-axis and sample size on y-axis
The optional setting controls the three-dimensional power by sample size (x-axis) and effect
size (y-axis) chart. By default, the chart is suppressed. When specified, the chart displays.
Effect size on y-axis and sample size on x-axis
The optional setting controls the three-dimensional power by sample size (y-axis) and effect
size (x-axis) chart. By default, the chart is suppressed. When specified, the chart displays.
Vertical rotation
The optional setting sets the vertical rotation degrees (clockwise from the left) for the three-
dimensional chart. You can use the mouse to rotate the chart vertically. The setting takes
effect when the three-dimensional plot is requested. The value must be a single integer value
less than or equal to 359. The default value is 10.
Horizontal rotation
The optional setting sets the horizontal rotation degrees (clockwise from the front) for the
three-dimensional chart. You can use the mouse to rotate the chart horizontally. The setting
takes effect when the three-dimensional plot is requested. The value must be a single integer
value less than or equal to 359. The default value is 325.
Range of sample size
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range of the sample size
is used.
Lower bound
Controls the lower bound for the three-dimensional power by sample size chart. The value
must be greater than 1, and cannot be greater than the Upper bound value.
Upper bound
Controls the upper bound for the three-dimensional power by sample size chart. The value
must be greater than the Lower bound value and cannot be greater than 5000.
Range of effect size
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range of the effect size
is used.
Lower bound
Controls the lower bound for the three-dimensional power by effect size chart. The value
must be greater than, or equal to, -5.0 and cannot be greater than the Upper bound value.
6 IBM SPSS Statistics Base V27
Upper bound
Controls the upper bound for the three-dimensional power by effect size chart. The value
must be greater than the Lower bound value and cannot be greater than 5.0.
Power Analysis of Independent-Samples T Test
This feature requires IBM SPSS Statistics Base Edition.
Power analysis plays a pivotal role in a study plan, design, and conduction. The calculation of power is
usually before any sample data have been collected, except possibly from a small pilot study. The precise
estimation of the power may tell investigators how likely it is that a statistically significant difference will
be detected based on a finite sample size under a true alternative hypothesis. If the power is too low,
there is little chance of detecting a significant difference, and non-significant results are likely even if real
differences truly exist.
In independent-samples analysis, the observed data contain two independent samples. It is assumed
that the data in each sample independently and identically follow a normal distribution with a fixed mean
and variance, and draws statistical inference about the difference of the two means.
1. From the menus choose:
Analyze > Power Analysis > Means > Independent-Samples T Test
2. Select a test assumption setting (Estimate sample size or Estimate power).
3. When Estimate sample size is selected, enter an appropriate Power for sample size estimation
value (the value must be a single value between 0 and 1) and a Group size ratio value for specifying
the ratio of the sample sizes (the value must be a single value between 0.01 and 100.
4. When Estimate power is selected, enter values to specify the sample size for the two groups for
comparison Sample size for group 1 and Sample size for group 2. The values must be an integers
greater than 1.
5. When a single population mean is required, enter a Population mean difference value. When single
value is specified, it denotes the population mean difference μd.
Note: The value cannot be 0 when Estimate sample size is selected.
6. When multiple population means are required for the specified group pairs, enter values for
Population mean for group 1 and Population mean for group 2. When multiple values are specified,
they denote the population mean difference μ1 and μ2.
Note: The two values cannot be the same when Estimate sample size is selected.
7. Specify whether the population standard deviations are Equal for two groups or Not equal for two
groups.
• When the population standard deviations are equal for two groups, enter a value for Pooled
standard deviation that denotes σ, and assumes that the two group variances are equal, or σ1 = σ2
= σ.
• When the population standard deviations are not equal for two groups, enter values for Standard
deviation for group 1 and Standard deviation for group 2 that denote σ1 and σ2.
Note: When the values for Standard deviation for group 1 and Standard deviation for group 2 are
identical, they are treated as a single value.
8. Select whether the test is one or two-sided.
Nondirectional (two-sided) analysis
When selected, a two-sided test is used. This is the default setting.
Directional (one-sided) analysis
When selected, power is computed for a one-sided test.
9. Optionally, specify the significance level of the Type I error rate for the test in the Significance level
field. The value must be a single double value between 0 and 1. The default value is 0.05.
Chapter 1. Core features 7
10. You can optionally click Plot to specify “Power Analysis of Independent-Samples T Test: Plot” on
page 8 settings (chart output, two-dimensional plot settings, three-dimensional plot settings, and
tooltips).
Note: Plot is available only when Estimate power is selected as the test assumption.
Power Analysis of Independent-Samples T Test: Plot
You can control the plots that are output to illustrate the two and three-dimensional power by sample
ratio, effect size, or mean difference charts. You can also control the display of tool tips and the vertical/
horizontal rotation degrees for three-dimensional charts.
Two-Dimensional Plot
Power estimation versus sample size ratio
When enabled, this optional setting provides options for controlling the two-dimensional power by
sample size ratio chart. The setting is disabled by default.
Range of sample size ratio
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range of the sample size
is used.
Lower bound
Controls the lower bound for the two-dimensional power by sample size ratio chart. The
value must be between 0.01 and 100 and cannot be greater than the Upper bound value.
Upper bound
Controls the upper bound for the two-dimensional power by sample size ratio chart. The
value must be between 0.01 and 100 and must be greater than the Lower bound value.
Power estimation versus effect size (or mean difference)
By default, this optional setting is disabled. When enabled, the chart displays in the output. When
no integer values are specified for the Lower bound or Upper bound fields, the default plot range
of the effect size (or mean difference) is used.
Range of effect size (or mean difference)
When selected, the lower and upper bound options are available.
Lower bound
Controls the lower bound for the two-dimensional power by effect size chart. The value
must be greater than, or equal to, -5.0 and cannot be greater than the Upper bound value.
Upper bound
Controls the upper bound for the two-dimensional power by effect size chart. The value
must be greater than the Lower bound value and cannot be greater than 5.0.
Three-Dimensional Plot
Power estimation versus
Provides options for controlling the three-dimensional power by sample size ratio (x-axis) and
effect size (y-axis) chart, the vertical/horizontal rotation settings, and the user specified plot range
of sample/effect size. This setting is disabled by default.
Effect size (or mean difference) on x-axis and sample size on y-axis
The optional setting controls the three-dimensional power by sample size ratio (x-axis) and
effect size (y-axis) chart. By default, the chart is suppressed. When specified, the chart
displays.
Effect size (or mean difference) on y-axis and sample size on x-axis
The optional setting controls the three-dimensional power by sample size (y-axis) and effect
size (x-axis) chart. By default, the chart is suppressed. When specified, the chart displays.
Vertical rotation
The optional setting sets the vertical rotation degrees (clockwise from the left) for the three-
dimensional chart. You can use the mouse to rotate the chart vertically. The setting takes
8 IBM SPSS Statistics Base V27
effect when the three-dimensional plot is requested. The value must be a single integer value
less than or equal to 359. The default value is 10.
Horizontal rotation
The optional setting sets the horizontal rotation degrees (clockwise from the front) for the
three-dimensional chart. You can use the mouse to rotate the chart horizontally. The setting
takes effect when the three-dimensional plot is requested. The value must be a single integer
value less than or equal to 359. The default value is 325.
Range of sample size ratio
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range of the sample size
is used.
Lower bound
Controls the lower bound for the three-dimensional power by sample size ratio chart. The
value must be between 0.01 and 100 and cannot be greater than the Upper bound value.
Upper bound
Controls the upper bound for the three-dimensional power by sample size ratio chart. The
value must be between 0.01 and 100 and must be greater than the Lower bound value.
Range of effect size (or mean difference)
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range of the effect size
is used.
Lower bound
Controls the lower bound for the three-dimensional power by effect size chart. The value
must be greater than, or equal to, -5.0 and cannot be greater than the Upper bound value.
Upper bound
Controls the upper bound for the three-dimensional power by effect size chart. The value
must be greater than the Lower bound value and cannot be greater than 5000.
Power Analysis of One-Way ANOVA
This feature requires IBM SPSS Statistics Base Edition.
Power analysis plays a pivotal role in a study plan, design, and conduction. The calculation of power is
usually before any sample data have been collected, except possibly from a small pilot study. The precise
estimation of the power may tell investigators how likely it is that a statistically significant difference will
be detected based on a finite sample size under a true alternative hypothesis. If the power is too low,
there is little chance of detecting a significant difference, and non-significant results are likely even if real
differences truly exist.
Analysis of variance (ANOVA) is a statistical method of estimating the means of several populations which
are often assumed to be normally distributed. The One-way ANOVA, a common type of ANOVA, is an
extension of the two-sample t-test. The procedure provides approaches for estimating the power for two
types of hypothesis to compare the multiple group means, the overall test, and the test with specified
contrasts. The over test focuses on the null hypothesis that all group means are equal. The test with
specified contrasts breaks down the overall ANOVA hypotheses into smaller but more describable and
useful pieces of the means.
1. From the menus choose:
Analyze > Power Analysis > Means > One-way ANOVA
2. Select a test assumption setting (Estimate sample size or Estimate power).
3. When Estimate sample size is selected, enter an appropriate Power for sample size estimation value
(the value must be a single value between 0 and 1).
4. Enter a Pooled population standard deviation value. The value must be a single numeric greater than
0.
Chapter 1. Core features 9
5. Specify the Group sizes and Group means values. At least two group size values must be specified
(each value must be less than, or equal to, 2). At least two group mean values must also be specified
(the number of specified values must equal the group size values).
6. Optionally, specify Group weights values. Group weights assign the group size weights when
Estimate power is selected.
Note: The Group weights settings are ignored when Group sizes values are specified.
7. Optionally, specify the significance level of the Type I error rate for the test in the Significance level
field. The value must be a single double value between 0 and 1. The default value is 0.05.
8. You can optionally click Contrast to specify “Power Analysis of One-way ANOVA: Contrast” on page
10 settings (contrast test and pairwise differences), or click Plot to specify “Power Analysis of One-
way ANOVA: Plot” on page 10 settings (chart output, two-dimensional plot settings, three-
dimensional plot settings, and tooltips).
Note: Plot is available only when Group sizes values are specified and Estimate power is selected.
Power Analysis of One-way ANOVA: Contrast
You can specify the following contrast, coefficient, and pairwise differences settings for your Power
Analysis of One-way ANOVA:
Contrast Test
Test with linear contrasts
When enabled, the contrast and coefficient settings are available.
Test direction
Nondirectional (two-sided) analysis
When selected, a two-sided test is used. This is the default setting.
Directional (one-sided) analysis
When selected, power is computed for a one-sided test.
Coefficients
Use the table to specify the contrast coefficients and request the contrast test. The table
values are optional. The number of specified values must be equal to the values specified for
Group sizes and Group means. The sum for all specified values must equal 0, otherwise the
last value will automatically be adjusted.
Pairwise Differences
Estimate the power of testing for pairwise differences
Controls whether or not to estimate the power of testing for the pairwise differences. Be default,
the optional setting is disabled, which suppresses output for the pairwise differences.
Adjust the significance level by
Determines the adjustment of multiple comparisons.
Bonferroni correction
Uses the Bonferroni correction in estimating the power of pairwise differences. This is the
default setting.
Sidak correction
Uses the Sidak correction in estimating the power of pairwise differences.
Least significant difference (LSD)
Uses the LSD correction in estimating the power of pairwise differences.
Power Analysis of One-way ANOVA: Plot
You can control the plots that are output to illustrate the two and three-dimensional power by sample and
effect size charts. You can also control the display of tool tips and the vertical/horizontal rotation degrees
for three-dimensional charts.
10 IBM SPSS Statistics Base V27
Two-Dimensional Plot
Power estimation versus total sample size
When enabled, this optional setting provides options for controlling the two-dimensional power by
total sample size chart. The setting is disabled by default.
Range of total sample size
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range of the total
sample size is used.
Lower bound
Controls the lower bound for the two-dimensional power by total sample size chart. The
value must be greater than, or equal to:
• 2 x the number of integers specified for Group sizes
• 2 x the sum of the integers specified for Group sizes / by the smallest integer value for
Group sizes
The value cannot be greater than the Upper bound value.
Upper bound
Controls the upper bound for the two-dimensional power by total sample size chart. The
value must be less than, or equal to:
• 5000 / by the largest integer value specified for Group sizes x the sum of the integers
specified for Group sizes
The value must be greater than the Lower bound value and cannot be greater than
2147483647.
Power estimation versus pooled standard deviation
By default, this optional setting is disabled. The setting controls the two-dimensional power by
pooled standard deviation chart. When enabled, the chart displays in the output. When no integer
values are specified for the Lower bound or Upper bound fields, the default plot range of the
pooled standard deviation is used.
Note:
The plot is disabled when the specified Group means values are all the same.
Range of pooled standard deviation
When selected, the lower and upper bound options are available.
Lower bound
Controls the lower bound for the two-dimensional power by pooled standard deviation
chart. The value must be greater than 0 and cannot be greater than the Upper bound
value.
Upper bound
Controls the upper bound for the two-dimensional power by pooled standard deviation
chart. The value must be greater than the Lower bound value.
Three-Dimensional Plot
Power estimation versus
Provides options for controlling the three-dimensional power by total sample size (x-axis) and
effect size (y-axis) chart, the vertical/horizontal rotation settings, and the user specified plot range
of sample/effect size. This setting is disabled by default.
Note:
The plot is disabled when the specified Group means values are all the same.
Pooled standard deviation on x-axis and total sample size on y-axis
The optional setting controls the three-dimensional power by total sample size (x-axis) and
pooled standard deviation (y-axis) chart. By default, the chart is suppressed. When specified,
the chart displays.
Chapter 1. Core features 11
Pooled standard deviation on y-axis and total sample size on x-axis
The optional setting controls the three-dimensional power by total sample size (y-axis) and
pooled standard deviation (x-axis) chart. By default, the chart is suppressed. When specified,
the chart displays.
Vertical rotation
The optional setting sets the vertical rotation degrees (clockwise from the left) for the three-
dimensional chart. You can use the mouse to rotate the chart vertically. The setting takes
effect when the three-dimensional plot is requested. The value must be a single integer value
less than or equal to 359. The default value is 10.
Horizontal rotation
The optional setting sets the horizontal rotation degrees (clockwise from the front) for the
three-dimensional chart. You can use the mouse to rotate the chart horizontally. The setting
takes effect when the three-dimensional plot is requested. The value must be a single integer
value less than or equal to 359. The default value is 325.
Range of total sample size
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range of the sample size
is used.
Lower bound
Controls the lower bound for the three-dimensional power by total sample size chart. The
value must be greater than 0 and cannot be greater than the Upper bound value.
Upper bound
Controls the upper bound for the three-dimensional power by total sample size chart. The
value must be greater than the Lower bound value.
Range of pooled standard deviation
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range of the effect size
is used.
Lower bound
Controls the lower bound for the three-dimensional power by pooled standard deviation
chart. The value must be greater than 0 and cannot be greater than the Upper bound
value.
Upper bound
Controls the upper bound for the three-dimensional power by pooled standard deviation
chart. The value must be greater than the Lower bound value.
Proportions
The following statistics features are included in IBM SPSS Statistics Base Edition.
Power Analysis of Related-Sample Binomial Test
This feature requires IBM SPSS Statistics Base Edition.
Power analysis plays a pivotal role in a study plan, design, and conduction. The calculation of power is
usually before any sample data have been collected, except possibly from a small pilot study. The precise
estimation of the power may tell investigators how likely it is that a statistically significant difference will
be detected based on a finite sample size under a true alternative hypothesis. If the power is too low,
there is little chance of detecting a significant difference, and non-significant results are likely even if real
differences truly exist.
Binomial distribution is based on a sequence of Bernoulli trials. It can be used to model experiments,
including a fixed number of total trials, which are assumed to be independent of each other. Each trial
leads to a dichotomous result, with the same probability for a successful outcome.
The related-sample binomial estimates the power of McNemar’s test to compare two proportion
parameters based on the matched pair subjects sampled from two related binomial populations.
12 IBM SPSS Statistics Base V27
1. From the menus choose:
Analyze > Power Analysis > Proportions > Related-Sample Binomial Test
2. Select a test assumption setting (Estimate sample size or Estimate power).
3. When selecting Estimate power, enter the appropriate Total number of pairs value. The value must
be a positive integer greater than, or equal to, 2. When selecting Estimate sample size, enter an
appropriate Power for sample size estimation value. The value must be a single value between 0 and
1.
4. Select to specify testing values for either Proportions or Counts.
• When Proportions is selected, enter values in the Proportion 1 and Proportion 2 fields. The values
must be between 0 and 1.
• When Counts is selected, enter values in the Count 1 and Count 2 fields. The values must be
between 0 and value specified for Total number of pairs.
Proportions Notes:
• Proportions is the only available option when a Power value is specified.
• When Test values are marginal is not selected: 0 < Proportion 1 + Proportion 2 ≤ 1
• When Test values are marginal is selected:
– Proportion 1 * Proportion 2 > 0
– Proportion 1 < 1
– Proportion 2 < 1
– The values for Proportion 1 and Proportion 2 cannot be the same.
Counts Notes:
• When Test values are marginal is not selected: 0 < Count 1 + Count 2 ≤ Total number of pairs
• When Test values are marginal is selected:
– Count 1 * Count 2 > 0
– Count 1 < Total number of pairs
– Count 2 < Total number of pairs
5. You can optionally select Test values are marginal to control whether or not the specified proportions
or counts values are marginal. When Test values are marginal is enabled, you must specify a
Correlation between matched pairs value. The value must be a single value between -1 and 1.
6. Select a method for estimating the power.
Normal approximation
Enables normal approximation. This is the default setting.
Binomial enumeration
Enables the binomial enumeration method. Optionally, use the Time limit field to specify the
maximum number of minutes allowed to estimate the sample size. When the time limit is reached,
the analysis is terminated and a warning message is displayed. When specified, the value must be
a single positive integer to denote the number of minutes. The default setting is 5 minutes.
7. Select whether the test is one or two-sided.
Nondirectional (two-sided) analysis
When selected, a two-sided test is used. This is the default setting.
Directional (one-sided) analysis
When selected, power is computed for a one-sided test.
8. Optionally, specify the significance level of the Type I error rate for the test in the Significance level
field. The value must be a single double value between 0 and 1. The default value is 0.05.
9. You can optionally click Plot to specify “Power Analysis of Related-Sample Binomial Test” on page 12
settings (chart output, two-dimensional plot settings, three-dimensional plot settings, and tooltips).
Chapter 1. Core features 13
Note: Plot is available only when Estimate power is selected as the test assumption and Binomial
enumeration is not selected.
Power Analysis of Related-Sample Binomial: Plot
You can control the plots that are output to illustrate the two and three-dimensional power estimation
charts. You can also control the display of tool tips and the vertical/horizontal rotation degrees for three-
dimensional charts.
Two-Dimensional Plot
Provides options for controlling the two-dimensional power estimation versus charts. This setting is
disabled by default.
Power estimation versus total number of pairs
When enabled, this optional setting controls the two-dimensional power by total number of pairs
chart. The setting is disabled by default. When selected, this setting displays the chart.
Plot range of total number of pairs
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range is used.
Lower bound
Controls the lower bound for the two-dimensional power estimation versus total number
of pairs chart. The value must be greater than 1, and cannot be greater than the Upper
bound value.
Upper bound
Controls the upper bound for the two-dimensional power estimation versus total number
of pairs chart. The value must be greater than the Lower bound value and cannot be
greater than 2500.
Power estimation versus risk difference
When enabled, this optional setting controls the two-dimensional power by risk difference chart.
The setting is disabled by default. When selected, this setting displays the chart.
Power estimation versus risk ratio
When enabled, this optional setting control the two-dimensional power by risk ratio chart. The
setting is disabled by default.
Plot range of risk ratio
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range is used.
Lower bound
Controls the lower bound for the two-dimensional power estimation versus risk ratio chart.
The value cannot be greater than the Upper bound value.
Upper bound
Controls the upper bound for the two-dimensional power estimation versus risk ratio
chart. The value must be greater than the Lower bound value and cannot be greater than
10.
Power estimation versus odds ratio
When enabled, this optional setting controls the two-dimensional power by odds ratio chart. The
setting is disabled by default. When selected, this setting displays the chart.
Plot range of odds ratio
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range is used.
Lower bound
Controls the lower bound for the two-dimensional power estimation versus odds ratio
chart. The value cannot be greater than the Upper bound value.
14 IBM SPSS Statistics Base V27
Upper bound
Controls the upper bound for the two-dimensional power estimation versus odds ratio
chart. The value must be greater than the Lower bound value and cannot be greater than
10.
Three-Dimensional Plot
Provides options for controlling the three-dimensional power estimation versus charts. This setting is
disabled by default.
Power estimation versus discordant proportions
When enabled, this optional setting controls the three-dimensional power by discordant
proportions chart. The setting is disabled by default. When selected, this setting displays the
chart.
Power estimation versus marginal proportions
When enabled, this optional setting controls the three-dimensional power by marginal proportions
chart. The setting is disabled by default. When selected, this setting displays the chart.
Note: This setting is available only when Test values are marginal is selected.
Vertical rotation
The optional setting sets the vertical rotation degrees (clockwise from the left) for the three-
dimensional chart. You can use the mouse to rotate the chart vertically. The setting takes effect
when the three-dimensional plot is requested. The value must be a single integer value less than
or equal to 359. The default value is 10.
Horizontal rotation
The optional setting sets the horizontal rotation degrees (clockwise from the front) for the three-
dimensional chart. You can use the mouse to rotate the chart horizontally. The setting takes effect
when the three-dimensional plot is requested. The value must be a single integer value less than
or equal to 359. The default value is 325.
Power Analysis of Independent-Sample Binomial Test
This feature requires IBM SPSS Statistics Base Edition.
Power analysis plays a pivotal role in a study plan, design, and conduction. The calculation of power is
usually before any sample data have been collected, except possibly from a small pilot study. The precise
estimation of the power may tell investigators how likely it is that a statistically significant difference will
be detected based on a finite sample size under a true alternative hypothesis. If the power is too low,
there is little chance of detecting a significant difference, and non-significant results are likely even if real
differences truly exist.
The binomial distribution is based on a sequence of Bernoulli trials. It can be used to model those
experiments including a fixed number of total trials that are assumed to be independent of each other.
Each trial leads to a dichotomous result, with the same probability for a "successful" outcome. The
independent-sample binomial test compares two independent proportion parameters.
1. From the menus choose:
Analyze > Power Analysis > Proportions > Independent-Samples Binomial Test
2. Select a test assumption setting (Estimate sample size or Estimate power).
3. When Estimate sample size is selected, enter an appropriate Power for sample size estimation
value (the value must be a single value between 0 and 1) and a Group size ratio value for specifying
the ratio of the sample sizes (the value must be a single value between 0.01 and 100.
4. When Estimate power is selected, enter values to specify the total number of trials for both group 1
and group 2. The values must be an integers greater than 1.
5. Specify the proportion parameters for the two groups. Both values must be between 0 and 1.
Note: The two values cannot be the same when a Power value is specified.
6. Optionally, specify the significance level of the Type I error rate for the test in the Significance level
field. The value must be a single double value between 0 and 1. The default value is 0.05.
Chapter 1. Core features 15
7. Select the desired test assumptions:
Chi-squared test
Estimates the power based on Pearson’s chi-squared test. This is the default setting.
Standard deviation is pooled
This optional setting controls whether the estimation of the standard deviation is pooled or
unpooled. The setting is enabled by default.
Apply continuity correction
This optional setting controls whether or not the continuity correction is used. The setting is
disabled by default.
T-test
Estimates the power based on Student’s t-test.
Standard deviation is pooled
This optional setting controls whether the estimation of the standard deviation is pooled or
unpooled. The setting is enabled by default.
Likelihood ratio test
Estimates the power based on the likelihood ratio test.
Fisher’s exact test
Estimates the power based on Fisher’s exact test.
Notes:
• In some cases, Fisher’s exact test may take an extended amount of time to complete.
• All plots are blocked when Fisher’s exact test is selected.
8. Select a method for estimating the power.
Normal approximation
Enables normal approximation. This is the default setting.
Binomial enumeration
Enables the binomial enumeration method. Optionally, use the Time limit field to specify the
maximum number of minutes allowed to estimate the sample size. When the time limit is
reached, the analysis is terminated and a warning message is displayed. When specified, the
value must be a single positive integer to denote the number of minutes. The default setting is 5
minutes.
9. Select whether the test is one or two-sided.
Nondirectional (two-sided) analysis
When selected, a two-sided test is used. This is the default setting.
Directional (one-sided) analysis
When selected, power is computed for a one-sided test.
10. You can optionally click Plot to specify “Power Analysis of Independent-Samples Binomial Test:
Plot” on page 16 settings (chart output, two-dimensional plot settings, three-dimensional plot
settings, and tooltips).
Note: Plot is available only when Estimate power is selected as the test assumption and Binomial
enumeration is not selected.
Power Analysis of Independent-Samples Binomial Test: Plot
You can control the plots that are output to illustrate the two and three-dimensional power estimation
charts. You can also control the display of tool tips and the vertical/horizontal rotation degrees for three-
dimensional charts.
Two-Dimensional Plot
Provides options for controlling the two-dimensional power estimation versus charts. This setting is
disabled by default.
16 IBM SPSS Statistics Base V27
Power estimation versus group size ratio
When enabled, this optional setting controls the two-dimensional power by group size ratio chart.
The setting is disabled by default. When selected, this setting displays the chart.
Plot range of group size ratio
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range is used.
Lower bound
Controls the lower bound for the two-dimensional power estimation versus total number
of pairs chart. The value must be greater than .01, and cannot be greater than the Upper
bound value.
Upper bound
Controls the upper bound for the two-dimensional power estimation versus total number
of pairs chart. The value must be greater than the Lower bound value and cannot be
greater than 100.
Power estimation versus risk difference
When enabled, this optional setting controls the two-dimensional power by risk difference chart.
The setting is disabled by default. When selected, this setting displays the chart.
Power estimation versus risk ratio
When enabled, this optional setting control the two-dimensional power by risk ratio chart. The
setting is disabled by default.
Plot range of risk ratio
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range is used.
Lower bound
Controls the lower bound for the two-dimensional power estimation versus risk ratio chart.
The value cannot be greater than the Upper bound value.
Upper bound
Controls the upper bound for the two-dimensional power estimation versus risk ratio
chart. The value must be greater than the Lower bound value and cannot be greater than
10.
Power estimation versus odds ratio
When enabled, this optional setting controls the two-dimensional power by odds ratio chart. The
setting is disabled by default. When selected, this setting displays the chart.
Plot range of odds ratio
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range is used.
Lower bound
Controls the lower bound for the two-dimensional power estimation versus odds ratio
chart. The value cannot be greater than the Upper bound value.
Upper bound
Controls the upper bound for the two-dimensional power estimation versus odds ratio
chart. The value must be greater than the Lower bound value and cannot be greater than
10.
Three-Dimensional Plot
Provides options for controlling the three-dimensional power estimation versus charts. This setting is
disabled by default.
Power estimation versus proportions
When selected, this optional setting provides the following power by proportion options:
proportion of group 1 on x-axis and proportion of group 2 on y-axis
Controls the three-dimensional power by proportion of Group 1 (x -axis) and proportion of
Group 2 (y-axis) chart. The setting is disabled by default. When selected, this setting displays
the chart.
Chapter 1. Core features 17
proportion of group 1 on y-axis and proportion of group 2 on x-axis
Controls the three-dimensional power by proportion of Group 2 (x -axis) and proportion of
Group 1 (y-axis) chart. The setting is disabled by default. When selected, this setting displays
the chart.
Power estimation versus group sizes
When selected, this optional setting provides the following power by group sizes options:
size of group 1 on x-axis and size of group 2 on y-axis
Controls the three-dimensional power by number of trials in Group 1 (x -axis) and number of
trials in Group 2 (y-axis) chart. The setting is disabled by default. When selected, this setting
displays the chart.
size of group 1 on y-axis and size of group 2 on x-axis
Controls the three-dimensional power by number of trials in Group 2 (x -axis) and number of
trials in Group 1 (y-axis) chart. The setting is disabled by default. When selected, this setting
displays the chart.
User specified plot range of size of group 1
When selected, the lower and upper bound options for the group 1 plot range are available.
When no integer values are specified for the Lower bound or Upper bound fields, the default
plot range is used.
Lower bound
Controls the lower bound for the two-dimensional power estimation versus odds ratio
chart. The value must be greater than or equal to 2 and cannot be greater than the Upper
bound value.
Upper bound
Controls the upper bound for the two-dimensional power estimation versus odds ratio
chart. The value must be greater than the Lower bound value and cannot be greater than
2500.
User specified plot range of size of group 2
When selected, the lower and upper bound options for the group 2 plot range are available.
When no integer values are specified for the Lower bound or Upper bound fields, the default
plot range is used.
Lower bound
Controls the lower bound for the two-dimensional power estimation versus odds ratio
chart. The value must be greater than or equal to 2 and cannot be greater than the Upper
bound value.
Upper bound
Controls the upper bound for the two-dimensional power estimation versus odds ratio
chart. The value must be greater than the Lower bound value and cannot be greater than
2500.
Vertical rotation
The optional setting sets the vertical rotation degrees (clockwise from the left) for the three-
dimensional chart. You can use the mouse to rotate the chart vertically. The setting takes effect
when the three-dimensional plot is requested. The value must be a single integer value less than
or equal to 359. The default value is 10.
Horizontal rotation
The optional setting sets the horizontal rotation degrees (clockwise from the front) for the three-
dimensional chart. You can use the mouse to rotate the chart horizontally. The setting takes effect
when the three-dimensional plot is requested. The value must be a single integer value less than
or equal to 359. The default value is 325.
Power Analysis of One-Sample Binomial Test
This feature requires IBM SPSS Statistics Base Edition.
Power analysis plays a pivotal role in a study plan, design, and conduction. The calculation of power is
usually before any sample data have been collected, except possibly from a small pilot study. The precise
18 IBM SPSS Statistics Base V27
estimation of the power may tell investigators how likely it is that a statistically significant difference will
be detected based on a finite sample size under a true alternative hypothesis. If the power is too low,
there is little chance of detecting a significant difference, and non-significant results are likely even if real
differences truly exist.
Binomial distribution is based on a sequence of Bernoulli trials. It can be used to model experiments,
including a fixed number of total trials, which are assumed to be independent of each other. Each trial
leads to a dichotomous result, with the same probability for a successful outcome.
The one-sample binomial test makes statistical inference about the proportion parameter by comparing it
with a hypothesized value. The methods for estimating the power for such a test are either the normal
approximation or the binomial enumeration.
1. From the menus choose:
Analyze > Power Analysis > Proportions > One-Sample Binomial Test
2. Select a test assumption setting (Estimate sample size or Estimate power).
3. When selecting Estimate power, enter the appropriate Total number of trials value. The value must
be an integer greater than, or equal to, 1. When selecting Estimate sample size, enter an appropriate
Power for sample size estimation value. The value must be a single value between 0 and 1.
4. Enter a value that specifies the alternative hypothesis value of the proportion parameter in the
Population proportion field. The value must be a single numeric.
Note: When a Power value is specified, the Population proportionvalue cannot be equal to the Null
value.
5. Optionally, enter a value that specifies the null hypothesis value of the proportion parameter to be
tested in the Null value field. The value must be a single numeric between 0 and 1. The default value
is 0.50.
6. Select a method for estimating the power.
Normal approximation
Enables normal approximation. This is the default setting.
Apply continuity correction
Control whether or not the continuity correction is used for the normal approximation method.
Binomial enumeration
Enables the binomial enumeration method. Optionally, use the Time limit field to specify the
maximum number of minutes allowed to estimate the sample size. When the time limit is reached,
the analysis is terminated and a warning message is displayed. When specified, the value must be
a single positive integer to denote the number of minutes. The default setting is 5 minutes.
Note: The selected power estimation method has no effect when the Total number of trials value
exceeds 500.
7. Select whether the test is one or two-sided.
Nondirectional (two-sided) analysis
When selected, a two-sided test is used. This is the default setting.
Directional (one-sided) analysis
When selected, power is computed for a one-sided test.
8. Optionally, specify the significance level of the Type I error rate for the test in the Significance level
field. The value must be a single double value between 0 and 1. The default value is 0.05.
9. You can optionally click Plot to specify “Power Analysis of One-Sample Binomial: Plot” on page 20
settings (chart output, two-dimensional plot settings, three-dimensional plot settings, and tooltips).
Note: Plot is available only when Estimate power is selected as the test assumption and Binomial
enumeration is not selected.
Chapter 1. Core features 19
Power Analysis of One-Sample Binomial: Plot
You can control the plots that are output to illustrate the two and three-dimensional power by charts. You
can also control the display of tool tips and the vertical/horizontal rotation degrees for three-dimensional
charts.
Two-Dimensional Plot
Provides options for controlling the two-dimensional power estimation versus charts. This setting is
disabled by default.
Power estimation versus null hypothesis value
When enabled, this optional setting controls the two-dimensional power by null value chart. The
setting is disabled by default. When selected, this setting displays the chart.
Power estimation versus alternative hypothesis value
When enabled, this optional setting controls the two-dimensional power by alternative value
chart. The setting is disabled by default. When selected, this setting displays the chart.
Power estimation versus the difference between hypothesized values
When enabled, this optional setting controls the two-dimensional power by difference between
hypothesized values chart. The setting is disabled by default.
Power estimation versus total number of trials
When enabled, this optional setting controls the two-dimensional power by total number of trials
chart. The setting is disabled by default. When selected, this setting displays the chart.
Plot range of total number of trials
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range is used.
Lower bound
Controls the lower bound for the two-dimensional power estimation versus total number
of trials chart. The value must be greater than 0, and cannot be greater than the Upper
bound value.
Upper bound
Controls the upper bound for the two-dimensional power estimation versus total number
of trials chart. The value must be greater than the Lower bound value and cannot be
greater than 5000.
Three-Dimensional Plot
Provides options for controlling the three-dimensional power estimation versus charts. This setting is
disabled by default.
Power estimation versus total number of trials
When selected, this setting enables the following options.
on x-axis and the difference between hypothesized values on y-axis
The optional setting controls the three-dimensional power by total number of trials (x -axis)
and difference between hypothesized values (y-axis) chart. By default, the chart is
suppressed. When specified, the chart displays.
on y-axis and the difference between hypothesized values on x-axis
The optional setting controls the three-dimensional power by total number of trials (y-axis)
and difference between hypothesized values (x -axis) chart. By default, the chart is
suppressed. When specified, the chart displays.
Plot range of total number of trials
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range is used.
Lower bound
Controls the lower bound for the three-dimensional power estimation versus total number
of trials chart. The value must be greater than 0, and cannot be greater than the Upper
bound value.
20 IBM SPSS Statistics Base V27
Upper bound
Controls the upper bound for the three-dimensional power estimation versus total number
of trials chart. The value must be greater than the Lower bound value and cannot be
greater than 5000.
Power estimation versus null hypothesis value
When selected, this setting enables the following options.
on x-axis and alternative hypothesis value on y-axis
The optional setting controls the three-dimensional power by null (x -axis) and alternative
value (y-axis) chart. By default, the chart is suppressed. When specified, the chart displays.
on y-axis and alternative hypothesis value on x-axis
The optional setting controls the three-dimensional power by null (y-axis) and alternative
value (x -axis) chart.. By default, the chart is suppressed. When specified, the chart displays.
Vertical rotation
The optional setting sets the vertical rotation degrees (clockwise from the left) for the three-
dimensional chart. You can use the mouse to rotate the chart vertically. The setting takes
effect when the three-dimensional plot is requested. The value must be a single integer value
less than or equal to 359. The default value is 10.
Horizontal rotation
The optional setting sets the horizontal rotation degrees (clockwise from the front) for the
three-dimensional chart. You can use the mouse to rotate the chart horizontally. The setting
takes effect when the three-dimensional plot is requested. The value must be a single integer
value less than or equal to 359. The default value is 325.
Correlations
The following statistics features are included in IBM SPSS Statistics Base Edition.
Power Analysis of One-Sample Pearson Correlation Test
This feature requires IBM SPSS Statistics Base Edition.
Power analysis plays a pivotal role in a study plan, design, and conduction. The calculation of power is
usually before any sample data have been collected, except possibly from a small pilot study. The precise
estimation of the power may tell investigators how likely it is that a statistically significant difference will
be detected based on a finite sample size under a true alternative hypothesis. If the power is too low,
there is little chance of detecting a significant difference, and non-significant results are likely even if real
differences truly exist.
Pearson’s product-moment correlation coefficient measures the strength of linear association between
two scale random variables that are assumed to follow a bivariate normal distribution. By convention, it is
a dimensionless quantity and obtained by standardizing the covariance between two continuous
variables, thereby ranging between -1 and 1.
The test uses Fisher’s asymptotic method to estimate the power for the one-sample Pearson correlation.
1. From the menus choose:
Analyze > Power Analysis > Correlations > Pearson Product-Moment
2. Select a test assumption setting (Estimate sample size or Estimate power).
3. When selecting Estimate power, enter the appropriate Sample size in pairs value. The value must be
a single integer greater than 3. When selecting Estimate sample size, enter a Power for sample size
estimation value. The value must be a single value between 0 and 1.
4. Enter a value that specifies the alternative hypothesis value of the correlation parameter in the
Pearson correlation parameter field. The value must be a single numeric between -1 and 1.
Note: When a Power value is specified, the Pearson correlation parameter value cannot be -1 or 1
and cannot be equal Null value.
Chapter 1. Core features 21
5. Optionally, enter a value that specifies the null hypothesis value of the correlation parameter to be
tested in the Null value field. The value must be a single numeric between -1 and 1. The default value
is 0.
Note: When a Power value is specified, Null value cannot be -1 or 1.
6. Optionally, select Use bias-correction formiula in the power estimation to specify whether the bias
adjustment is involved or ignored. The setting is enabled by default, which includes the bias
adjustment term in the power estimation. When the setting is not selected, the bias adjustment term is
ignored.
7. Select whether the test is one or two-sided.
Nondirectional (two-sided) analysis
When selected, a two-sided test is used. This is the default setting.
Directional (one-sided) analysis
When selected, power is computed for a one-sided test.
8. Optionally, specify the significance level of the Type I error rate for the test in the Significance level
field. The value must be a single double value between 0 and 1. The default value is 0.05.
9. You can optionally click Plot to specify “Power Analysis of One-Sample Pearson Correlation: Plot” on
page 22 settings (chart output, two-dimensional plot settings, three-dimensional plot settings, and
tooltips).
Note: Plot is available only when Estimate power is selected as the test assumption.
Power Analysis of One-Sample Pearson Correlation: Plot
You can control the plots that are output to illustrate the two and three-dimensional power by charts. You
can also control the display of tool tips and the vertical/horizontal rotation degrees for three-dimensional
charts.
Two-Dimensional Plot
Provides options for controlling the two-dimensional power estimation versus charts. The settings are
disabled by default.
Power estimation versus null hypothesis value
When enabled, this optional setting controls the two-dimensional power by null value chart. The
setting is disabled by default. When selected, this setting displays the chart.
Power estimation versus alternative hypothesis value
When enabled, this optional setting controls the two-dimensional power by alternative value
chart. The setting is disabled by default. When selected, this setting displays the chart.
Power estimation versus the difference between hypothesized values
When enabled, this optional setting controls the two-dimensional power by difference between
hypothesized values chart. The setting is disabled by default.
Power estimation versus sample size (in pairs)
When enabled, this optional setting controls the two-dimensional power by sample size chart. The
setting is disabled by default. When selected, this setting displays the chart.
Plot range of sample size
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range is used.
Lower bound
Controls the lower bound for the two-dimensional power estimation by sample size chart.
The value must be greater than or equal to 4, and cannot be greater than the Upper bound
value.
Upper bound
Controls the upper bound for the two-dimensional power estimation by sample size chart.
The value must be greater than the Lower bound value and cannot be greater than 5000.
22 IBM SPSS Statistics Base V27
Three-Dimensional Plot
Provides options for controlling the three-dimensional power estimation versus charts. This setting is
disabled by default.
Power estimation versus sample size
When selected, this setting enables the following options.
on x-axis and the difference between hypothesized values on y-axis
The optional setting controls the three-dimensional power by sample size (x -axis) and
difference between hypothesized values (y-axis) chart. By default, the chart is suppressed.
When specified, the chart displays.
on y-axis and the difference between hypothesized values on x-axis
The optional setting controls the three-dimensional power by sample size (y -axis) and
difference between hypothesized values (x-axis) chart. By default, the chart is suppressed.
When specified, the chart displays
Plot range of sample size (in pairs)
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range is used.
Lower bound
Controls the lower bound for the three-dimensional power estimation by sample size
chart. The value must be greater than or equal to 4, and cannot be greater than the Upper
bound value.
Upper bound
Controls the upper bound for the three-dimensional power estimation by sample size
chart. The value must be greater than the Lower bound value and cannot be greater than
5000.
Power estimation versus null hypothesis value
When selected, this setting enables the following options.
on x-axis and alternative hypothesis value on y-axis
The optional setting controls the three-dimensional power by null (x -axis) and alternative
value (y-axis) chart. By default, the chart is suppressed. When specified, the chart displays.
on y-axis and alternative hypothesis value on x-axis
The optional setting controls the three-dimensional power by null (y-axis) and alternative
value (x -axis) chart.. By default, the chart is suppressed. When specified, the chart displays.
Vertical rotation
The optional setting sets the vertical rotation degrees (clockwise from the left) for the three-
dimensional chart. You can use the mouse to rotate the chart vertically. The setting takes
effect when the three-dimensional plot is requested. The value must be a single integer value
less than or equal to 359. The default value is 10.
Horizontal rotation
The optional setting sets the horizontal rotation degrees (clockwise from the front) for the
three-dimensional chart. You can use the mouse to rotate the chart horizontally. The setting
takes effect when the three-dimensional plot is requested. The value must be a single integer
value less than or equal to 359. The default value is 325.
Power Analysis of One-Sample Spearman Correlation Test
This feature requires IBM SPSS Statistics Base Edition.
Power analysis plays a pivotal role in a study plan, design, and conduction. The calculation of power is
usually before any sample data have been collected, except possibly from a small pilot study. The precise
estimation of the power may tell investigators how likely it is that a statistically significant difference will
be detected based on a finite sample size under a true alternative hypothesis. If the power is too low,
there is little chance of detecting a significant difference, and non-significant results are likely even if real
differences truly exist.
Chapter 1. Core features 23
Spearman rank-order correlation coefficient is a rank-based nonparametric statistic to measure the
monotonic relationship between two variables that are usually censored and not normally distributed.
The Spearman rank-order correlation is equal to the Pearson correlation between the rank values of the
two variables, thereby also ranging between -1 and 1. Detecting the power of the Spearman rank
correlation test is an important topic in the analysis of hydrological time series data.
The test uses Fisher’s asymptotic method to estimate the power for the one-sample Spearman rank-
order correlation.
1. From the menus choose:
Analyze > Power Analysis > Correlations > Spearman Rank-Order
2. Select a test assumption setting (Estimate sample size or Estimate power).
3. When selecting Estimate power, enter the appropriate Sample size in pairs value. The value must be
a single integer greater than 3. When selecting Estimate sample size, enter a Power for sample size
estimation value. The value must be a single value between 0 and 1.
4. Enter a value that specifies the alternative hypothesis value of the correlation parameter in the
Spearman correlation parameter field. The value must be a single numeric between -1 and 1.
Note: When a Power value is specified, the Spearman correlation parameter value cannot be -1 or 1
and cannot be equal Null value.
5. Optionally, enter a value that specifies the null hypothesis value of the correlation parameter to be
tested in the Null value field. The value must be a single numeric between -1 and 1. The default value
is 0.
Note: When a Power value is specified, Null value cannot be -1 or 1.
6. Optionally, select an option that determines how the asymptotic variance is estimated for the power
analysis.
Bonett and Wright
Estimates the variance suggested by Bonett and Wright. This is the default setting.
Fieller, Hartley and Pearson
Estimates the variance suggested by Fieller, Hartley and Pearson.
Caruso and Cliff
Estimates the variance suggested by Caruso and Cliff.
7. Select whether the test is one or two-sided.
Nondirectional (two-sided) analysis
When selected, a two-sided test is used. This is the default setting.
Directional (one-sided) analysis
When selected, power is computed for a one-sided test.
8. Optionally, specify the significance level of the Type I error rate for the test in the Significance level
field. The value must be a single double value between 0 and 1. The default value is 0.05.
9. You can optionally click Plot to specify “Power Analysis of One-Sample Spearman Correlation: Plot” on
page 24 settings (chart output, two-dimensional plot settings, three-dimensional plot settings, and
tooltips).
Note: Plot is available only when Estimate power is selected as the test assumption.
Power Analysis of One-Sample Spearman Correlation: Plot
You can control the plots that are output to illustrate the two and three-dimensional power by charts. You
can also control the display of tool tips and the vertical/horizontal rotation degrees for three-dimensional
charts.
Two-Dimensional Plot
Provides options for controlling the two-dimensional power estimation versus charts. The settings are
disabled by default.
24 IBM SPSS Statistics Base V27
Power estimation versus null hypothesis value
When enabled, this optional setting controls the two-dimensional power by null value chart. The
setting is disabled by default. When selected, this setting displays the chart.
Power estimation versus alternative hypothesis value
When enabled, this optional setting controls the two-dimensional power by alternative value
chart. The setting is disabled by default. When selected, this setting displays the chart.
Power estimation versus the difference between hypothesized values
When enabled, this optional setting controls the two-dimensional power by difference between
hypothesized values chart. The setting is disabled by default.
Power estimation versus sample size (in pairs)
When enabled, this optional setting controls the two-dimensional power by sample size chart. The
setting is disabled by default. When selected, this setting displays the chart.
Plot range of sample size
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range is used.
Lower bound
Controls the lower bound for the two-dimensional power estimation by sample size chart.
The value must be greater than or equal to 4, and cannot be greater than the Upper bound
value.
Upper bound
Controls the upper bound for the two-dimensional power estimation by sample size chart.
The value must be greater than the Lower bound value and cannot be greater than 5000.
Three-Dimensional Plot
Provides options for controlling the three-dimensional power estimation versus charts. This setting is
disabled by default.
Power estimation versus sample size
When selected, this setting enables the following options.
on x-axis and the difference between hypothesized values on y-axis
The optional setting controls the three-dimensional power by sample size (x -axis) and
difference between hypothesized values (y-axis) chart. By default, the chart is suppressed.
When specified, the chart displays.
on y-axis and the difference between hypothesized values on x-axis
The optional setting controls the three-dimensional power by sample size (y -axis) and
difference between hypothesized values (x-axis) chart. By default, the chart is suppressed.
When specified, the chart displays
Plot range of sample size (in pairs)
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range is used.
Lower bound
Controls the lower bound for the three-dimensional power estimation by sample size
chart. The value must be greater than or equal to 4, and cannot be greater than the Upper
bound value.
Upper bound
Controls the upper bound for the three-dimensional power estimation by sample size
chart. The value must be greater than the Lower bound value and cannot be greater than
5000.
Power estimation versus null hypothesis value
When selected, this setting enables the following options.
on x-axis and alternative hypothesis value on y-axis
The optional setting controls the three-dimensional power by null (x -axis) and alternative
value (y-axis) chart. By default, the chart is suppressed. When specified, the chart displays.
Chapter 1. Core features 25
on y-axis and alternative hypothesis value on x-axis
The optional setting controls the three-dimensional power by null (y-axis) and alternative
value (x -axis) chart.. By default, the chart is suppressed. When specified, the chart displays.
Vertical rotation
The optional setting sets the vertical rotation degrees (clockwise from the left) for the three-
dimensional chart. You can use the mouse to rotate the chart vertically. The setting takes
effect when the three-dimensional plot is requested. The value must be a single integer value
less than or equal to 359. The default value is 10.
Horizontal rotation
The optional setting sets the horizontal rotation degrees (clockwise from the front) for the
three-dimensional chart. You can use the mouse to rotate the chart horizontally. The setting
takes effect when the three-dimensional plot is requested. The value must be a single integer
value less than or equal to 359. The default value is 325.
Power Analysis of Partial Pearson Correlation Test
This feature requires IBM SPSS Statistics Base Edition.
Power analysis plays a pivotal role in a study plan, design, and conduction. The calculation of power is
usually before any sample data have been collected, except possibly from a small pilot study. The precise
estimation of the power may tell investigators how likely it is that a statistically significant difference will
be detected based on a finite sample size under a true alternative hypothesis. If the power is too low,
there is little chance of detecting a significant difference, and non-significant results are likely even if real
differences truly exist.
Partial correlation can be explained as the association between two random variables after eliminating
the effect of another or several other variables. It is a useful measurement in the presence of
confounding. Similar to the Pearson correlation coefficient, partial correlation coefficient is also a
dimensionless quantity ranging between -1 and 1.
The test uses Fisher’s asymptotic method to estimate the power for the one-sample Pearson correlation.
1. From the menus choose:
Analyze > Power Analysis > Correlations > Partial
2. Select a test assumption setting (Estimate sample size or Estimate power).
3. When selecting Estimate power, enter the appropriate Sample size in pairs value. The value must be
a single integer greater than 3. When selecting Estimate sample size, enter a Power for sample size
estimation value. The value must be a single value between 0 and 1.
4. Enter a value that specifies the number of the variables assumed to be partialed out. The value must
be a single integer greater than or equal to 0.
5. Enter a value that specifies the alternative hypothesis value of the partial correlation parameter in the
Partial Pearson correlation parameter field. The value must be a single numeric between -1 and 1.
Note: When a Power value is specified, the Partial Pearson correlation parameter value cannot be -1
or 1 and cannot be equal Null value.
6. Optionally, enter a value that specifies the null hypothesis value of the partial correlation parameter to
be tested in the Null value field. The value must be a single numeric between -1 and 1. The default
value is 0.
Note: When a Power value is specified, Null value cannot be -1 or 1.
7. Select whether the test is one or two-sided.
Nondirectional (two-sided) analysis
When selected, a two-sided test is used. This is the default setting.
Directional (one-sided) analysis
When selected, power is computed for a one-sided test.
8. Optionally, specify the significance level of the Type I error rate for the test in the Significance level
field. The value must be a single double value between 0 and 1. The default value is 0.05.
26 IBM SPSS Statistics Base V27
9. You can optionally click Plot to specify “Power Analysis of Partial Pearson Correlation: Plot” on page
27 settings (chart output, two-dimensional plot settings, three-dimensional plot settings, and
tooltips).
Note: Plot is available only when Estimate power is selected as the test assumption.
Power Analysis of Partial Pearson Correlation: Plot
You can control the plots that are output to illustrate the two and three-dimensional power by charts. You
can also control the display of tool tips and the vertical/horizontal rotation degrees for three-dimensional
charts.
Two-Dimensional Plot
Provides options for controlling the two-dimensional power estimation versus charts. The settings are
disabled by default.
Power estimation versus null hypothesis value
When enabled, this optional setting controls the two-dimensional power by null value chart. The
setting is disabled by default. When selected, this setting displays the chart.
Power estimation versus alternative hypothesis value
When enabled, this optional setting controls the two-dimensional power by alternative value
chart. The setting is disabled by default. When selected, this setting displays the chart.
Power estimation versus the number of variables partialed out
When enabled, this optional setting controls the two-dimensional power by number of partialed-
out variables chart. The setting is disabled by default. When selected, this setting displays the
chart.
Power estimation versus the difference between hypothesized values
When enabled, this optional setting controls the two-dimensional power by difference between
hypothesized values chart. The setting is disabled by default.
Power estimation versus sample size
When enabled, this optional setting controls the two-dimensional power by sample size chart. The
setting is disabled by default. When selected, this setting displays the chart.
Plot range of sample size
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range is used.
Lower bound
Controls the lower bound for the two-dimensional power estimation by sample size chart.
The value must be greater than or equal to 4, and cannot be greater than the Upper bound
value.
Upper bound
Controls the upper bound for the two-dimensional power estimation by sample size chart.
The value must be greater than the Lower bound value and cannot be greater than 5000.
Three-Dimensional Plot
Provides options for controlling the three-dimensional power estimation versus charts. This setting is
disabled by default.
Power estimation versus sample size
When selected, this setting enables the following options.
on x-axis and the difference between hypothesized values on y-axis
The optional setting controls the three-dimensional power by sample size (x -axis) and
difference between hypothesized values (y-axis) chart. By default, the chart is suppressed.
When specified, the chart displays.
on y-axis and the difference between hypothesized values on x-axis
The optional setting controls the three-dimensional power by sample size (y -axis) and
difference between hypothesized values (x-axis) chart. By default, the chart is suppressed.
When specified, the chart displays
Chapter 1. Core features 27
Plot range of sample size (in pairs)
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range is used.
Lower bound
Controls the lower bound for the three-dimensional power estimation by sample size
chart. The value must be greater than or equal to 4, and cannot be greater than the Upper
bound value.
Upper bound
Controls the upper bound for the three-dimensional power estimation by sample size
chart. The value must be greater than the Lower bound value and cannot be greater than
5000.
Power estimation versus null hypothesis value
When selected, this setting enables the following options.
on x-axis and alternative hypothesis value on y-axis
The optional setting controls the three-dimensional power by null (x -axis) and alternative
value (y-axis) chart. By default, the chart is suppressed. When specified, the chart displays.
on y-axis and alternative hypothesis value on x-axis
The optional setting controls the three-dimensional power by null (y-axis) and alternative
value (x -axis) chart.. By default, the chart is suppressed. When specified, the chart displays.
Vertical rotation
The optional setting sets the vertical rotation degrees (clockwise from the left) for the three-
dimensional chart. You can use the mouse to rotate the chart vertically. The setting takes
effect when the three-dimensional plot is requested. The value must be a single integer value
less than or equal to 359. The default value is 10.
Horizontal rotation
The optional setting sets the horizontal rotation degrees (clockwise from the front) for the
three-dimensional chart. You can use the mouse to rotate the chart horizontally. The setting
takes effect when the three-dimensional plot is requested. The value must be a single integer
value less than or equal to 359. The default value is 325.
Regression
The following statistics features are included in IBM SPSS Statistics Base Edition.
Power Analysis of Univariate Linear Regression Test
This feature requires IBM SPSS Statistics Base Edition.
Power analysis plays a pivotal role in a study plan, design, and conduction. The calculation of power is
usually before any sample data have been collected, except possibly from a small pilot study. The precise
estimation of the power may tell investigators how likely it is that a statistically significant difference will
be detected based on a finite sample size under a true alternative hypothesis. If the power is too low,
there is little chance of detecting a significant difference, and non-significant results are likely even if real
differences truly exist.
Univariate linear regression is a basic and standard statistical approach in which researchers use the
values of several variables to explain or predict values of a scale outcome.
The Power Analysis of Univariate Linear Regression test estimates the power of the type III F-test in
univariate multiple linear regression models. With the effect size represented by multiple (partial)
correlations, approaches for both fixed and random predictors are provided. For fixed predictors, the
power estimation is based on the non-central F-distribution. For random predictors, it is assumed that the
target variable and the predictors jointly follow a multivariate normal distribution. In which case, power
estimation is based on the distribution of the sample multiple correlation coefficient.
1. From the menus choose:
Analyze > Power Analysis > Regression > Univariate Linear
28 IBM SPSS Statistics Base V27
2. Select a test assumption setting (Estimate sample size or Estimate power).
3. When selecting Estimate power, enter an appropriate Sample size for power estimation value. The
value must be a single integer greater than or equal to the total number of model predictors +2 (when
Include the intercept term in the model is enabled). Otherwise the value must be a single integer
greater than or equal to the total number of model predictors +1.
When selecting Estimate sample size, enter an appropriate Power for sample size estimation value.
The value must be a single value between 0 and 1.
4. Specify the value of the multiple partial correlation coefficient in the Population multiple partial
correlation field. The value must be a single value between -1 and 1.
Note: When a Power value is specified, the Population multiple partial correlation value cannot be 0.
The following settings are enabled when Population multiple partial correlation is selected:
Total number of predictors in the model
Specify the number of either the total predictors, or the predictors in the full model (not including
the intercept, if applicable). The value must be a single integer greater than or equal to 1.
Number of test predictors
Specify the number of either the test predictors, or the predictors in the nested model (not
including the intercept, if applicable). The value must be greater than or equal to 1, but no larger
than the Total number of predictors in the model value.
5. Specify R-squared values for multiple correlation coefficients for both Full model and Nested model.
The values must be a single values between 0 and 1.
Note: When a Power value is specified, the Full model value must be greater than the Nested model
value.
The following settings are enabled when R-squared values for is selected:
Total number of predictors – Full Model
Specify the number of either the total predictors, or the predictors in the full model (not including
the intercept, if applicable). The value must be a single integer greater than or equal to 1.
Total number of predictors – Nested Model
Specify the number of either the total predictors, or the predictors in the nested model (not
including the intercept, if applicable). The value must be greater than or equal to 1, but less than
the Total number of predictors in the model value.
6. Optionally, specify the significance level of the Type I error rate for the test in the Significance level
field. The value must be a single double value between 0 and 1. The default value is 0.05.
7. You can optionally select the Include the intercept term in the model setting. The setting is enabled
by default. When not selected, the intercept term is excluded from the power analysis.
8. You can optionally select whether model predictors are Fixed or Random. Fixed is the default setting.
9. You can optionally click Plot to specify “Power Analysis of Univariate Linear Regression: Plot” on page
29 settings (chart output, two-dimensional plot settings, and three-dimensional plot settings).
Note: Plot is available only when Estimate power is selected as the test assumption.
Power Analysis of Univariate Linear Regression: Plot
You can control the plots that are output to illustrate the two and three-dimensional power by charts. You
can also control the display of tool tips and the vertical/horizontal rotation degrees for three-dimensional
charts.
Two-Dimensional Plot
Provides options for controlling the two-dimensional power estimation versus charts. The settings are
disabled by default.
Chapter 1. Core features 29
Power estimation versus the multiple partial correlation
When enables, this optional setting controls the two-dimensional power by multiple partial
correlation coefficient chart. The setting is disabled by default. When selected, this setting
displays the chart.
Power estimation versus sample size
When enabled, this optional setting controls the two-dimensional power by sample size chart. The
setting is disabled by default. When selected, this setting displays the chart.
Plot range of sample size
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range is used.
Lower bound
Controls the lower bound for the two-dimensional power estimation by sample size chart.
The value must be greater than or equal to 4, and cannot be greater than the Upper bound
value.
Upper bound
Controls the upper bound for the two-dimensional power estimation by sample size chart.
The value must be greater than the Lower bound value and cannot be greater than 5000.
Three-Dimensional Plot
Provides options for controlling the three-dimensional power estimation versus charts, the vertical/
horizontal rotation settings, and the user specified plot range of sample size. This setting is disabled
by default.
Power estimation versus sample size
When enabled, this optional setting controls the three-dimensional power by sample size charts.
The setting is disabled by default. When selected, this setting displays the chart.
on x-axis and the multiple partial correlation on y-axis
This optional setting controls the three-dimensional power by sample size (x-axis) and multiple
partial correlation coefficient (y-axis) chart. The setting is disabled by default. When selected, this
setting displays the chart.
on y-axis and the multiple partial correlation on x-axis
This optional setting controls the three-dimensional power by sample size (y-axis) and multiple
partial correlation coefficient (x-axis) chart. The setting is disabled by default. When selected, this
setting displays the chart.
Plot range of sample size
When selected, the lower and upper bound options are available. When no integer values are
specified for the Lower bound or Upper bound fields, the default plot range is used.
Lower bound
Controls the lower bound for the two-dimensional power estimation by sample size chart. The
value must be greater than or equal to 4, and cannot be greater than the Upper bound value.
Upper bound
Controls the upper bound for the two-dimensional power estimation by sample size chart. The
value must be greater than the Lower bound value and cannot be greater than 5000.
Vertical rotation
The optional setting sets the vertical rotation degrees (clockwise from the left) for the three-
dimensional chart. You can use the mouse to rotate the chart vertically. The setting takes effect
when the three-dimensional plot is requested. The value must be a single integer value less than
or equal to 359. The default value is 10.
Horizontal rotation
The optional setting sets the horizontal rotation degrees (clockwise from the front) for the three-
dimensional chart. You can use the mouse to rotate the chart horizontally. The setting takes effect
when the three-dimensional plot is requested. The value must be a single integer value less than
or equal to 359. The default value is 325.
30 IBM SPSS Statistics Base V27
Codebook
Codebook reports the dictionary information — such as variable names, variable labels, value labels,
missing values — and summary statistics for all or specified variables and multiple response sets in the
active dataset. For nominal and ordinal variables and multiple response sets, summary statistics include
counts and percents. For scale variables, summary statistics include mean, standard deviation, and
quartiles.
Note: Codebook ignores split file status. This includes split-file groups created for multiple imputation of
missing values (available in the Missing Values add-on option).
To Obtain a Codebook
1. From the menus choose:
Analyze > Reports > Codebook
2. Click the Variables tab.
3. Select one or more variables and/or multiple response sets.
Optionally, you can:
• Control the variable information that is displayed.
• Control the statistics that are displayed (or exclude all summary statistics).
• Control the order in which variables and multiple response sets are displayed.
• Change the measurement level for any variable in the source list in order to change the summary
statistics displayed. See the topic “Codebook Statistics Tab” on page 33 for more information.
Changing Measurement Level
You can temporarily change the measurement level for variables. (You cannot change the measurement
level for multiple response sets. They are always treated as nominal.)
1. Right-click a variable in the source list.
2. Select a measurement level from the pop-up menu.
This changes the measurement level temporarily. In practical terms, this is only useful for numeric
variables. The measurement level for string variables is restricted to nominal or ordinal, which are both
treated the same by the Codebook procedure.
Codebook Output Tab
The Output tab controls the variable information included for each variable and multiple response set, the
order in which the variables and multiple response sets are displayed, and the contents of the optional
file information table.
Variable Information
This controls the dictionary information displayed for each variable.
Position. An integer that represents the position of the variable in file order. This is not available for
multiple response sets.
Label. The descriptive label associated with the variable or multiple response set.
Type. Fundamental data type. This is either Numeric, String, or Multiple Response Set.
Format. The display format for the variable, such as A4, F8.2, or DATE11. This is not available for multiple
response sets.
Measurement level. The possible values are Nominal, Ordinal, Scale, and Unknown. The value displayed
is the measurement level stored in the dictionary and is not affected by any temporary measurement level
override specified by changing the measurement level in the source variable list on the Variables tab. This
is not available for multiple response sets.
Chapter 1. Core features 31
Note: The measurement level for numeric variables may be “unknown” prior to the first data pass when
the measurement level has not been explicitly set, such as data read from an external source or newly
created variables. See the topic for more information.
Role. Some dialogs support the ability to pre-select variables for analysis based on defined roles.
Value labels. Descriptive labels associated with specific data values.
• If Count or Percent is selected on the Statistics tab, defined value labels are included in the output even
if you don’t select Value labels here.
• For multiple dichotomy sets, “value labels” are either the variable labels for the elementary variables in
the set or the labels of counted values, depending on how the set is defined. See the topic for more
information.
Missing values. User-defined missing values. If Count or Percent is selected on the Statistics tab, defined
value labels are included in the output even if you don’t select Missing values here. This is not available
for multiple response sets.
Custom attributes. User-defined custom variable attributes. Output includes both the names and values
for any custom variable attributes associated with each variable. See the topic for more information. This
is not available for multiple response sets.
Reserved attributes. Reserved system variable attributes. You can display system attributes, but you
should not alter them. System attribute names start with a dollar sign ($) . Non-display attributes, with
names that begin with either “@” or “$@”, are not included. Output includes both the names and values
for any system attributes associated with each variable. This is not available for multiple response sets.
File Information
The optional file information table can include any of the following file attributes:
File name. Name of the IBM SPSS Statistics data file. If the dataset has never been saved in IBM SPSS
Statistics format, then there is no data file name. (If there is no file name displayed in the title bar of the
Data Editor window, then the active dataset does not have a file name.)
Location. Directory (folder) location of the IBM SPSS Statistics data file. If the dataset has never been
saved in IBM SPSS Statistics format, then there is no location.
Number of cases. Number of cases in the active dataset. This is the total number of cases, including any
cases that may be excluded from summary statistics due to filter conditions.
Label. This is the file label (if any) defined by the FILE LABEL command.
Documents. Data file document text.
Weight status. If weighting is on, the name of the weight variable is displayed. See the topic for more
information.
Custom attributes. User-defined custom data file attributes. Data file attributes defined with the
DATAFILE ATTRIBUTE command.
Reserved attributes. Reserved system data file attributes. You can display system attributes, but you
should not alter them. System attribute names start with a dollar sign ($) . Non-display attributes, with
names that begin with either “@” or “$@”, are not included. Output includes both the names and values
for any system data file attributes.
Variable Display Order
The following alternatives are available for controlling the order in which variables and multiple response
sets are displayed.
Alphabetical. Alphabetic order by variable name.
File. The order in which variables appear in the dataset (the order in which they are displayed in the Data
Editor). In ascending order, multiple response sets are displayed last, after all selected variables.
Measurement level. Sort by measurement level. This creates four sorting groups: nominal, ordinal, scale,
and unknown. Multiple response sets are treated as nominal.
32 IBM SPSS Statistics Base V27
Note: The measurement level for numeric variables may be “unknown” prior to the first data pass when
the measurement level has not been explicitly set, such as data read from an external source or newly
created variables.
Variable list. The order in which variables and multiple response sets appear in the selected variables list
on the Variables tab.
Custom attribute name. The list of sort order options also includes the names of any user-defined
custom variable attributes. In ascending order, variables that don’t have the attribute sort to the top,
followed by variables that have the attribute but no defined value for the attribute, followed by variables
with defined values for the attribute in alphabetic order of the values.
Maximum Number of Categories
If the output includes value labels, counts, or percents for each unique value, you can suppress this
information from the table if the number of values exceeds the specified value. By default, this
information is suppressed if the number of unique values for the variable exceeds 200.
Codebook Statistics Tab
The Statistics tab allows you to control the summary statistics that are included in the output, or suppress
the display of summary statistics entirely.
Counts and Percents
For nominal and ordinal variables, multiple response sets, and labeled values of scale variables, the
available statistics are:
Count. The count or number of cases having each value (or range of values) of a variable.
Percent. The percentage of cases having a particular value.
Central Tendency and Dispersion
For scale variables, the available statistics are:
Mean. A measure of central tendency. The arithmetic average, the sum divided by the number of cases.
Standard Deviation. A measure of dispersion around the mean. In a normal distribution, 68% of cases fall
within one standard deviation of the mean and 95% of cases fall within two standard deviations. For
example, if the mean age is 45, with a standard deviation of 10, 95% of the cases would be between 25
and 65 in a normal distribution.
Quartiles. Displays values corresponding to the 25th, 50th, and 75th percentiles.
Note: You can temporarily change the measurement level associated with a variable (and thereby change
the summary statistics displayed for that variable) in the source variable list on the Variables tab.
Frequencies
The Frequencies procedure provides statistics and graphical displays that are useful for describing many
types of variables. The Frequencies procedure is a good place to start looking at your data.
For a frequency report and bar chart, you can arrange the distinct values in ascending or descending
order, or you can order the categories by their frequencies. The frequencies report can be suppressed
when a variable has many distinct values. You can label charts with frequencies (the default) or
percentages.
Example
What is the distribution of a company’s customers by industry type? From the output, you might learn
that 37.5% of your customers are in government agencies, 24.9% are in corporations, 28.1% are in
academic institutions, and 9.4% are in the healthcare industry. For continuous, quantitative data,
such as sales revenue, you might learn that the average product sale is $3,576, with a standard
deviation of $1,078.
Chapter 1. Core features 33
Statistics and plots
Frequency counts, percentages, cumulative percentages, mean, median, mode, sum, standard
deviation, variance, range, minimum and maximum values, standard error of the mean, skewness and
kurtosis (both with standard errors), quartiles, user-specified percentiles, bar charts, pie charts, and
histograms.
Data considerations
Data
Use numeric codes or strings to code categorical variables (nominal or ordinal level measurements).
Assumptions
The tabulations and percentages provide a useful description for data from any distribution, especially
for variables with ordered or unordered categories. Most of the optional summary statistics, such as
the mean and standard deviation, are based on normal theory and are appropriate for quantitative
variables with symmetric distributions. Robust statistics, such as the median, quartiles, and
percentiles, are appropriate for quantitative variables that may or may not meet the assumption of
normality.
Obtaining frequency tables
1. From the menus choose:
Analyze > Descriptive Statistics > Frequencies…
2. Select one or more categorical or quantitative variables.
3. Optionally, select Create APA style tables to create output tables that adhere to APA style guidelines.
4. Optionally, you can:
• Click Statistics for descriptive statistics for quantitative variables.
• Click Charts for bar charts, pie charts, and histograms.
• Click Format for the order in which results are displayed.
• Click Style to specify conditions for automatically changing properties of pivot tables based on
specific conditions.
• Click Bootstrap to derive robust estimates of standard errors and confidence intervals for estimates
such as the mean, median, proportion, odds ratio, correlation coefficient or regression coefficient. It
may also be used for constructing hypothesis tests.
Frequencies Statistics
Percentile Values. Values of a quantitative variable that divide the ordered data into groups so that a
certain percentage is above and another percentage is below. Quartiles (the 25th, 50th, and 75th
percentiles) divide the observations into four groups of equal size. If you want an equal number of groups
other than four, select Cut points for n equal groups. You can also specify individual percentiles (for
example, the 95th percentile, the value below which 95% of the observations fall).
Central Tendency. Statistics that describe the location of the distribution include the mean, median,
mode, and sum of all the values.
• Mean. A measure of central tendency. The arithmetic average, the sum divided by the number of cases.
• Median. The value above and below which half of the cases fall, the 50th percentile. If there is an even
number of cases, the median is the average of the two middle cases when they are sorted in ascending
or descending order. The median is a measure of central tendency not sensitive to outlying values
(unlike the mean, which can be affected by a few extremely high or low values).
• Mode. The most frequently occurring value. If several values share the greatest frequency of
occurrence, each of them is a mode. The Frequencies procedure reports only the smallest of such
multiple modes.
• Sum. The sum or total of the values, across all cases with nonmissing values.
34 IBM SPSS Statistics Base V27
Dispersion. Statistics that measure the amount of variation or spread in the data include the standard
deviation, variance, range, minimum, maximum, and standard error of the mean.
• Std. deviation. A measure of dispersion around the mean. In a normal distribution, 68% of cases fall
within one standard deviation of the mean and 95% of cases fall within two standard deviations. For
example, if the mean age is 45, with a standard deviation of 10, 95% of the cases would be between 25
and 65 in a normal distribution.
• Variance. A measure of dispersion around the mean, equal to the sum of squared deviations from the
mean divided by one less than the number of cases. The variance is measured in units that are the
square of those of the variable itself.
• Range. The difference between the largest and smallest values of a numeric variable, the maximum
minus the minimum.
• Minimum. The smallest value of a numeric variable.
• Maximum. The largest value of a numeric variable.
• S. E. mean. A measure of how much the value of the mean may vary from sample to sample taken from
the same distribution. It can be used to roughly compare the observed mean to a hypothesized value
(that is, you can conclude the two values are different if the ratio of the difference to the standard error
is less than -2 or greater than +2).
Distribution. Skewness and kurtosis are statistics that describe the shape and symmetry of the
distribution. These statistics are displayed with their standard errors.
• Skewness. A measure of the asymmetry of a distribution. The normal distribution is symmetric and has a
skewness value of 0. A distribution with a significant positive skewness has a long right tail. A
distribution with a significant negative skewness has a long left tail. As a guideline, a skewness value
more than twice its standard error is taken to indicate a departure from symmetry.
• Kurtosis. A measure of the extent to which there are outliers. For a normal distribution, the value of the
kurtosis statistic is zero. Positive kurtosis indicates that the data exhibit more extreme outliers than a
normal distribution. Negative kurtosis indicates that the data exhibit less extreme outliers than a normal
distribution.
Values are group midpoints. If the values in your data are midpoints of groups (for example, ages of all
people in their thirties are coded as 35), select this option to estimate the median and percentiles for the
original, ungrouped data.
Frequencies Charts
Note: Charts are not produced in the output when Perform bootstrapping is enabled on the Bootstrap
dialog.
Chart Type
A pie chart displays the contribution of parts to a whole. Each slice of a pie chart corresponds to a
group that is defined by a single grouping variable. A bar chart displays the count for each distinct
value or category as a separate bar, allowing you to compare categories visually. A histogram also has
bars, but they are plotted along an equal interval scale. The height of each bar is the count of values of
a quantitative variable falling within the interval. A histogram shows the shape, center, and spread of
the distribution. A normal curve superimposed on a histogram helps you judge whether the data are
normally distributed.
Chart Values
For bar charts, the scale axis can be labeled by frequency counts or percentages.
Frequencies Format
Order by. The frequency table can be arranged according to the actual values in the data or according to
the count (frequency of occurrence) of those values, and the table can be arranged in either ascending or
descending order. However, if you request a histogram or percentiles, Frequencies assumes that the
variable is quantitative and displays its values in ascending order.
Chapter 1. Core features 35
Multiple Variables. If you produce statistics tables for multiple variables, you can either display all
variables in a single table (Compare variables) or display a separate statistics table for each variable
(Organize output by variables).
Suppress tables with many categories. This option prevents the display of tables with more than the
specified number of values.
Descriptives
The Descriptives procedure displays univariate summary statistics for several variables in a single table
and calculates standardized values (z scores). Variables can be ordered by the size of their means (in
ascending or descending order), alphabetically, or by the order in which you select the variables (the
default).
When z scores are saved, they are added to the data in the Data Editor and are available for charts, data
listings, and analyses. When variables are recorded in different units (for example, gross domestic
product per capita and percentage literate), a z-score transformation places variables on a common scale
for easier visual comparison.
Example. If each case in your data contains the daily sales totals for each member of the sales staff (for
example, one entry for Bob, one entry for Kim, and one entry for Brian) collected each day for several
months, the Descriptives procedure can compute the average daily sales for each staff member and can
order the results from highest average sales to lowest average sales.
Statistics. Sample size, mean, minimum, maximum, standard deviation, variance, range, sum, standard
error of the mean, and kurtosis and skewness with their standard errors.
Descriptives Data Considerations
Data. Use numeric variables after you have screened them graphically for recording errors, outliers, and
distributional anomalies. The Descriptives procedure is very efficient for large files (thousands of cases).
Assumptions. Most of the available statistics (including z scores) are based on normal theory and are
appropriate for quantitative variables (interval- or ratio-level measurements) with symmetric
distributions. Avoid variables with unordered categories or skewed distributions. The distribution of z
scores has the same shape as that of the original data; therefore, calculating z scores is not a remedy for
problem data.
To Obtain Descriptive Statistics
1. From the menus choose:
Analyze > Descriptive Statistics > Descriptives…
2. Select one or more variables.
Optionally, you can:
• Select Save standardized values as variables to save z scores as new variables.
• Click Options for optional statistics and display order.
Descriptives Options
Mean and Sum. The mean, or arithmetic average, is displayed by default.
Dispersion. Statistics that measure the spread or variation in the data include the standard deviation,
variance, range, minimum, maximum, and standard error of the mean.
• Std. deviation. A measure of dispersion around the mean. In a normal distribution, 68% of cases fall
within one standard deviation of the mean and 95% of cases fall within two standard deviations. For
example, if the mean age is 45, with a standard deviation of 10, 95% of the cases would be between 25
and 65 in a normal distribution.
• Variance. A measure of dispersion around the mean, equal to the sum of squared deviations from the
mean divided by one less than the number of cases. The variance is measured in units that are the
square of those of the variable itself.
36 IBM SPSS Statistics Base V27
• Range. The difference between the largest and smallest values of a numeric variable, the maximum
minus the minimum.
• Minimum. The smallest value of a numeric variable.
• Maximum. The largest value of a numeric variable.
• S.E. mean. A measure of how much the value of the mean may vary from sample to sample taken from
the same distribution. It can be used to roughly compare the observed mean to a hypothesized value
(that is, you can conclude the two values are different if the ratio of the difference to the standard error
is less than -2 or greater than +2).
Distribution. Kurtosis and skewness are statistics that characterize the shape and symmetry of the
distribution. These statistics are displayed with their standard errors.
• Kurtosis. A measure of the extent to which there are outliers. For a normal distribution, the value of the
kurtosis statistic is zero. Positive kurtosis indicates that the data exhibit more extreme outliers than a
normal distribution. Negative kurtosis indicates that the data exhibit less extreme outliers than a normal
distribution.
• Skewness. A measure of the asymmetry of a distribution. The normal distribution is symmetric and has a
skewness value of 0. A distribution with a significant positive skewness has a long right tail. A
distribution with a significant negative skewness has a long left tail. As a guideline, a skewness value
more than twice its standard error is taken to indicate a departure from symmetry.
Display Order. By default, the variables are displayed in the order in which you selected them. Optionally,
you can display variables alphabetically, by ascending means, or by descending means.
DESCRIPTIVES Command Additional Features
The command syntax language also allows you to:
• Save standardized scores (z scores) for some but not all variables (with the VARIABLES subcommand).
• Specify names for new variables that contain standardized scores (with the VARIABLES subcommand).
• Exclude from the analysis cases with missing values for any variable (with the MISSING subcommand).
• Sort the variables in the display by the value of any statistic, not just the mean (with the SORT
subcommand).
See the Command Syntax Reference for complete syntax information.
Explore
The Explore procedure produces summary statistics and graphical displays, either for all of your cases or
separately for groups of cases. There are many reasons for using the Explore procedure–data screening,
outlier identification, description, assumption checking, and characterizing differences among
subpopulations (groups of cases). Data screening may show that you have unusual values, extreme
values, gaps in the data, or other peculiarities. Exploring the data can help to determine whether the
statistical techniques that you are considering for data analysis are appropriate. The exploration may
indicate that you need to transform the data if the technique requires a normal distribution. Or you may
decide that you need nonparametric tests.
Example. Look at the distribution of maze-learning times for rats under four different reinforcement
schedules. For each of the four groups, you can see if the distribution of times is approximately normal
and whether the four variances are equal. You can also identify the cases with the five largest and five
smallest times. The boxplots and stem-and-leaf plots graphically summarize the distribution of learning
times for each of the groups.
Statistics and plots. Mean, median, 5% trimmed mean, standard error, variance, standard deviation,
minimum, maximum, range, interquartile range, skewness and kurtosis and their standard errors,
confidence interval for the mean (and specified confidence level), percentiles, Huber’s M-estimator,
Andrews’ wave estimator, Hampel’s redescending M-estimator, Tukey’s biweight estimator, the five
largest and five smallest values, the Kolmogorov-Smirnov statistic with a Lilliefors significance level for
Chapter 1. Core features 37
testing normality, and the Shapiro-Wilk statistic. Boxplots, stem-and-leaf plots, histograms, normality
plots, and spread-versus-level plots with Levene tests and transformations.
Explore Data Considerations
Data. The Explore procedure can be used for quantitative variables (interval- or ratio-level
measurements). A factor variable (used to break the data into groups of cases) should have a reasonable
number of distinct values (categories). These values may be short string or numeric. The case label
variable, used to label outliers in boxplots, can be short string, long string (first 15 bytes), or numeric.
Assumptions. The distribution of your data does not have to be symmetric or normal.
To Explore Your Data
1. From the menus choose:
Analyze > Descriptive Statistics > Explore…
2. Select one or more dependent variables.
Optionally, you can:
• Select one or more factor variables, whose values will define groups of cases.
• Select an identification variable to label cases.
• Click Statistics for robust estimators, outliers, percentiles, and frequency tables.
• Click Plots for histograms, normal probability plots and tests, and spread-versus-level plots with
Levene’s statistics.
• Click Options for the treatment of missing values.
Explore Statistics
Descriptives. These measures of central tendency and dispersion are displayed by default. Measures of
central tendency indicate the location of the distribution; they include the mean, median, and 5%
trimmed mean. Measures of dispersion show the dissimilarity of the values; these include standard error,
variance, standard deviation, minimum, maximum, range, and interquartile range. The descriptive
statistics also include measures of the shape of the distribution; skewness and kurtosis are displayed
with their standard errors. The 95% level confidence interval for the mean is also displayed; you can
specify a different confidence level.
M-estimators. Robust alternatives to the sample mean and median for estimating the location. The
estimators calculated differ in the weights they apply to cases. Huber’s M-estimator, Andrews’ wave
estimator, Hampel’s redescending M-estimator, and Tukey’s biweight estimator are displayed.
Outliers. Displays the five largest and five smallest values with case labels.
Percentiles. Displays the values for the 5th, 10th, 25th, 50th, 75th, 90th, and 95th percentiles.
Explore Plots
Boxplots. These alternatives control the display of boxplots when you have more than one dependent
variable. Factor levels together generates a separate display for each dependent variable. Within a
display, boxplots are shown for each of the groups defined by a factor variable. Dependents together
generates a separate display for each group defined by a factor variable. Within a display, boxplots are
shown side by side for each dependent variable. This display is particularly useful when the different
variables represent a single characteristic measured at different times.
Descriptive. The Descriptive group allows you to choose stem-and-leaf plots and histograms.
Normality plots with tests. Displays normal probability and detrended normal probability plots. The
Kolmogorov-Smirnov statistic, with a Lilliefors significance level for testing normality, is displayed. If non-
integer weights are specified, the Shapiro-Wilk statistic is calculated when the weighted sample size lies
between 3 and 50. For no weights or integer weights, the statistic is calculated when the weighted
sample size lies between 3 and 5,000.
38 IBM SPSS Statistics Base V27
Spread vs. Level with Levene Test. Controls data transformation for spread-versus-level plots. For all
spread-versus-level plots, the slope of the regression line and Levene’s robust tests for homogeneity of
variance are displayed. If you select a transformation, Levene’s tests are based on the transformed data.
If no factor variable is selected, spread-versus-level plots are not produced. Power estimation produces
a plot of the natural logs of the interquartile ranges against the natural logs of the medians for all cells, as
well as an estimate of the power transformation for achieving equal variances in the cells. A spread-
versus-level plot helps to determine the power for a transformation to stabilize (make more equal)
variances across groups. Transformed allows you to select one of the power alternatives, perhaps
following the recommendation from power estimation, and produces plots of transformed data. The
interquartile range and median of the transformed data are plotted. Untransformed produces plots of the
raw data. This is equivalent to a transformation with a power of 1.
Explore Power Transformations
These are the power transformations for spread-versus-level plots. To transform data, you must select a
power for the transformation. You can choose one of the following alternatives:
• Natural log. Natural log transformation. This is the default.
• 1/square root. For each data value, the reciprocal of the square root is calculated.
• Reciprocal. The reciprocal of each data value is calculated.
• Square root. The square root of each data value is calculated.
• Square. Each data value is squared.
• Cube. Each data value is cubed.
Explore Options
Missing Values. Controls the treatment of missing values.
• Exclude cases listwise. Cases with missing values for any dependent or factor variable are excluded
from all analyses. This is the default.
• Exclude cases pairwise. Cases with no missing values for variables in a group (cell) are included in the
analysis of that group. The case may have missing values for variables used in other groups.
• Report values. Missing values for factor variables are treated as a separate category. All output is
produced for this additional category. Frequency tables include categories for missing values. Missing
values for a factor variable are included but labeled as missing.
EXAMINE Command Additional Features
The Explore procedure uses EXAMINE command syntax. The command syntax language also allows you
to:
• Request total output and plots in addition to output and plots for groups defined by the factor variables
(with the TOTAL subcommand).
• Specify a common scale for a group of boxplots (with the SCALE subcommand).
• Specify interactions of the factor variables (with the VARIABLES subcommand).
• Specify percentiles other than the defaults (with the PERCENTILES subcommand).
• Calculate percentiles according to any of five methods (with the PERCENTILES subcommand).
• Specify any power transformation for spread-versus-level plots (with the PLOT subcommand).
• Specify the number of extreme values to be displayed (with the STATISTICS subcommand).
• Specify parameters for the M-estimators, robust estimators of location (with the MESTIMATORS
subcommand).
See the Command Syntax Reference for complete syntax information.
Chapter 1. Core features 39
Crosstabs
The Crosstabs procedure forms two-way and multiway tables and provides a variety of tests and
measures of association for two-way tables. The structure of the table and whether categories are
ordered determine what test or measure to use.
With the exception of partial gamma coefficients, Crosstabs’ statistics and measures of association are
computed separately for each two-way table. If you specify a row, a column, and a layer factor (control
variable), the Crosstabs procedure forms one panel of associated statistics and measures for each value
of the layer factor (or a combination of values for two or more control variables). For example, if gender is
a layer factor for a table of married (yes, no) against life (is life exciting, routine, or dull), the results for a
two-way table for the females are computed separately from those for the males and printed as panels
following one another.
Example. Are customers from small companies more likely to be profitable in sales of services (for
example, training and consulting) than those from larger companies? From a crosstabulation, you might
learn that the majority of small companies (fewer than 500 employees) yield high service profits, while
the majority of large companies (more than 2,500 employees) yield low service profits.
Statistics and measures of association. Pearson chi-square, likelihood-ratio chi-square, linear-by-linear
association test, Fisher’s exact test, Yates’ corrected chi-square, Pearson’s r, Spearman’s rho,
contingency coefficient, phi, Cramér’s V, symmetric and asymmetric lambdas, Goodman and Kruskal’s
tau, uncertainty coefficient, gamma, Somers’ d, Kendall’s tau-b, Kendall’s tau-c, eta coefficient, Cohen’s
kappa, relative risk estimate, odds ratio, McNemar test, Cochran’s and Mantel-Haenszel statistics, and
column proportions statistics.
Crosstabs Data Considerations
Data. To define the categories of each table variable, use values of a numeric or string (eight or fewer
bytes) variable. For example, for gender, you could code the data as 1 and 2 or as male and female.
Assumptions. Some statistics and measures assume ordered categories (ordinal data) or quantitative
values (interval or ratio data), as discussed in the section on statistics. Others are valid when the table
variables have unordered categories (nominal data). For the chi-square-based statistics (phi, Cramér’s V,
and contingency coefficient), the data should be a random sample from a multinomial distribution.
Note: Ordinal variables can be either numeric codes that represent categories (for example, 1 = low, 2 =
medium, 3 = high) or string values. However, the alphabetic order of string values is assumed to reflect
the true order of the categories. For example, for a string variable with the values of low, medium, high,
the order of the categories is interpreted as high, low, medium–which is not the correct order. In general,
it is more reliable to use numeric codes to represent ordinal data.
To Obtain Crosstabulations
1. From the menus choose:
Analyze > Descriptive Statistics > Crosstabs…
2. Select one or more row variables and one or more column variables.
Optionally, you can:
• Select one or more control variables.
• Click Statistics for tests and measures of association for two-way tables or subtables.
• Click Cells for observed and expected values, percentages, and residuals.
• Click Format for controlling the order of categories.
Crosstabs layers
If you select one or more layer variables, a separate crosstabulation is produced for each category of each
layer variable (control variable). For example, if you have one row variable, one column variable, and one
layer variable with two categories, you get a two-way table for each category of the layer variable. To
make another layer of control variables, click Next. Subtables are produced for each combination of
40 IBM SPSS Statistics Base V27
categories for each first-layer variable, each second-layer variable, and so on. If statistics and measures
of association are requested, they apply to two-way subtables only.
Crosstabs clustered bar charts
Display clustered bar charts. A clustered bar chart helps summarize your data for groups of cases. There
is one cluster of bars for each value of the variable you specified under Rows. The variable that defines
the bars within each cluster is the variable you specified under Columns. There is one set of differently
colored or patterned bars for each value of this variable. If you specify more than one variable under
Columns or Rows, a clustered bar chart is produced for each combination of two variables.
Crosstabs displaying layer variables in table layers
Display layer variables in table layers. You can choose to display the layer variables (control variables)
as table layers in the crosstabulation table. This allows you to create views that show the overall statistics
for row and column variables as well as permitting drill down on categories of layer variables.
An example that uses the data file demo.sav (available in the Samples directory of the installation
directory) is shown below and was obtained as follows:
1. Select Income category in thousands (inccat) as the row variable, Owns PDA (ownpda) as the column
variable and Level of Education (ed) as the layer variable.
2. Select Display layer variables in table layers.
3. Select Column in the Cell Display subdialog.
4. Run the Crosstabs procedure, double-click the crosstabulation table and select College degree from
the Level of education drop down list.
The selected view of the crosstabulation table shows the statistics for respondents who have a college
degree.
Crosstabs statistics
Chi-square. For tables with two rows and two columns, select Chi-square to calculate the Pearson chi-
square, the likelihood-ratio chi-square, Fisher’s exact test, and Yates’ corrected chi-square (continuity
correction). For 2 × 2 tables, Fisher’s exact test is computed when a table that does not result from
missing rows or columns in a larger table has a cell with an expected frequency of less than 5. Yates’
corrected chi-square is computed for all other 2 × 2 tables. For tables with any number of rows and
columns, select Chi-square to calculate the Pearson chi-square and the likelihood-ratio chi-square. When
both table variables are quantitative, Chi-square yields the linear-by-linear association test.
Correlations. For tables in which both rows and columns contain ordered values, Correlations yields
Spearman’s correlation coefficient, rho (numeric data only). Spearman’s rho is a measure of association
between rank orders. When both table variables (factors) are quantitative, Correlations yields the
Pearson correlation coefficient, r, a measure of linear association between the variables.
Nominal. For nominal data (no intrinsic order, such as Catholic, Protestant, and Jewish), you can select
Contingency coefficient, Phi (coefficient) and Cramér’s V, Lambda (symmetric and asymmetric lambdas
and Goodman and Kruskal’s tau), and Uncertainty coefficient.
• Contingency coefficient. A measure of association based on chi-square. The value ranges between 0 and
1, with 0 indicating no association between the row and column variables and values close to 1
indicating a high degree of association between the variables. The maximum value possible depends on
the number of rows and columns in a table.
• Phi and Cramer’s V. Phi is a chi-square-based measure of association that involves dividing the chi-
square statistic by the sample size and taking the square root of the result. Cramer’s V is a measure of
association based on chi-square.
• Lambda. A measure of association that reflects the proportional reduction in error when values of the
independent variable are used to predict values of the dependent variable. A value of 1 means that the
independent variable perfectly predicts the dependent variable. A value of 0 means that the
independent variable is no help in predicting the dependent variable.
Chapter 1. Core features 41
• Uncertainty coefficient. A measure of association that indicates the proportional reduction in error when
values of one variable are used to predict values of the other variable. For example, a value of 0.83
indicates that knowledge of one variable reduces error in predicting values of the other variable by 83%.
The program calculates both symmetric and asymmetric versions of the uncertainty coefficient.
Ordinal. For tables in which both rows and columns contain ordered values, select Gamma (zero-order
for 2-way tables and conditional for 3-way to 10-way tables), Kendall’s tau-b, and Kendall’s tau-c. For
predicting column categories from row categories, select Somers’ d.
• Gamma. A symmetric measure of association between two ordinal variables that ranges between -1
and 1. Values close to an absolute value of 1 indicate a strong relationship between the two variables.
Values close to 0 indicate little or no relationship. For 2-way tables, zero-order gammas are displayed.
For 3-way to n-way tables, conditional gammas are displayed.
• Somers’ d. A measure of association between two ordinal variables that ranges from -1 to 1. Values
close to an absolute value of 1 indicate a strong relationship between the two variables, and values
close to 0 indicate little or no relationship between the variables. Somers’ d is an asymmetric extension
of gamma that differs only in the inclusion of the number of pairs not tied on the independent variable. A
symmetric version of this statistic is also calculated.
• Kendall’s tau-b. A nonparametric measure of correlation for ordinal or ranked variables that take ties
into account. The sign of the coefficient indicates the direction of the relationship, and its absolute value
indicates the strength, with larger absolute values indicating stronger relationships. Possible values
range from -1 to 1, but a value of -1 or +1 can be obtained only from square tables.
• Kendall’s tau-c. A nonparametric measure of association for ordinal variables that ignores ties. The sign
of the coefficient indicates the direction of the relationship, and its absolute value indicates the
strength, with larger absolute values indicating stronger relationships. Possible values range from -1 to
1, but a value of -1 or +1 can be obtained only from square tables.
Nominal by Interval. When one variable is categorical and the other is quantitative, select Eta. The
categorical variable must be coded numerically.
• Eta. A measure of association that ranges from 0 to 1, with 0 indicating no association between the row
and column variables and values close to 1 indicating a high degree of association. Eta is appropriate for
a dependent variable measured on an interval scale (for example, income) and an independent variable
with a limited number of categories (for example, gender). Two eta values are computed: one treats the
row variable as the interval variable, and the other treats the column variable as the interval variable.
Kappa. Cohen’s kappa measures the agreement between the evaluations of two raters when both are
rating the same object. A value of 1 indicates perfect agreement. A value of 0 indicates that agreement is
no better than chance. Kappa is based on a square table in which row and column values represent the
same scale. Any cell that has observed values for one variable but not the other is assigned a count of 0.
Kappa is not computed if the data storage type (string or numeric) is not the same for the two variables.
For string variable, both variables must have the same defined length.
Risk. For 2 x 2 tables, a measure of the strength of the association between the presence of a factor and
the occurrence of an event. If the confidence interval for the statistic includes a value of 1, you cannot
assume that the factor is associated with the event. The odds ratio can be used as an estimate or relative
risk when the occurrence of the factor is rare.
McNemar. A nonparametric test for two related dichotomous variables. Tests for changes in responses
using the chi-square distribution. Useful for detecting changes in responses due to experimental
intervention in “before-and-after” designs. For larger square tables, the McNemar-Bowker test of
symmetry is reported.
Cochran’s and Mantel-Haenszel statistics. Cochran’s and Mantel-Haenszel statistics can be used to test
for independence between a dichotomous factor variable and a dichotomous response variable,
conditional upon covariate patterns defined by one or more layer (control) variables. Note that while other
statistics are computed layer by layer, the Cochran’s and Mantel-Haenszel statistics are computed once
for all layers.
42 IBM SPSS Statistics Base V27
Crosstabs cell display
To help you uncover patterns in the data that contribute to a significant chi-square test, the Crosstabs
procedure displays expected frequencies and three types of residuals (deviates) that measure the
difference between observed and expected frequencies. Each cell of the table can contain any
combination of counts, percentages, and residuals selected.
Counts. The number of cases actually observed and the number of cases expected if the row and column
variables are independent of each other. You can choose to hide counts that are less than a specified
integer. Hidden values will be displayed as
2. Select one or more variables.
Optionally, you can:
• Select one or more grouping variables to divide your data into subgroups.
• Click Options to change the output title, add a caption below the output, or exclude cases with missing
values.
• Click Statistics for optional statistics.
• Select Display cases to list the cases in each subgroup. By default, the system lists only the first 100
cases in your file. You can raise or lower the value for Limit cases to first n or deselect that item to list
all cases.
Summarize Options
Summarize allows you to change the title of your output or add a caption that will appear below the
output table. You can control line wrapping in titles and captions by typing \n wherever you want to insert
a line break in the text.
You can also choose to display or suppress subheadings for totals and to include or exclude cases with
missing values for any of the variables used in any of the analyses. Often it is desirable to denote missing
44 IBM SPSS Statistics Base V27
cases in output with a period or an asterisk. Enter a character, phrase, or code that you would like to have
appear when a value is missing; otherwise, no special treatment is applied to missing cases in the output.
Summarize Statistics
You can choose one or more of the following subgroup statistics for the variables within each category of
each grouping variable: sum, number of cases, mean, median, grouped median, standard error of the
mean, minimum, maximum, range, variable value of the first category of the grouping variable, variable
value of the last category of the grouping variable, standard deviation, variance, kurtosis, standard error
of kurtosis, skewness, standard error of skewness, percentage of total sum, percentage of total N,
percentage of sum in, percentage of N in, geometric mean, harmonic mean. The order in which the
statistics appear in the Cell Statistics list is the order in which they will be displayed in the output.
Summary statistics are also displayed for each variable across all categories.
First. Displays the first data value encountered in the data file.
Geometric Mean. The nth root of the product of the data values, where n represents the number of cases.
Grouped Median. Median that is calculated for data that is coded into groups. For example, with age data,
if each value in the 30s is coded 35, each value in the 40s is coded 45, and so on, the grouped median is
the median calculated from the coded data.
Harmonic Mean. Used to estimate an average group size when the sample sizes in the groups are not
equal. The harmonic mean is the total number of samples divided by the sum of the reciprocals of the
sample sizes.
Kurtosis. A measure of the extent to which there are outliers. For a normal distribution, the value of the
kurtosis statistic is zero. Positive kurtosis indicates that the data exhibit more extreme outliers than a
normal distribution. Negative kurtosis indicates that the data exhibit less extreme outliers than a normal
distribution.
Last. Displays the last data value encountered in the data file.
Maximum. The largest value of a numeric variable.
Mean. A measure of central tendency. The arithmetic average, the sum divided by the number of cases.
Median. The value above and below which half of the cases fall, the 50th percentile. If there is an even
number of cases, the median is the average of the two middle cases when they are sorted in ascending or
descending order. The median is a measure of central tendency not sensitive to outlying values (unlike
the mean, which can be affected by a few extremely high or low values).
Minimum. The smallest value of a numeric variable.
N. The number of cases (observations or records).
Percent of Total N. Percentage of the total number of cases in each category.
Percent of Total Sum. Percentage of the total sum in each category.
Range. The difference between the largest and smallest values of a numeric variable, the maximum minus
the minimum.
Skewness. A measure of the asymmetry of a distribution. The normal distribution is symmetric and has a
skewness value of 0. A distribution with a significant positive skewness has a long right tail. A distribution
with a significant negative skewness has a long left tail. As a guideline, a skewness value more than twice
its standard error is taken to indicate a departure from symmetry.
Standard Deviation. A measure of dispersion around the mean. In a normal distribution, 68% of cases fall
within one standard deviation of the mean and 95% of cases fall within two standard deviations. For
example, if the mean age is 45, with a standard deviation of 10, 95% of the cases would be between 25
and 65 in a normal distribution.
Standard Error of Kurtosis. The ratio of kurtosis to its standard error can be used as a test of normality
(that is, you can reject normality if the ratio is less than -2 or greater than +2). A large positive value for
kurtosis indicates that the tails of the distribution are longer than those of a normal distribution; a
Chapter 1. Core features 45
negative value for kurtosis indicates shorter tails (becoming like those of a box-shaped uniform
distribution).
Standard Error of Mean. A measure of how much the value of the mean may vary from sample to sample
taken from the same distribution. It can be used to roughly compare the observed mean to a
hypothesized value (that is, you can conclude the two values are different if the ratio of the difference to
the standard error is less than -2 or greater than +2).
Standard Error of Skewness. The ratio of skewness to its standard error can be used as a test of normality
(that is, you can reject normality if the ratio is less than -2 or greater than +2). A large positive value for
skewness indicates a long right tail; an extreme negative value indicates a long left tail.
Sum. The sum or total of the values, across all cases with nonmissing values.
Variance. A measure of dispersion around the mean, equal to the sum of squared deviations from the
mean divided by one less than the number of cases. The variance is measured in units that are the square
of those of the variable itself.
Means
The Means procedure calculates subgroup means and related univariate statistics for dependent
variables within categories of one or more independent variables. Optionally, you can obtain a one-way
analysis of variance, eta, and tests for linearity.
Example. Measure the average amount of fat absorbed by three different types of cooking oil, and
perform a one-way analysis of variance to see whether the means differ.
Statistics. Sum, number of cases, mean, median, grouped median, standard error of the mean, minimum,
maximum, range, variable value of the first category of the grouping variable, variable value of the last
category of the grouping variable, standard deviation, variance, kurtosis, standard error of kurtosis,
skewness, standard error of skewness, percentage of total sum, percentage of total N, percentage of sum
in, percentage of N in, geometric mean, and harmonic mean. Options include analysis of variance, eta, eta
squared, and tests for linearity R and R 2.
Means Data Considerations
Data. The dependent variables are quantitative, and the independent variables are categorical. The
values of categorical variables can be numeric or string.
Assumptions. Some of the optional subgroup statistics, such as the mean and standard deviation, are
based on normal theory and are appropriate for quantitative variables with symmetric distributions.
Robust statistics, such as the median, are appropriate for quantitative variables that may or may not meet
the assumption of normality. Analysis of variance is robust to departures from normality, but the data in
each cell should be symmetric. Analysis of variance also assumes that the groups come from populations
with equal variances. To test this assumption, use Levene’s homogeneity-of-variance test, available in the
One-Way ANOVA procedure.
To Obtain Subgroup Means
1. From the menus choose:
Analyze > Compare Means > Means…
2. Select one or more dependent variables.
3. Use one of the following methods to select categorical independent variables:
• Select one or more independent variables. Separate results are displayed for each independent
variable.
• Select one or more layers of independent variables. Each layer further subdivides the sample. If you
have one independent variable in Layer 1 and one independent variable in Layer 2, the results are
displayed in one crossed table, as opposed to separate tables for each independent variable.
4. Optionally, click Options for optional statistics, an analysis of variance table, eta, eta squared, R, and R
2.
46 IBM SPSS Statistics Base V27
Means Options
You can choose one or more of the following subgroup statistics for the variables within each category of
each grouping variable: sum, number of cases, mean, median, grouped median, standard error of the
mean, minimum, maximum, range, variable value of the first category of the grouping variable, variable
value of the last category of the grouping variable, standard deviation, variance, kurtosis, standard error
of kurtosis, skewness, standard error of skewness, percentage of total sum, percentage of total N,
percentage of sum in, percentage of N in, geometric mean, and harmonic mean. You can change the order
in which the subgroup statistics appear. The order in which the statistics appear in the Cell Statistics list is
the order in which they are displayed in the output. Summary statistics are also displayed for each
variable across all categories.
First. Displays the first data value encountered in the data file.
Geometric Mean. The nth root of the product of the data values, where n represents the number of cases.
Grouped Median. Median that is calculated for data that is coded into groups. For example, with age data,
if each value in the 30s is coded 35, each value in the 40s is coded 45, and so on, the grouped median is
the median calculated from the coded data.
Harmonic Mean. Used to estimate an average group size when the sample sizes in the groups are not
equal. The harmonic mean is the total number of samples divided by the sum of the reciprocals of the
sample sizes.
Kurtosis. A measure of the extent to which there are outliers. For a normal distribution, the value of the
kurtosis statistic is zero. Positive kurtosis indicates that the data exhibit more extreme outliers than a
normal distribution. Negative kurtosis indicates that the data exhibit less extreme outliers than a normal
distribution.
Last. Displays the last data value encountered in the data file.
Maximum. The largest value of a numeric variable.
Mean. A measure of central tendency. The arithmetic average, the sum divided by the number of cases.
Median. The value above and below which half of the cases fall, the 50th percentile. If there is an even
number of cases, the median is the average of the two middle cases when they are sorted in ascending or
descending order. The median is a measure of central tendency not sensitive to outlying values (unlike
the mean, which can be affected by a few extremely high or low values).
Minimum. The smallest value of a numeric variable.
N. The number of cases (observations or records).
Percent of total N. Percentage of the total number of cases in each category.
Percent of total sum. Percentage of the total sum in each category.
Range. The difference between the largest and smallest values of a numeric variable, the maximum minus
the minimum.
Skewness. A measure of the asymmetry of a distribution. The normal distribution is symmetric and has a
skewness value of 0. A distribution with a significant positive skewness has a long right tail. A distribution
with a significant negative skewness has a long left tail. As a guideline, a skewness value more than twice
its standard error is taken to indicate a departure from symmetry.
Standard Deviation. A measure of dispersion around the mean. In a normal distribution, 68% of cases fall
within one standard deviation of the mean and 95% of cases fall within two standard deviations. For
example, if the mean age is 45, with a standard deviation of 10, 95% of the cases would be between 25
and 65 in a normal distribution.
Standard Error of Kurtosis. The ratio of kurtosis to its standard error can be used as a test of normality
(that is, you can reject normality if the ratio is less than -2 or greater than +2). A large positive value for
kurtosis indicates that the tails of the distribution are longer than those of a normal distribution; a
negative value for kurtosis indicates shorter tails (becoming like those of a box-shaped uniform
distribution).
Chapter 1. Core features 47
Standard Error of Mean. A measure of how much the value of the mean may vary from sample to sample
taken from the same distribution. It can be used to roughly compare the observed mean to a
hypothesized value (that is, you can conclude the two values are different if the ratio of the difference to
the standard error is less than -2 or greater than +2).
Standard Error of Skewness. The ratio of skewness to its standard error can be used as a test of normality
(that is, you can reject normality if the ratio is less than -2 or greater than +2). A large positive value for
skewness indicates a long right tail; an extreme negative value indicates a long left tail.
Sum. The sum or total of the values, across all cases with nonmissing values.
Variance. A measure of dispersion around the mean, equal to the sum of squared deviations from the
mean divided by one less than the number of cases. The variance is measured in units that are the square
of those of the variable itself.
Statistics for First Layer
Anova table and eta. Displays a one-way analysis-of-variance table and calculates eta and eta-squared
(measures of association) for each independent variable in the first layer.
Test for linearity. Calculates the sum of squares, degrees of freedom, and mean square associated with
linear and nonlinear components, as well as the F ratio, R and R-squared. Linearity is not calculated if the
independent variable is a short string.
OLAP Cubes
The OLAP (Online Analytical Processing) Cubes procedure calculates totals, means, and other univariate
statistics for continuous summary variables within categories of one or more categorical grouping
variables. A separate layer in the table is created for each category of each grouping variable.
Example. Total and average sales for different regions and product lines within regions.
Statistics. Sum, number of cases, mean, median, grouped median, standard error of the mean, minimum,
maximum, range, variable value of the first category of the grouping variable, variable value of the last
category of the grouping variable, standard deviation, variance, kurtosis, standard error of kurtosis,
skewness, standard error of skewness, percentage of total cases, percentage of total sum, percentage of
total cases within grouping variables, percentage of total sum within grouping variables, geometric mean,
and harmonic mean.
OLAP Cubes Data Considerations
Data. The summary variables are quantitative (continuous variables measured on an interval or ratio
scale), and the grouping variables are categorical. The values of categorical variables can be numeric or
string.
Assumptions. Some of the optional subgroup statistics, such as the mean and standard deviation, are
based on normal theory and are appropriate for quantitative variables with symmetric distributions.
Robust statistics, such as the median and range, are appropriate for quantitative variables that may or
may not meet the assumption of normality.
To Obtain OLAP Cubes
1. From the menus choose:
Analyze > Reports > OLAP Cubes…
2. Select one or more continuous summary variables.
3. Select one or more categorical grouping variables.
Optionally:
• Select different summary statistics (click Statistics). You must select one or more grouping variables
before you can select summary statistics.
• Calculate differences between pairs of variables and pairs of groups that are defined by a grouping
variable (click Differences).
48 IBM SPSS Statistics Base V27
• Create custom table titles (click Title).
• Hide counts that are less than a specified integer. Hidden values will be displayed as
2. Select one or more quantitative test variables.
3. Optionally, you can:
• Select success criteria settings under the Define Success section:
Last Value
The last or highest value among the sorted distinct values in the data is used. This applies to
numeric or string variables. This is the default setting.
First Value
The first or lowest value among the sorted distinct values in the data is used. This applies to
numeric or string variables.
Chapter 1. Core features 51
Value(s)
One or more parenthesized specific values. Multiple values must be separated by spaces. This
applies to numeric or string variables. String variable values should be enclosed in single quotes.
Midpoint
Values at or above the middle of the range of observed values in the data. This applies only to
numeric data.
Cut Point
Values at or above a specified value. This applies only to numeric data.
• Click Confidence Intervals… to specify which types of confidence intervals are displayed, or to
suppress all confidence intervals.
• Click Tests… to specify which types of test statistics are displayed, or to suppress all tests.
• Click Missing Values… to control the treatment of missing data.
• Click Bootstrap… for deriving robust estimates of standard errors and confidence intervals for
estimates such as the mean, median, proportion, odds ratio, correlation coefficient or regression
coefficient.
4. Click OK.
One-Sample Proportions: Confidence Intervals
The Confidence Intervals dialog provides options for specifying the coverage level and for selecting which
types of confidence intervals are displayed.
Coverage Level
Specifies the confidence interval percentage. A numeric value in the range (0,100) must be specified.
95 is the default setting.
Interval Type(s)
Provides options for specifying which types of confidence intervals are displayed. Available options
include:
• Agresti-Coull
• Anscombe
• Clopper-Pearson (Exact)
• Jeffreys
• Logit
• Wald
• Wald (Continuity Corrected)
• Wilson Score
• Wilson Score (Continuity Corrected)
Specifying Confidence Intervals for One-Sample Proportions
1. From the menus choose:
Analyze > Compare Means > One-Sample Proportions…
2. Click Confidence Intervals to specify which types of confidence intervals are displayed, or to suppress
all confidence intervals.
One-Sample Proportions: Tests
The Tests dialog provides options for specifying which types of test statistics are displayed.
All
All test statistics display in the output.
None
No test statistics display in the output.
52 IBM SPSS Statistics Base V27
Exact Binomial
Displays exact binomial probabilities.
Mid-p Adjusted Binomial
Displays mid-p adjusted binomial probabilities. This is a default setting.
Score
Displays the Score Z test statistic. This is a default setting.
Score (Continuity Corrected)
Displays the continuity-corrected score Z test statistic.
Wald
Displays the Wald Z test statistic.
Wald (Continuity Corrected)
Displays the continuity-corrected Wald Z test statistic.
Test Value
Specifies a test value between 0 and 1. The default value is 0.5.
Obtaining One-Sample Proportions tests
1. From the menus choose:
Analyze > Compare Means > One-Sample Proportions…
2. In the One-Sample Proportions dialog, click Tests.
3. Select one or more of the available tests.
One-Sample Proportions: Missing Values
The Missing Values dialog provides options for dealing with missing values.
Missing Data Scope
Exclude cases analysis by analysis
Indicates inclusion of all cases with sufficient data on the variables used in each particular
analysis. This is the default setting.
Exclude cases listwise
Indicates inclusion of all cases with sufficient data on all variables used across all analyses.
User Missing Values
Exclude treats user missing values as missing. Include ignores user missing value designations and
treats user missing values as valid.
Defining missing value settings for One-Sample Proportions
1. From the menus choose:
Analyze > Compare Means > One-Sample Proportions…
2. In the One-Sample Proportions dialog, click Missing Values.
3. Select the desired missing values settings.
Paired-Samples Proportions
The Paired-Samples Proportions procedure provides tests and confidence intervals for the difference in
two related or paired binomial proportions. The data are assumed to be from a simple random sample,
and each hypothesis test or confidence interval is a separate test or individual interval. Output includes
observed proportions, estimates of differences in population proportions, asymptotic standard errors of
population differences under null and alternative hypotheses, specified test statistics with two-sided
probabilities, and specified confidence intervals for differences in proportions.
Example
Chapter 1. Core features 53
Statistics
Agresti-Min, Bonett-Price, Newcombe, Wald, Wald (continuity corrected), Exact Binomial, Mid-p
Adjusted Binomial, McNemar, McNemar (continuity corrected).
Data Considerations
Data
• A variable list containing at least two variables is required.
• If a single list of variables is specified, each member of the list is paired with every other member of
the list.
Assumptions
• If two lists of variables are separated by WITH without the (PAIRED) keyword, each member of the
first list is paired with each member of the second list.
• If two lists of variables are separated by WITH and the second list is followed by (PAIRED),
members of the two lists in order are paired: the first member of the first list is paired with the first
member of the second list, the second members of each list are paired, etc. Unmatched variables
are ignored and a warning message is issued.
Obtaining Paired-Samples Proportions tests
1. From the menus choose:
Analyze > Compare Means > Paired-Samples Proportions…
2. Select one or more quantitative test variables.
3. Optionally, you can:
• Select success criteria settings under the Define Success section:
Last Value
The last or highest value among the sorted distinct values in the data is used. This applies to
numeric or string variables. This is the default setting.
First Value
The first or lowest value among the sorted distinct values in the data is used. This applies to
numeric or string variables.
Value(s)
One or more parenthesized specific values. Multiple values must be separated by spaces. This
applies to numeric or string variables. String variable values should be enclosed in single quotes.
Midpoint
Values at or above the middle of the range of observed values in the data. This applies only to
numeric data.
Cut Point
Values at or above a specified value. This applies only to numeric data.
• Click Confidence Intervals… to specify which types of confidence intervals are displayed, or to
suppress all confidence intervals.
• Click Tests… to specify which types of test statistics are displayed, or to suppress all tests.
• Click Missing Values… to control the treatment of missing data.
• Click Bootstrap… for deriving robust estimates of standard errors and confidence intervals for
estimates such as the mean, median, proportion, odds ratio, correlation coefficient or regression
coefficient.
4. Click OK.
Paired-Samples Proportions: Confidence Intervals
The Confidence Intervals dialog provides options for specifying the coverage level and for selecting which
types of confidence intervals are displayed.
54 IBM SPSS Statistics Base V27
Coverage Level
Specifies the confidence interval percentage. A numeric value in the range (0,100) must be specified.
95 is the default setting.
Interval Type(s)
Provides options for specifying which types of confidence intervals are displayed. Available options
include:
• Agresti-Min
• Bonett-Price
• Newcombe
• Wald
• Wald (Continuity Corrected)
Specifying Confidence Intervals for Paired-Samples Proportions
1. From the menus choose:
Analyze > Compare Means > Paired-Samples Proportions…
2. Click Confidence Intervals to specify which types of confidence intervals are displayed, or to suppress
all confidence intervals.
Paired-Samples Proportions: Tests
The Tests dialog provides options for specifying which types of test statistics are displayed.
All
All test statistics display in the output.
None
No test statistics display in the output.
Exact Binomial
Displays exact binomial probabilities.
Mid-p Adjusted Binomial
Displays mid-p adjusted binomial probabilities. This is a default setting.
McNemar
Displays the McNemar Z test statistic. This is a default setting.
McNemar (Continuity Corrected)
Displays the continuity-corrected McNemar Z test statistic.
Wald
Displays the Wald Z test statistic.
Wald (Continuity Corrected)
Displays the continuity-corrected Wald Z test statistic.
Obtaining Paired-Samples Proportions tests
1. From the menus choose:
Analyze > Compare Means > Paired-Samples Proportions…
2. In the Paired-Samples Proportions dialog, click Tests.
3. Select one or more of the available tests.
Paired-Samples Proportions: Missing Values
The Missing Values dialog provides options for dealing with missing values.
Chapter 1. Core features 55
Missing Data Scope
Exclude cases analysis by analysis
Indicates inclusion of all cases with sufficient data on the variables used in each particular
analysis. This is the default setting.
Exclude cases listwise
Indicates inclusion of all cases with sufficient data on all variables used across all analyses.
User Missing Values
Exclude treats user missing values as missing. Include ignores user missing value designations and
treats user missing values as valid.
Defining missing value settings for Paired-Samples Proportions
1. From the menus choose:
Analyze > Compare Means > Paired-Samples Proportions…
2. In the Paired-Samples Proportions dialog, click Missing Values.
3. Select the desired missing values settings.
Independent-Samples Proportions
The Independent-Samples Proportions procedure provides tests and confidence intervals for the
difference in two independent binomial proportions. The data are assumed to be from a simple random
sample, and each hypothesis test or confidence interval is a separate test or individual interval. Output
includes observed proportions, estimates of differences in population proportions, asymptotic standard
errors of population differences under null and alternative hypotheses, specified test statistics with two-
sided probabilities, and specified confidence intervals for differences in proportions.
Example
Statistics
Agresti-Min, Bonett-Price, Newcombe, Wald, Wald (continuity corrected), Exact Binomial, Mid-p
Adjusted Binomial, McNemar, McNemar (continuity corrected).
Data Considerations
Data
• At least one dependent variable and a single variable to identify the two groups to be compared are
required.
• The grouping variable can be either numeric or string.
Assumptions
Obtaining Independent-Samples Proportions tests
1. From the menus choose:
Analyze > Compare Means > Independent-Samples Proportions…
2. Select one or more quantitative test variables.
3. Select a single Grouping Variable that identifies the two groups to be compared.
4. Optionally, specify settings for the selected Grouping Variable.
• When Value(s) is selected, you can specify two numeric or string values within parentheses for the
values to be compared. String values should be enclosed in single quotes. Cases with other values
are ignored.
• Midpoint applies only to numeric variables. Cases at or above the midpoint of the distribution of the
grouping variable are assigned to the second group, cases below the midpoint are assigned to the
first group.
56 IBM SPSS Statistics Base V27
• Cut Point applies only the numeric variables and allows specification with parentheses of a single
numeric value. Cases at or above the cut point on the grouping variable are assigned to the second
group, cases below the cut point are assigned to the first group.
5. Optionally, you can:
• Select success criteria settings under the Define Success section:
Last Value
The last or highest value among the sorted distinct values in the data is used. This applies to
numeric or string variables. This is the default setting.
First Value
The first or lowest value among the sorted distinct values in the data is used. This applies to
numeric or string variables.
Value(s)
One or more parenthesized specific values. Multiple values must be separated by spaces. This
applies to numeric or string variables. String variable values should be enclosed in single quotes.
Midpoint
Values at or above the middle of the range of observed values in the data. This applies only to
numeric data.
Cut Point
Values at or above a specified value. This applies only to numeric data.
• Click Confidence Intervals… to specify which types of confidence intervals are displayed, or to
suppress all confidence intervals.
• Click Tests… to specify which types of test statistics are displayed, or to suppress all tests.
• Click Missing Values… to control the treatment of missing data.
• Click Bootstrap… for deriving robust estimates of standard errors and confidence intervals for
estimates such as the mean, median, proportion, odds ratio, correlation coefficient or regression
coefficient.
6. Click OK.
Independent-Samples Proportions: Confidence Intervals
The Confidence Intervals dialog provides options for specifying the coverage level and for selecting which
types of confidence intervals are displayed.
Coverage Level
Specifies the confidence interval percentage. A numeric value in the range (0,100) must be specified.
95 is the default setting.
Interval Type(s)
Provides options for specifying which types of confidence intervals are displayed. Available options
include:
• Agresti-Caffo
• Brown-Li-Jeffreys
• Hauck-Anderson
• Newcombe
• Newcombe (Continuity Corrected)
• Wald
• Wald (Continuity Corrected)
Specifying Confidence Intervals for Independent-Samples Proportions
1. From the menus choose:
Analyze > Compare Means > Independent-Samples Proportions…
Chapter 1. Core features 57
2. Click Confidence Intervals to specify which types of confidence intervals are displayed, or to suppress
all confidence intervals.
Independent-Samples Proportions: Tests
The Tests dialog provides options for specifying which types of test statistics are displayed.
All
All test statistics display in the output.
None
No test statistics display in the output.
Hauck-Anderson
Displays the Hauck-Anderson Z test statistic.
Wald
Displays the Wald Z test statistic.
Wald (Continuity Corrected)
Displays the continuity-corrected Wald Z test statistic.
Wald H0
Displays the Wald Z test statistic using variance estimates under H0.
Wald H0 (Continuity Corrected)
Displays the continuity-corrected Wald Z test statistic using variance estimates under H0.
Obtaining Independent-Samples Proportions tests
1. From the menus choose:
Analyze > Compare Means > Independent-Samples Proportions…
2. In the Independent-Samples Proportions dialog, click Tests.
3. Select one or more of the available tests.
Independent-Samples Proportions: Missing Values
The Missing Values dialog provides options for dealing with missing values.
Missing Data Scope
Exclude cases analysis by analysis
Indicates inclusion of all cases with sufficient data on the variables used in each particular
analysis. This is the default setting.
Exclude cases listwise
Indicates inclusion of all cases with sufficient data on all variables used across all analyses.
User Missing Values
Exclude treats user missing values as missing. Include ignores user missing value designations and
treats user missing values as valid.
Defining missing value settings for Independent-Samples Proportions
1. From the menus choose:
Analyze > Compare Means > Independent-Samples Proportions…
2. In the Independent-Samples Proportions dialog, click Missing Values.
3. Select the desired missing values settings.
T Tests
T Tests
Three types of t tests are available:
58 IBM SPSS Statistics Base V27
Independent-samples t test (two-sample t test). Compares the means of one variable for two groups of
cases. Descriptive statistics for each group and Levene’s test for equality of variances are provided, as
well as both equal- and unequal-variance t values and a 95% confidence interval for the difference in
means.
Paired-samples t test (dependent t test). Compares the means of two variables for a single group. This
test is also for matched pairs or case-control study designs. The output includes descriptive statistics for
the test variables, the correlation between the variables, descriptive statistics for the paired differences,
the t test, and a 95% confidence interval.
One-sample t test. Compares the mean of one variable with a known or hypothesized value. Descriptive
statistics for the test variables are displayed along with the t test. A 95% confidence interval for the
difference between the mean of the test variable and the hypothesized test value is part of the default
output.
Independent-Samples T Test
The Independent-Samples T Test procedure compares means for two groups of cases and automates the
t-test effect size computation. Ideally, for this test, the subjects should be randomly assigned to two
groups, so that any difference in response is due to the treatment (or lack of treatment) and not to other
factors. This is not the case if you compare average income for males and females. A person is not
randomly assigned to be a male or female. In such situations, you should ensure that differences in other
factors are not masking or enhancing a significant difference in means. Differences in average income
may be influenced by factors such as education (and not by sex alone).
Example
Patients with high blood pressure are randomly assigned to a placebo group and a treatment group.
The placebo subjects receive an inactive pill, and the treatment subjects receive a new drug that is
expected to lower blood pressure. After the subjects are treated for two months, the two-sample t
test is used to compare the average blood pressures for the placebo group and the treatment group.
Each patient is measured once and belongs to one group.
Statistics
For each variable: sample size, mean, standard deviation, standard error of the mean, and the
estimation of the effect size for the t-test. For the difference in means: mean, standard error, and
confidence interval (you can specify the confidence level). Tests: Levene’s test for equality of
variances and both pooled-variances and separate-variances t tests for equality of means.
Data Considerations
Data
The values of the quantitative variable of interest are in a single column in the data file. The procedure
uses a grouping variable with two values to separate the cases into two groups. The grouping variable
can be numeric (values such as 1 and 2 or 6.25 and 12.5) or short string (such as yes and no). As an
alternative, you can use a quantitative variable, such as age, to split the cases into two groups by
specifying a cutpoint (cutpoint 21 splits age into an under-21 group and a 21-and-over group).
Assumptions
For the equal-variance t test, the observations should be independent, random samples from normal
distributions with the same population variance. For the unequal-variance t test, the observations
should be independent, random samples from normal distributions. The two-sample t test is fairly
robust to departures from normality. When checking distributions graphically, look to see that they
are symmetric and have no outliers.
Obtaining an Independent-Samples T Test
1. From the menus choose:
Analyze > Compare Means > Independent-Samples T Test…
2. Select one or more quantitative test variables. A separate t test is computed for each variable.
Chapter 1. Core features 59
3. Select a single grouping variable, and then click Define Groups to specify two codes for the groups
that you want to compare.
4. Optionally, you can:
• Select Estimate effect sizes to control the estimation of the t-test effect size.
• Click Options to control the treatment of missing data and the level of the confidence interval.
• Click Bootstrap for deriving robust estimates of standard errors and confidence intervals for
estimates such as the mean, median, proportion, odds ratio, correlation coefficient or regression
coefficient.
Independent-Samples T-Test Define Groups
For numeric grouping variables, define the two groups for the t-test by specifying two values or a cutpoint:
• Use specified values. Enter a value for Group 1 and another value for Group 2. Cases with any other
values are excluded from the analysis. Numbers need not be integers (for example, 6.25 and 12.5 are
valid).
• Cutpoint. Enter a number that splits the values of the grouping variable into two sets. All cases with
values that are less than the cutpoint form one group, and cases with values that are greater than or
equal to the cutpoint form the other group.
For string grouping variables, enter a string for Group 1 and another value for Group 2, such as yes and no.
Cases with other strings are excluded from the analysis.
Independent-Samples T Test Options
Confidence Interval. By default, a 95% confidence interval for the difference in means is displayed. Enter
a value between 1 and 99 to request a different confidence level.
Missing Values. When you test several variables, and data are missing for one or more variables, you can
tell the procedure which cases to include (or exclude).
• Exclude cases analysis by analysis. Each t test uses all cases that have valid data for the tested
variables. Sample sizes may vary from test to test.
• Exclude cases listwise. Each t test uses only cases that have valid data for all variables that are used in
the requested t tests. The sample size is constant across tests.
Paired-Samples T Test
The Paired-Samples T Test procedure compares the means of two variables for a single group. The
procedure computes the differences between values of the two variables for each case and tests whether
the average differs from 0. The procedure also automates the t-test effect size computation.
Example
In a study on high blood pressure, all patients are measured at the beginning of the study, given a
treatment, and measured again. Thus, each subject has two measures, often called before and after
measures. An alternative design for which this test is used is a matched-pairs or case-control study, in
which each record in the data file contains the response for the patient and also for his or her matched
control subject. In a blood pressure study, patients and controls might be matched by age (a 75-year-
old patient with a 75-year-old control group member).
Statistics
For each variable: mean, sample size, standard deviation, and standard error of the mean. For each
pair of variables: correlation, average difference in means, t test, confidence interval for mean
difference (you can specify the confidence level), and the estimation of the effect size for the t-test.
Standard deviation and standard error of the mean difference.
60 IBM SPSS Statistics Base V27
Data considerations
Data
For each paired test, specify two quantitative variables (interval level of measurement or ratio level of
measurement). For a matched-pairs or case-control study, the response for each test subject and its
matched control subject must be in the same case in the data file.
Assumptions
Observations for each pair should be made under the same conditions. The mean differences should
be normally distributed. Variances of each variable can be equal or unequal.
Obtaining a Paired-Samples T Test
1. From the menus choose:
Analyze > Compare Means > Paired-Samples T Test…
2. Select one or more pairs of variables.
3. Optionally, change/select a Estimate effect sizes option. The settings control how the standardizer is
computed in estimating the Cohen’s d and Hedges’ correction for each variable pair.
Standard deviation of the difference
The denominator used in estimating the effect size. Cohen’s d uses the sample standard deviation
of the mean difference. Hedges’ correction uses the sample standard deviation of the mean
difference adjusted by a correction factor.
Corrected standard deviation of the difference
The denominator used in estimating the effect size. Cohen’s d uses the sample standard deviation
of the mean difference adjusted by the correlation between measures. Hedges’ correction uses the
sample standard deviation of the mean difference adjusted by the correlation between measures,
plus a correction factor.
Average of variances
The denominator used in estimating the effect size. Cohen’s d uses the square root of the average
variance of measures. Hedges’ correction uses the square root of the average variance of
measures, plus a correction factor.
4. Optionally, you can:
• Select Estimate effect sizes to control the estimation of the t-test effect size. When the setting is
selected, you can further control how the standardizer is computed in estimating the Cohen’s d and
Hedges’ correction for each variable pair.
• Click Options to control the treatment of missing data and the level of the confidence interval.
• Click Bootstrap for deriving robust estimates of standard errors and confidence intervals for
estimates such as the mean, median, proportion, odds ratio, correlation coefficient or regression
coefficient.
Paired-Samples T Test Options
Confidence Interval. By default, a 95% confidence interval for the difference in means is displayed. Enter
a value between 1 and 99 to request a different confidence level.
Missing Values. When you test several variables, and data are missing for one or more variables, you can
tell the procedure which cases to include (or exclude):
• Exclude cases analysis by analysis. Each t test uses all cases that have valid data for the tested pair of
variables. Sample sizes may vary from test to test.
• Exclude cases listwise. Each t test uses only cases that have valid data for all pairs of tested variables.
The sample size is constant across tests.
T TEST Command Additional Features
The command syntax language also allows you to:
• Produce both one-sample and independent-samples t tests by running a single command.
Chapter 1. Core features 61
• Test a variable against each variable on a list in a paired t test (with the PAIRS subcommand).
• Control the estimation of the t-test effect size (with the ES subcommand).
See the Command Syntax Reference for complete syntax information.
One-Sample T Test
The One-Sample T Test procedure tests whether the mean of a single variable differs from a specified
constant and automates the t-test effect size computation.
Examples
A researcher might want to test whether the average IQ score for a group of students differs from
100. Or a cereal manufacturer can take a sample of boxes from the production line and check whether
the mean weight of the samples differs from 1.3 pounds at the 95% confidence level.
Statistics
For each test variable: mean, standard deviation, standard error of the mean, and the estimation of
the effect size for the t-test. The average difference between each data value and the hypothesized
test value, a t test that tests that this difference is 0, and a confidence interval for this difference (you
can specify the confidence level).
Data Considerations
Data
To test the values of a quantitative variable against a hypothesized test value, choose a quantitative
variable and enter a hypothesized test value.
Assumptions
This test assumes that the data are normally distributed; however, this test is fairly robust to
departures from normality.
Obtaining a One-Sample T Test
1. From the menus choose:
Analyze > Compare Means > One-Sample T Test…
2. Select one or more variables to be tested against the same hypothesized value.
3. Enter a numeric test value against which each sample mean is compared.
4. Optionally, you can:
• Select Estimate effect sizes to control the estimation of the t-test effect size.
• Click Options to control the treatment of missing data and the level of the confidence interval.
One-Sample T Test Options
Confidence Interval. By default, a 95% confidence interval for the difference between the mean and the
hypothesized test value is displayed. Enter a value between 1 and 99 to request a different confidence
level.
Missing Values. When you test several variables, and data are missing for one or more variables, you can
tell the procedure which cases to include (or exclude).
• Exclude cases analysis by analysis. Each t test uses all cases that have valid data for the tested
variable. Sample sizes may vary from test to test.
• Exclude cases listwise. Each t test uses only cases that have valid data for all variables that are used in
any of the requested t tests. The sample size is constant across tests.
T TEST Command Additional Features
The command syntax language also allows you to:
• Produce both one-sample and independent-samples t tests by running a single command.
62 IBM SPSS Statistics Base V27
• Test a variable against each variable on a list in a paired t test (with the PAIRS subcommand).
• Control the estimation of the t-test effect size (with the ES subcommand).
See the Command Syntax Reference for complete syntax information.
T TEST Command Additional Features
The command syntax language also allows you to:
• Produce both one-sample and independent-samples t tests by running a single command.
• Test a variable against each variable on a list in a paired t test (with the PAIRS subcommand).
• Control the estimation of the t-test effect size (with the ES subcommand).
See the Command Syntax Reference for complete syntax information.
One-Way ANOVA
The One-Way ANOVA procedure produces a one-way analysis of variance for a quantitative dependent
variable by a single factor (independent) variable and estimates the effect size in one-way ANOVA.
Analysis of variance is used to test the hypothesis that several means are equal. This technique is an
extension of the two-sample t test.
In addition to determining that differences exist among the means, you may want to know which means
differ. There are two types of tests for comparing means: a priori contrasts and post hoc tests. Contrasts
are tests set up before running the experiment, and post hoc tests are run after the experiment has been
conducted. You can also test for trends across categories.
Example
Doughnuts absorb fat in various amounts when they are cooked. An experiment is set up involving
three types of fat: peanut oil, corn oil, and lard. Peanut oil and corn oil are unsaturated fats, and lard is
a saturated fat. Along with determining whether the amount of fat absorbed depends on the type of
fat used, you could set up an a priori contrast to determine whether the amount of fat absorption
differs for saturated and unsaturated fats.
Statistics
For each group: number of cases, mean, standard deviation, standard error of the mean, minimum,
maximum, 95% confidence interval for the mean, and the estimation of the effect size for in a one-
way ANOVA. Levene tests for homogeneity of variance, analysis-of-variance table and robust tests of
the equality of means for each dependent variable, user-specified a priori contrasts, and post hoc
range tests and multiple comparisons: Bonferroni, Sidak, Tukey’s honestly significant difference,
Hochberg’s GT2, Gabriel, Dunnett, Ryan-Einot-Gabriel-Welsch F test (R-E-G-W F), Ryan-Einot-
Gabriel-Welsch range test (R-E-G-W Q), Tamhane’s T2, Dunnett’s T3, Games-Howell, Dunnett’s C,
Duncan’s multiple range test, Student-Newman-Keuls (S-N-K), Tukey’s b, Waller-Duncan, Scheffé,
and least-significant difference.
Data considerations
Data
Factor variable values should be integers, and the dependent variable should be quantitative (interval
level of measurement).
Assumptions
Each group is an independent random sample from a normal population. Analysis of variance is robust
to departures from normality, although the data should be symmetric. The groups should come from
populations with equal variances. To test this assumption, use Levene’s homogeneity-of-variance
test.
Obtaining a One-Way analysis of variance
1. From the menus choose:
Analyze > Compare Means > One-Way ANOVA…
Chapter 1. Core features 63
2. Select one or more dependent variables.
3. Select a single independent factor variable.
Optionally, you can:
• Select Estimate effect size for overall tests to control the calculation of the effect size for the overall
test. When selected, the “ANOVA Effect Sizes” table displays in the output.
• Click Contrasts to partition the between-groups sums of squares into trend components or specify a
priori contrasts.
• Click Post Hoc to use post hoc range tests and pairwise multiple comparisons to determine which
means differ.
• Click Options to control the treatment of missing data and the level of the confidence interval.
• Click Bootstrap for deriving robust estimates of standard errors and confidence intervals for estimates
such as the mean, median, proportion, odds ratio, correlation coefficient or regression coefficient.
One-Way ANOVA Contrasts
You can partition the between-groups sums of squares into trend components or specify a priori
contrasts.
Polynomial
Partitions the between-groups sums of squares into trend components. You can test for a trend of the
dependent variable across the ordered levels of the factor variable. For example, you could test for a
linear trend (increasing or decreasing) in salary across the ordered levels of highest degree earned.
• Degree. You can choose a 1st, 2nd, 3rd, 4th, or 5th degree polynomial.
Coefficients
User-specified a priori contrasts to be tested by the t statistic. Enter a coefficient for each group
(category) of the factor variable and click Add after each entry. Each new value is added to the bottom
of the coefficient list. To specify additional sets of contrasts, click Next. Use Next and Previous to
move between sets of contrasts.
Estimate effect size for contrasts
Controls the calculation of the effect size for the overall test. When this setting is enabled, at least one
of the following options must be selected to calculate the effect sizes. This setting is enabled when at
least one contrast is specified and results in an ANOVA Effect Sizes table in the output.
Use pooled standard deviation for all the groups as the standardizer
Uses the pooled standard deviation for all the groups as the standardizer in estimating the effect
size. This is the default setting and is available when Estimate effect size for contrasts is
selected.
Use pooled standard deviation for those groups involved in the contrast as the standardizer
Uses the pooled standard deviation for the groups involved in the contrast as the standardizer.
The setting is available when Estimate effect size for contrasts is selected.
The order of the coefficients is important because it corresponds to the ascending order of the category
values of the factor variable. The first coefficient on the list corresponds to the lowest group value of the
factor variable, and the last coefficient corresponds to the highest value. For example, if there are six
categories of the factor variable, the coefficients –1, 0, 0, 0, 0.5, and 0.5 contrast the first group with the
fifth and sixth groups. For most applications, the coefficients should sum to 0. Sets that do not sum to 0
can also be used, but a warning message is displayed.
One-Way ANOVA Post Hoc Tests
Once you have determined that differences exist among the means, post hoc range tests and pairwise
multiple comparisons can determine which means differ. Range tests identify homogeneous subsets of
means that are not different from each other. Pairwise multiple comparisons test the difference between
each pair of means and yield a matrix where asterisks indicate significantly different group means at an
alpha level of 0.05.
64 IBM SPSS Statistics Base V27
Equal Variances Assumed
Tukey’s honestly significant difference test, Hochberg’s GT2, Gabriel, and Scheffé are multiple
comparison tests and range tests. Other available range tests are Tukey’s b, S-N-K (Student-Newman-
Keuls), Duncan, R-E-G-W F (Ryan-Einot-Gabriel-Welsch F test), R-E-G-W Q (Ryan-Einot-Gabriel-Welsch
range test), and Waller-Duncan. Available multiple comparison tests are Bonferroni, Tukey’s honestly
significant difference test, Sidak, Gabriel, Hochberg, Dunnett, Scheffé, and LSD (least significant
difference).
• LSD. Uses t tests to perform all pairwise comparisons between group means. No adjustment is made to
the error rate for multiple comparisons.
• Bonferroni. Uses t tests to perform pairwise comparisons between group means, but controls overall
error rate by setting the error rate for each test to the experimentwise error rate divided by the total
number of tests. Hence, the observed significance level is adjusted for the fact that multiple
comparisons are being made.
• Sidak. Pairwise multiple comparison test based on a t statistic. Sidak adjusts the significance level for
multiple comparisons and provides tighter bounds than Bonferroni.
• Scheffe. Performs simultaneous joint pairwise comparisons for all possible pairwise combinations of
means. Uses the F sampling distribution. Can be used to examine all possible linear combinations of
group means, not just pairwise comparisons.
• R-E-G-W F. Ryan-Einot-Gabriel-Welsch multiple stepdown procedure based on an F test.
• R-E-G-W Q. Ryan-Einot-Gabriel-Welsch multiple stepdown procedure based on the Studentized range.
• S-N-K. Makes all pairwise comparisons between means using the Studentized range distribution. With
equal sample sizes, it also compares pairs of means within homogeneous subsets, using a stepwise
procedure. Means are ordered from highest to lowest, and extreme differences are tested first.
• Tukey. Uses the Studentized range statistic to make all of the pairwise comparisons between groups.
Sets the experimentwise error rate at the error rate for the collection for all pairwise comparisons.
• Tukey’s b. Uses the Studentized range distribution to make pairwise comparisons between groups. The
critical value is the average of the corresponding value for the Tukey’s honestly significant difference
test and the Student-Newman-Keuls.
• Duncan. Makes pairwise comparisons using a stepwise order of comparisons identical to the order used
by the Student-Newman-Keuls test, but sets a protection level for the error rate for the collection of
tests, rather than an error rate for individual tests. Uses the Studentized range statistic.
• Hochberg’s GT2. Multiple comparison and range test that uses the Studentized maximum modulus.
Similar to Tukey’s honestly significant difference test.
• Gabriel. Pairwise comparison test that used the Studentized maximum modulus and is generally more
powerful than Hochberg’s GT2 when the cell sizes are unequal. Gabriel’s test may become liberal when
the cell sizes vary greatly.
• Waller-Duncan. Multiple comparison test based on a t statistic; uses a Bayesian approach.
• Dunnett. Pairwise multiple comparison t test that compares a set of treatments against a single control
mean. The last category is the default control category. Alternatively, you can choose the first category.
2-sided tests that the mean at any level (except the control category) of the factor is not equal to that of
the control category. < Control tests if the mean at any level of the factor is smaller than that of the
control category. > Control tests if the mean at any level of the factor is greater than that of the control
category.
Equal Variances Not Assumed
Multiple comparison tests that do not assume equal variances are Tamhane’s T2, Dunnett’s T3, Games-
Howell, and Dunnett’s C.
• Tamhane’s T2. Conservative pairwise comparisons test based on a t test. This test is appropriate when
the variances are unequal.
• Dunnett’s T3. Pairwise comparison test based on the Studentized maximum modulus. This test is
appropriate when the variances are unequal.
Chapter 1. Core features 65
• Games-Howell. Pairwise comparison test that is sometimes liberal. This test is appropriate when the
variances are unequal.
• Dunnett’s C. Pairwise comparison test based on the Studentized range. This test is appropriate when the
variances are unequal.
Note: You may find it easier to interpret the output from post hoc tests if you deselect Hide empty rows
and columns in the Table Properties dialog box (in an activated pivot table, choose Table Properties
from the Format menu).
Null Hypothesis test
Specifies how the significance level (alpha) is handled for the post hoc test.
Use the same significance level (alpha) as the settings in Options
When selected, uses same setting that is specified in the Options dialog.
Specify the significance level (alpha) for the post hoc test
When selected, you can specify the significance level (alpha) in the Level field.
Obtaining Post Hoc Tests for One-Way ANOVA
One-Way ANOVA Options
Statistics
Choose one or more of the following:
Descriptive
Calculates the number of cases, mean, standard deviation, standard error of the mean, minimum,
maximum, and 95% confidence intervals for each dependent variable for each group.
Fixed and random effects
Displays the standard deviation, standard error, and 95% confidence interval for the fixed-effects
model, and the standard error, 95% confidence interval, and estimate of between-components
variance for the random-effects model.
Homogeneity of variance test
Calculates the Levene statistic to test for the equality of group variances. This test is not
dependent on the assumption of normality.
Brown-Forsythe
Calculates the Brown-Forsythe statistic to test for the equality of group means. This statistic is
preferable to the F statistic when the assumption of equal variances does not hold.
Welch
Calculates the Welch statistic to test for the equality of group means. This statistic is preferable to
the F statistic when the assumption of equal variances does not hold.
Missing Values
Controls the treatment of missing values.
Exclude cases analysis by analysis
A case with a missing value for either the dependent or the factor variable for a given analysis is
not used in that analysis. Also, a case outside the range specified for the factor variable is not
used.
Exclude cases listwise
Cases with missing values for the factor variable or for any dependent variable included on the
dependent list in the main dialog box are excluded from all analyses. If you have not specified
multiple dependent variables, this has no effect.
Confidence Interval
By default, a 95% confidence interval for the difference between the mean and the hypothesized test
value is displayed. Enter a value between 1 and 99 to request a different confidence level.
66 IBM SPSS Statistics Base V27
Means plot
Displays a chart that plots the subgroup means (the means for each group defined by values of the
factor variable).
Specifying Options for One-Way ANOVA
ONEWAY Command Additional Features
The command syntax language also allows you to:
• Obtain fixed- and random-effects statistics. Standard deviation, standard error of the mean, and 95%
confidence intervals for the fixed-effects model. Standard error, 95% confidence intervals, and
estimate of between-components variance for random-effects model (using STATISTICS=EFFECTS).
• Specify alpha levels for the least significance difference, Bonferroni, Duncan, and Scheffé multiple
comparison tests (with the RANGES subcommand).
• Write a matrix of means, standard deviations, and frequencies, or read a matrix of means, frequencies,
pooled variances, and degrees of freedom for the pooled variances. These matrices can be used in
place of raw data to obtain a one-way analysis of variance (with the MATRIX subcommand).
See the Command Syntax Reference for complete syntax information.
GLM Univariate Analysis
The GLM Univariate procedure provides regression analysis and analysis of variance for one dependent
variable by one or more factors and/or variables. The factor variables divide the population into groups.
Using this General Linear Model procedure, you can test null hypotheses about the effects of other
variables on the means of various groupings of a single dependent variable. You can investigate
interactions between factors as well as the effects of individual factors, some of which may be random. In
addition, the effects of covariates and covariate interactions with factors can be included. For regression
analysis, the independent (predictor) variables are specified as covariates.
Both balanced and unbalanced models can be tested. A design is balanced if each cell in the model
contains the same number of cases. In addition to testing hypotheses, GLM Univariate produces
estimates of parameters.
Commonly used a priori contrasts are available to perform hypothesis testing. Additionally, after an
overall F test has shown significance, you can use post hoc tests to evaluate differences among specific
means. Estimated marginal means give estimates of predicted mean values for the cells in the model, and
profile plots (interaction plots) of these means allow you to easily visualize some of the relationships.
Residuals, predicted values, Cook’s distance, and leverage values can be saved as new variables in your
data file for checking assumptions.
WLS Weight allows you to specify a variable used to give observations different weights for a weighted
least-squares (WLS) analysis, perhaps to compensate for a different precision of measurement.
Example. Data are gathered for individual runners in the Chicago marathon for several years. The time in
which each runner finishes is the dependent variable. Other factors include weather (cold, pleasant, or
hot), number of months of training, number of previous marathons, and gender. Age is considered a
covariate. You might find that gender is a significant effect and that the interaction of gender with weather
is significant.
Methods. Type I, Type II, Type III, and Type IV sums of squares can be used to evaluate different
hypotheses. Type III is the default.
Statistics. Post hoc range tests and multiple comparisons: least significant difference, Bonferroni, Sidak,
Scheffé, Ryan-Einot-Gabriel-Welsch multiple F, Ryan-Einot-Gabriel-Welsch multiple range, Student-
Newman-Keuls, Tukey’s honestly significant difference, Tukey’s b, Duncan, Hochberg’s GT2, Gabriel,
Waller-Duncan t test, Dunnett (one-sided and two-sided), Tamhane’s T2, Dunnett’s T3, Games-Howell,
and Dunnett’s C. Descriptive statistics: observed means, standard deviations, and counts for all of the
dependent variables in all cells. Levene tests for homogeneity of variance.
Chapter 1. Core features 67
Plots. Spread-versus-level, residual, and profile (interaction).
GLM Univariate Data Considerations
Data. The dependent variable is quantitative. Factors are categorical. They can have numeric values or
string values of up to eight characters. Covariates are quantitative variables that are related to the
dependent variable.
Assumptions. The data are a random sample from a normal population; in the population, all cell
variances are the same. Analysis of variance is robust to departures from normality, although the data
should be symmetric. To check assumptions, you can use homogeneity of variances tests and spread-
versus-level plots. You can also examine residuals and residual plots.
To Obtain GLM Univariate Tables
1. From the menus choose:
Analyze > General Linear Model > Univariate…
2. Select a dependent variable.
3. Select variables for Fixed Factor(s), Random Factor(s), and Covariate(s), as appropriate for your data.
4. Optionally, you can use WLS Weight to specify a weight variable for weighted least-squares analysis. If
the value of the weighting variable is zero, negative, or missing, the case is excluded from the analysis.
A variable already used in the model cannot be used as a weighting variable.
GLM Model
Figure 1. Univariate Model dialog box
Specify Model. A full factorial model contains all factor main effects, all covariate main effects, and all
factor-by-factor interactions. It does not contain covariate interactions. Select Custom to specify only a
subset of interactions or to specify factor-by-covariate interactions. You must indicate all of the terms to
be included in the model.
Factors and Covariates. The factors and covariates are listed.
Model. The model depends on the nature of your data. After selecting Custom, you can select the main
effects and interactions that are of interest in your analysis.
Sum of squares. The method of calculating the sums of squares. For balanced or unbalanced models
with no missing cells, the Type III sum-of-squares method is most commonly used.
68 IBM SPSS Statistics Base V27
Include intercept in model. The intercept is usually included in the model. If you can assume that the
data pass through the origin, you can exclude the intercept.
Build Terms and Custom Terms
Build terms
Use this choice when you want to include non-nested terms of a certain type (such as main effects)
for all combinations of a selected set of factors and covariates.
Build custom terms
Use this choice when you want to include nested terms or when you want to explicitly build any term
variable by variable. Building a nested term involves the following steps:
Sum of Squares
For the model, you can choose a type of sums of squares. Type III is the most commonly used and is the
default.
Type I. This method is also known as the hierarchical decomposition of the sum-of-squares method.
Each term is adjusted for only the term that precedes it in the model. Type I sums of squares are
commonly used for:
• A balanced ANOVA model in which any main effects are specified before any first-order interaction
effects, any first-order interaction effects are specified before any second-order interaction effects, and
so on.
• A polynomial regression model in which any lower-order terms are specified before any higher-order
terms.
• A purely nested model in which the first-specified effect is nested within the second-specified effect,
the second-specified effect is nested within the third, and so on. (This form of nesting can be specified
only by using syntax.)
Type II. This method calculates the sums of squares of an effect in the model adjusted for all other
“appropriate” effects. An appropriate effect is one that corresponds to all effects that do not contain the
effect being examined. The Type II sum-of-squares method is commonly used for:
• A balanced ANOVA model.
• Any model that has main factor effects only.
• Any regression model.
• A purely nested design. (This form of nesting can be specified by using syntax.)
Type III. The default. This method calculates the sums of squares of an effect in the design as the sums
of squares, adjusted for any other effects that do not contain the effect, and orthogonal to any effects (if
any) that contain the effect. The Type III sums of squares have one major advantage in that they are
invariant with respect to the cell frequencies as long as the general form of estimability remains constant.
Hence, this type of sums of squares is often considered useful for an unbalanced model with no missing
cells. In a factorial design with no missing cells, this method is equivalent to the Yates’ weighted-squares-
of-means technique. The Type III sum-of-squares method is commonly used for:
• Any models listed in Type I and Type II.
• Any balanced or unbalanced model with no empty cells.
Type IV. This method is designed for a situation in which there are missing cells. For any effect F in the
design, if F is not contained in any other effect, then Type IV = Type III = Type II. When F is contained in
other effects, Type IV distributes the contrasts being made among the parameters in F to all higher-level
effects equitably. The Type IV sum-of-squares method is commonly used for:
• Any models listed in Type I and Type II.
• Any balanced model or unbalanced model with empty cells.
Chapter 1. Core features 69
GLM Contrasts
Contrasts are used to test for differences among the levels of a factor. You can specify a contrast for each
factor in the model (in a repeated measures model, for each between-subjects factor). Contrasts
represent linear combinations of the parameters.
GLM Univariate. Hypothesis testing is based on the null hypothesis LB = 0, where L is the contrast
coefficients matrix and B is the parameter vector. When a contrast is specified, an L matrix is created. The
columns of the L matrix corresponding to the factor match the contrast. The remaining columns are
adjusted so that the L matrix is estimable.
The output includes an F statistic for each set of contrasts. Also displayed for the contrast differences are
Bonferroni-type simultaneous confidence intervals based on Student’s t distribution.
Available Contrasts
Available contrasts are deviation, simple, difference, Helmert, repeated, and polynomial. For deviation
contrasts and simple contrasts, you can choose whether the reference category is the last or first
category.
Contrast Types
Deviation. Compares the mean of each level (except a reference category) to the mean of all of the levels
(grand mean). The levels of the factor can be in any order.
Simple. Compares the mean of each level to the mean of a specified level. This type of contrast is useful
when there is a control group. You can choose the first or last category as the reference.
Difference. Compares the mean of each level (except the first) to the mean of previous levels.
(Sometimes called reverse Helmert contrasts.)
Helmert. Compares the mean of each level of the factor (except the last) to the mean of subsequent
levels.
Repeated. Compares the mean of each level (except the last) to the mean of the subsequent level.
Polynomial. Compares the linear effect, quadratic effect, cubic effect, and so on. The first degree of
freedom contains the linear effect across all categories; the second degree of freedom, the quadratic
effect; and so on. These contrasts are often used to estimate polynomial trends.
GLM Profile Plots
Profile plots (interaction plots) are useful for comparing marginal means in your model. A profile plot is a
line plot in which each point indicates the estimated marginal mean of a dependent variable (adjusted for
any covariates) at one level of a factor. The levels of a second factor can be used to make separate lines.
Each level in a third factor can be used to create a separate plot. All fixed and random factors, if any, are
available for plots. For multivariate analyses, profile plots are created for each dependent variable. In a
repeated measures analysis, both between-subjects factors and within-subjects factors can be used in
profile plots. GLM Multivariate and GLM Repeated Measures are available only if you have the Advanced
Statistics option installed.
A profile plot of one factor shows whether the estimated marginal means are increasing or decreasing
across levels. For two or more factors, parallel lines indicate that there is no interaction between factors,
which means that you can investigate the levels of only one factor. Nonparallel lines indicate an
interaction.
70 IBM SPSS Statistics Base V27
Figure 2. Nonparallel plot (left) and parallel plot (right)
After a plot is specified by selecting factors for the horizontal axis and, optionally, factors for separate
lines and separate plots, the plot must be added to the Plots list.
Chart Type
The chart can be a line chart or a bar chart
Error Bars
You can include error bars that represent the confidence interval or a number of standard errors. The
confidence interval is based on the significance level specified on the Options dialog.
Include reference line for grand mean
Includes a reference line that represents the overall grand mean.
Y axis starts at 0
For line charts with all positive or all negative values, forces the Y axis to start at 0. Bar charts always
start (or include) 0.
GLM Options
Optional statistics are available from this dialog box. Statistics are calculated using a fixed-effects model.
Display. Select Descriptive statistics to produce observed means, standard deviations, and counts for all
of the dependent variables in all cells. Estimates of effect size gives a partial eta-squared value for each
effect and each parameter estimate. The eta-squared statistic describes the proportion of total variability
attributable to a factor. Select Observed power to obtain the power of the test when the alternative
hypothesis is set based on the observed value. Select Parameter estimates to produce the parameter
estimates, standard errors, t tests, confidence intervals, and the observed power for each test. Select
Contrast coefficient matrix to obtain the L matrix.
Homogeneity tests produces Levene tests of the homogeneity of variance for each dependent variable
across all level combinations of the between-subjects factors, for between-subjects factors only. The
spread-versus-level and residual plots options are useful for checking assumptions about the data. This
item is disabled if there are no factors. Select Residual plot to produce an observed-by-predicted-by-
standardized residual plot for each dependent variable. These plots are useful for investigating the
assumption of equal variance. Select Lack of fit to check if the relationship between the dependent
variable and the independent variables can be adequately described by the model. General estimable
function(s) allows you to construct custom hypothesis tests based on the general estimable function(s).
Rows in any contrast coefficient matrix are linear combinations of the general estimable function(s).
Heteroskedasticity Tests are available for testing whether the variance of the errors (for each dependent
variable) depends on the values of the independent variables. For the Breusch-Pagan test, Modified
Breusch-Pagan test, and F test you can specify the model on which the test is based. By default, the
model consists of a constant term, a term that is linear in the predicted values, a term that is quadratic in
the predicted values, and an error term.
Parameter estimates with robust standard errors displays a table of parameter estimates, along with
robust or heteroskedasticity-consistent (HC) standard errors; and t statistics, significance values, and
confidence intervals that use the robust standard errors. Five different methods are available for the
robust covariance matrix estimation.
Chapter 1. Core features 71
HC0
Based on the original asymptotic or large sample robust, empirical, or “sandwich” estimator of the
covariance matrix of the parameter estimates. The middle part of the sandwich contains squared OLS
(ordinary least squares) or squared weighted WLS (weighted least squares) residuals.
HC1
A finite-sample modification of HC0, multiplying it by N/(N-p), where N is the sample size and p is the
number of non-redundant parameters in the model.
HC2
A modification of HC0 that involves dividing the squared residual by 1-h, where h is the leverage for
the case.
HC3
A modification of HC0 that approximates a jackknife estimator. Squared residuals are divided by the
square of 1-h.
HC4
A modification of HC0 that divides the squared residuals by 1-h to a power that varies according to h,
N, and p, with an upper limit of 4.
Significance level. You might want to adjust the significance level used in post hoc tests and the
confidence level used for constructing confidence intervals. The specified value is also used to calculate
the observed power for the test. When you specify a significance level, the associated level of the
confidence intervals is displayed in the dialog box.
UNIANOVA Command Additional Features
The command syntax language also allows you to:
• Specify nested effects in the design (using the DESIGN subcommand).
• Specify tests of effects versus a linear combination of effects or a value (using the TEST subcommand).
• Specify multiple contrasts (using the CONTRAST subcommand).
• Include user-missing values (using the MISSING subcommand).
• Specify EPS criteria (using the CRITERIA subcommand).
• Construct a custom L matrix, M matrix, or K matrix (using the LMATRIX, MMATRIX, and KMATRIX
subcommands).
• For deviation or simple contrasts, specify an intermediate reference category (using the CONTRAST
subcommand).
• Specify metrics for polynomial contrasts (using the CONTRAST subcommand).
• Specify error terms for post hoc comparisons (using the POSTHOC subcommand).
• Compute estimated marginal means for any factor or factor interaction among the factors in the factor
list (using the EMMEANS subcommand).
• Specify names for temporary variables (using the SAVE subcommand).
• Construct a correlation matrix data file (using the OUTFILE subcommand).
• Construct a matrix data file that contains statistics from the between-subjects ANOVA table (using the
OUTFILE subcommand).
• Save the design matrix to a new data file (using the OUTFILE subcommand).
See the Command Syntax Reference for complete syntax information.
GLM Post Hoc Comparisons
Post hoc multiple comparison tests. Once you have determined that differences exist among the means,
post hoc range tests and pairwise multiple comparisons can determine which means differ. Comparisons
are made on unadjusted values. These tests are used for fixed between-subjects factors only. In GLM
Repeated Measures, these tests are not available if there are no between-subjects factors, and the post
hoc multiple comparison tests are performed for the average across the levels of the within-subjects
72 IBM SPSS Statistics Base V27
factors. For GLM Multivariate, the post hoc tests are performed for each dependent variable separately.
GLM Multivariate and GLM Repeated Measures are available only if you have the Advanced Statistics
option installed.
The Bonferroni and Tukey’s honestly significant difference tests are commonly used multiple comparison
tests. The Bonferroni test, based on Student’s t statistic, adjusts the observed significance level for the
fact that multiple comparisons are made. Sidak’s t test also adjusts the significance level and provides
tighter bounds than the Bonferroni test. Tukey’s honestly significant difference test uses the
Studentized range statistic to make all pairwise comparisons between groups and sets the
experimentwise error rate to the error rate for the collection for all pairwise comparisons. When testing a
large number of pairs of means, Tukey’s honestly significant difference test is more powerful than the
Bonferroni test. For a small number of pairs, Bonferroni is more powerful.
Hochberg’s GT2 is similar to Tukey’s honestly significant difference test, but the Studentized maximum
modulus is used. Usually, Tukey’s test is more powerful. Gabriel’s pairwise comparisons test also uses
the Studentized maximum modulus and is generally more powerful than Hochberg’s GT2 when the cell
sizes are unequal. Gabriel’s test may become liberal when the cell sizes vary greatly.
Dunnett’s pairwise multiple comparison t test compares a set of treatments against a single control
mean. The last category is the default control category. Alternatively, you can choose the first category.
You can also choose a two-sided or one-sided test. To test that the mean at any level (except the control
category) of the factor is not equal to that of the control category, use a two-sided test. To test whether
the mean at any level of the factor is smaller than that of the control category, select < Control. Likewise,
to test whether the mean at any level of the factor is larger than that of the control category, select >
Control.
Ryan, Einot, Gabriel, and Welsch (R-E-G-W) developed two multiple step-down range tests. Multiple step-
down procedures first test whether all means are equal. If all means are not equal, subsets of means are
tested for equality. R-E-G-W F is based on an F test and R-E-G-W Q is based on the Studentized range.
These tests are more powerful than Duncan’s multiple range test and Student-Newman-Keuls (which are
also multiple step-down procedures), but they are not recommended for unequal cell sizes.
When the variances are unequal, use Tamhane’s T2 (conservative pairwise comparisons test based on a t
test), Dunnett’s T3 (pairwise comparison test based on the Studentized maximum modulus), Games-
Howell pairwise comparison test (sometimes liberal), or Dunnett’s C (pairwise comparison test based
on the Studentized range). Note that these tests are not valid and will not be produced if there are
multiple factors in the model.
Duncan’s multiple range test, Student-Newman-Keuls (S-N-K), and Tukey’s b are range tests that rank
group means and compute a range value. These tests are not used as frequently as the tests previously
discussed.
The Waller-Duncan t test uses a Bayesian approach. This range test uses the harmonic mean of the
sample size when the sample sizes are unequal.
The significance level of the Scheffé test is designed to allow all possible linear combinations of group
means to be tested, not just pairwise comparisons available in this feature. The result is that the Scheffé
test is often more conservative than other tests, which means that a larger difference between means is
required for significance.
The least significant difference (LSD) pairwise multiple comparison test is equivalent to multiple
individual t tests between all pairs of groups. The disadvantage of this test is that no attempt is made to
adjust the observed significance level for multiple comparisons.
Tests displayed. Pairwise comparisons are provided for LSD, Sidak, Bonferroni, Games-Howell,
Tamhane’s T2 and T3, Dunnett’s C, and Dunnett’s T3. Homogeneous subsets for range tests are provided
for S-N-K, Tukey’s b, Duncan, R-E-G-W F, R-E-G-W Q, and Waller. Tukey’s honestly significant difference
test, Hochberg’s GT2, Gabriel’s test, and Scheffé’s test are both multiple comparison tests and range
tests.
GLM Options
Optional statistics are available from this dialog box. Statistics are calculated using a fixed-effects model.
Chapter 1. Core features 73
Display. Select Descriptive statistics to produce observed means, standard deviations, and counts for all
of the dependent variables in all cells. Estimates of effect size gives a partial eta-squared value for each
effect and each parameter estimate. The eta-squared statistic describes the proportion of total variability
attributable to a factor. Select Observed power to obtain the power of the test when the alternative
hypothesis is set based on the observed value. Select Parameter estimates to produce the parameter
estimates, standard errors, t tests, confidence intervals, and the observed power for each test. Select
Contrast coefficient matrix to obtain the L matrix.
Homogeneity tests produces Levene tests of the homogeneity of variance for each dependent variable
across all level combinations of the between-subjects factors, for between-subjects factors only. The
spread-versus-level and residual plots options are useful for checking assumptions about the data. This
item is disabled if there are no factors. Select Residual plot to produce an observed-by-predicted-by-
standardized residual plot for each dependent variable. These plots are useful for investigating the
assumption of equal variance. Select Lack of fit to check if the relationship between the dependent
variable and the independent variables can be adequately described by the model. General estimable
function(s) allows you to construct custom hypothesis tests based on the general estimable function(s).
Rows in any contrast coefficient matrix are linear combinations of the general estimable function(s).
Heteroskedasticity Tests are available for testing whether the variance of the errors (for each dependent
variable) depends on the values of the independent variables. For the Breusch-Pagan test, Modified
Breusch-Pagan test, and F test you can specify the model on which the test is based. By default, the
model consists of a constant term, a term that is linear in the predicted values, a term that is quadratic in
the predicted values, and an error term.
Parameter estimates with robust standard errors displays a table of parameter estimates, along with
robust or heteroskedasticity-consistent (HC) standard errors; and t statistics, significance values, and
confidence intervals that use the robust standard errors. Five different methods are available for the
robust covariance matrix estimation.
HC0
Based on the original asymptotic or large sample robust, empirical, or “sandwich” estimator of the
covariance matrix of the parameter estimates. The middle part of the sandwich contains squared OLS
(ordinary least squares) or squared weighted WLS (weighted least squares) residuals.
HC1
A finite-sample modification of HC0, multiplying it by N/(N-p), where N is the sample size and p is the
number of non-redundant parameters in the model.
HC2
A modification of HC0 that involves dividing the squared residual by 1-h, where h is the leverage for
the case.
HC3
A modification of HC0 that approximates a jackknife estimator. Squared residuals are divided by the
square of 1-h.
HC4
A modification of HC0 that divides the squared residuals by 1-h to a power that varies according to h,
N, and p, with an upper limit of 4.
Significance level. You might want to adjust the significance level used in post hoc tests and the
confidence level used for constructing confidence intervals. The specified value is also used to calculate
the observed power for the test. When you specify a significance level, the associated level of the
confidence intervals is displayed in the dialog box.
UNIANOVA Command Additional Features
The command syntax language also allows you to:
• Specify nested effects in the design (using the DESIGN subcommand).
• Specify tests of effects versus a linear combination of effects or a value (using the TEST subcommand).
• Specify multiple contrasts (using the CONTRAST subcommand).
• Include user-missing values (using the MISSING subcommand).
74 IBM SPSS Statistics Base V27
• Specify EPS criteria (using the CRITERIA subcommand).
• Construct a custom L matrix, M matrix, or K matrix (using the LMATRIX, MMATRIX, and KMATRIX
subcommands).
• For deviation or simple contrasts, specify an intermediate reference category (using the CONTRAST
subcommand).
• Specify metrics for polynomial contrasts (using the CONTRAST subcommand).
• Specify error terms for post hoc comparisons (using the POSTHOC subcommand).
• Compute estimated marginal means for any factor or factor interaction among the factors in the factor
list (using the EMMEANS subcommand).
• Specify names for temporary variables (using the SAVE subcommand).
• Construct a correlation matrix data file (using the OUTFILE subcommand).
• Construct a matrix data file that contains statistics from the between-subjects ANOVA table (using the
OUTFILE subcommand).
• Save the design matrix to a new data file (using the OUTFILE subcommand).
See the Command Syntax Reference for complete syntax information.
GLM Save
You can save values predicted by the model, residuals, and related measures as new variables in the Data
Editor. Many of these variables can be used for examining assumptions about the data. To save the values
for use in another IBM SPSS Statistics session, you must save the current data file.
Predicted Values. The values that the model predicts for each case.
• Unstandardized. The value the model predicts for the dependent variable.
• Weighted. Weighted unstandardized predicted values. Available only if a WLS variable was previously
selected.
• Standard error. An estimate of the standard deviation of the average value of the dependent variable for
cases that have the same values of the independent variables.
Diagnostics. Measures to identify cases with unusual combinations of values for the independent
variables and cases that may have a large impact on the model.
• Cook’s distance. A measure of how much the residuals of all cases would change if a particular case
were excluded from the calculation of the regression coefficients. A large Cook’s D indicates that
excluding a case from computation of the regression statistics changes the coefficients substantially.
• Leverage values. Uncentered leverage values. The relative influence of each observation on the model’s
fit.
Residuals. An unstandardized residual is the actual value of the dependent variable minus the value
predicted by the model. Standardized, Studentized, and deleted residuals are also available. If a WLS
variable was chosen, weighted unstandardized residuals are available.
• Unstandardized. The difference between an observed value and the value predicted by the model.
• Weighted. Weighted unstandardized residuals. Available only if a WLS variable was previously selected.
• Standardized. The residual divided by an estimate of its standard deviation. Standardized residuals,
which are also known as Pearson residuals, have a mean of 0 and a standard deviation of 1.
• Studentized. The residual divided by an estimate of its standard deviation that varies from case to case,
depending on the distance of each case’s values on the independent variables from the means of the
independent variables.
• Deleted. The residual for a case when that case is excluded from the calculation of the regression
coefficients. It is the difference between the value of the dependent variable and the adjusted predicted
value.
Chapter 1. Core features 75
Coefficient Statistics. Writes a variance-covariance matrix of the parameter estimates in the model to a
new dataset in the current session or an external IBM SPSS Statistics data file. Also, for each dependent
variable, there will be a row of parameter estimates, a row of standard errors of the parameter estimates,
a row of significance values for the t statistics corresponding to the parameter estimates, and a row of
residual degrees of freedom. For a multivariate model, there are similar rows for each dependent variable.
When Heteroskedasticity-consistent statistics is selected (only available for univariate models), the
variance-covariance matrix is calculated using a robust estimator, the row of standard errors displays the
robust standard errors, and the significance values reflect the robust errors. You can use this matrix file in
other procedures that read matrix files.
GLM Estimated Marginal Means
Select the factors and interactions for which you want estimates of the population marginal means in the
cells. These means are adjusted for the covariates, if any.
• Compare main effects. Provides uncorrected pairwise comparisons among estimated marginal means
for any main effect in the model, for both between- and within-subjects factors. This item is available
only if main effects are selected under the Display Means For list.
• Confidence interval adjustment. Select least significant difference (LSD), Bonferroni, or Sidak
adjustment to the confidence intervals and significance. This item is available only if Compare main
effects is selected.
Specifying Estimated Marginal Means
1. From the menus choose one of the procedures available under > Analyze > General Linear Model.
2. In the main dialog, click EM Means.
GLM Options
Optional statistics are available from this dialog box. Statistics are calculated using a fixed-effects model.
Display. Select Descriptive statistics to produce observed means, standard deviations, and counts for all
of the dependent variables in all cells. Estimates of effect size gives a partial eta-squared value for each
effect and each parameter estimate. The eta-squared statistic describes the proportion of total variability
attributable to a factor. Select Observed power to obtain the power of the test when the alternative
hypothesis is set based on the observed value. Select Parameter estimates to produce the parameter
estimates, standard errors, t tests, confidence intervals, and the observed power for each test. Select
Contrast coefficient matrix to obtain the L matrix.
Homogeneity tests produces Levene tests of the homogeneity of variance for each dependent variable
across all level combinations of the between-subjects factors, for between-subjects factors only. The
spread-versus-level and residual plots options are useful for checking assumptions about the data. This
item is disabled if there are no factors. Select Residual plot to produce an observed-by-predicted-by-
standardized residual plot for each dependent variable. These plots are useful for investigating the
assumption of equal variance. Select Lack of fit to check if the relationship between the dependent
variable and the independent variables can be adequately described by the model. General estimable
function(s) allows you to construct custom hypothesis tests based on the general estimable function(s).
Rows in any contrast coefficient matrix are linear combinations of the general estimable function(s).
Heteroskedasticity Tests are available for testing whether the variance of the errors (for each dependent
variable) depends on the values of the independent variables. For the Breusch-Pagan test, Modified
Breusch-Pagan test, and F test you can specify the model on which the test is based. By default, the
model consists of a constant term, a term that is linear in the predicted values, a term that is quadratic in
the predicted values, and an error term.
Parameter estimates with robust standard errors displays a table of parameter estimates, along with
robust or heteroskedasticity-consistent (HC) standard errors; and t statistics, significance values, and
confidence intervals that use the robust standard errors. Five different methods are available for the
robust covariance matrix estimation.
76 IBM SPSS Statistics Base V27
HC0
Based on the original asymptotic or large sample robust, empirical, or “sandwich” estimator of the
covariance matrix of the parameter estimates. The middle part of the sandwich contains squared OLS
(ordinary least squares) or squared weighted WLS (weighted least squares) residuals.
HC1
A finite-sample modification of HC0, multiplying it by N/(N-p), where N is the sample size and p is the
number of non-redundant parameters in the model.
HC2
A modification of HC0 that involves dividing the squared residual by 1-h, where h is the leverage for
the case.
HC3
A modification of HC0 that approximates a jackknife estimator. Squared residuals are divided by the
square of 1-h.
HC4
A modification of HC0 that divides the squared residuals by 1-h to a power that varies according to h,
N, and p, with an upper limit of 4.
Significance level. You might want to adjust the significance level used in post hoc tests and the
confidence level used for constructing confidence intervals. The specified value is also used to calculate
the observed power for the test. When you specify a significance level, the associated level of the
confidence intervals is displayed in the dialog box.
GLM Auxiliary Regression Model
The Auxiliary Regression Model dialog box specifies the model that is used to test for heteroskedasticity.
Use predicted values
Uses a model that consists of a constant term, a term that is linear in the predicted values, a term that
is quadratic in the predicted values, and an error term.
Use univariate model
Uses the model that is specified on the Model subdialog. An intercept term is included if the specified
model does not contain one.
Custom model
Uses the model that you explicitly specify.
Build terms
Use this choice when you want to include non-nested terms of a certain type (such as main
effects) for all combinations of a selected set of factors and covariates.
Build custom terms
Use this choice when you want to include nested terms or when you want to explicitly build any
term variable by variable. Building a nested term involves the following steps:
UNIANOVA Command Additional Features
The command syntax language also allows you to:
• Specify nested effects in the design (using the DESIGN subcommand).
• Specify tests of effects versus a linear combination of effects or a value (using the TEST subcommand).
• Specify multiple contrasts (using the CONTRAST subcommand).
• Include user-missing values (using the MISSING subcommand).
• Specify EPS criteria (using the CRITERIA subcommand).
• Construct a custom L matrix, M matrix, or K matrix (using the LMATRIX, MMATRIX, and KMATRIX
subcommands).
• For deviation or simple contrasts, specify an intermediate reference category (using the CONTRAST
subcommand).
• Specify metrics for polynomial contrasts (using the CONTRAST subcommand).
Chapter 1. Core features 77
• Specify error terms for post hoc comparisons (using the POSTHOC subcommand).
• Compute estimated marginal means for any factor or factor interaction among the factors in the factor
list (using the EMMEANS subcommand).
• Specify names for temporary variables (using the SAVE subcommand).
• Construct a correlation matrix data file (using the OUTFILE subcommand).
• Construct a matrix data file that contains statistics from the between-subjects ANOVA table (using the
OUTFILE subcommand).
• Save the design matrix to a new data file (using the OUTFILE subcommand).
See the Command Syntax Reference for complete syntax information.
Bivariate Correlations
The Bivariate Correlations procedure computes Pearson’s correlation coefficient, Spearman’s rho, and
Kendall’s tau-b with their significance levels. Correlations measure how variables or rank orders are
related. Before calculating a correlation coefficient, screen your data for outliers (which can cause
misleading results) and evidence of a linear relationship. Pearson’s correlation coefficient is a measure of
linear association. Two variables can be perfectly related, but if the relationship is not linear, Pearson’s
correlation coefficient is not an appropriate statistic for measuring their association.
Confidence interval settings are available for Pearson and Spearman.
Example
Is the number of games won by a basketball team correlated with the average number of points
scored per game? A scatterplot indicates that there is a linear relationship. Analyzing data from the
1994–1995 NBA season yields that Pearson’s correlation coefficient (0.581) is significant at the 0.01
level. You might suspect that the more games won per season, the fewer points the opponents
scored. These variables are negatively correlated (–0.401), and the correlation is significant at the
0.05 level.
Statistics
For each variable: number of cases with nonmissing values, mean, and standard deviation. For each
pair of variables: Pearson’s correlation coefficient, Spearman’s rho, Kendall’s tau-b, cross-product of
deviations, and covariance.
Data considerations
Data
Use symmetric quantitative variables for Pearson’s correlation coefficient and quantitative variables
or variables with ordered categories for Spearman’s rho and Kendall’s tau-b.
Assumptions
Pearson’s correlation coefficient assumes that each pair of variables is bivariate normal.
Obtaining Bivariate Correlations
From the menus choose:
Analyze > Correlate > Bivariate…
1. Select two or more numeric variables.
The following options are also available:
Correlation Coefficients
For quantitative, normally distributed variables, choose the Pearson correlation coefficient. If your
data are not normally distributed or have ordered categories, choose Kendall’s tau-b or
Spearman, which measure the association between rank orders. Correlation coefficients range in
value from –1 (a perfect negative relationship) and +1 (a perfect positive relationship). A value of 0
indicates no linear relationship. When interpreting your results, be careful not to draw any cause-
and-effect conclusions due to a significant correlation.
78 IBM SPSS Statistics Base V27
Test of Significance
You can select two-tailed or one-tailed probabilities. If the direction of association is known in
advance, select One-tailed. Otherwise, select Two-tailed.
Flag significant correlations
Correlation coefficients significant at the 0.05 level are identified with a single asterisk, and those
significant at the 0.01 level are identified with two asterisks.
Show only the lower triangle
When selected, only the correlation matrix table’s lower triangle is presented in the output. When
not selected, the full correlation matrix table is presented in the output. The setting allows table
output to adhere to APA style guidelines.
Show diagonal
When selected, the correlation matrix table’s lower triangle along with diagonal values are
presented in the output. The setting allows table output to adhere to APA style guidelines.
2. You can optionally select the following:
• Click Options… to specify Pearson correlation statistics and missing values settings.
• Click Style… to specify conditions for automatically changing properties of pivot tables based on
specific conditions.
• Click Bootstrap… for deriving robust estimates of standard errors and confidence intervals for
estimates such as the mean, median, proportion, odds ratio, correlation coefficient or regression
coefficient.
• Click Confidence Interval… to set the options for the estimation of the confidence intervals.
Bivariate Correlations Options
Statistics
For Pearson correlations, you can choose one or both of the following:
Means and standard deviations
Displayed for each variable. The number of cases with nonmissing values is also shown. Missing
values are handled on a variable-by-variable basis regardless of your missing values setting.
Cross-product deviations and covariances
Displayed for each pair of variables. The cross-product of deviations is equal to the sum of the
products of mean-corrected variables. This is the numerator of the Pearson correlation coefficient.
The covariance is an unstandardized measure of the relationship between two variables, equal to
the cross-product deviation divided by N–1.
Missing Values
You can choose one of the following:
Exclude cases pairwise
Cases with missing values for one or both of a pair of variables for a correlation coefficient are
excluded from the analysis. Since each coefficient is based on all cases that have valid codes on
that particular pair of variables, the maximum information available is used in every calculation.
This can result in a set of coefficients based on a varying number of cases.
Exclude cases listwise
Cases with missing values for any variable are excluded from all correlations.
Bivariate Correlations Confidence Interval
The Confidence Interval dialog provides options for the estimation of the confidence intervals. The dialog
is available when Pearson, Kendall’s tau-b, or Spearman is selected on the Bivariate Correlations dialog.
Estimate confidence interval of bivariate correlation parameter
Controls the confidence interval estimation of bivariate correlation parameter. When selected,
confidence interval estimation occurs.
Chapter 1. Core features 79
Confidence interval (%)
Specifies the confidence level for all confidence intervals produced. Specify a numeric value
between 0 and 100. 95 is the default value.
Pearson Correlation
The Apply the bias adjustment setting controls whether the bias adjustment is applied. By
default, the setting is not selected, which does not take the bias term into consideration. When
selected, the bias adjustment to the estimation of the confidence limits is applied. The setting is
available when Pearson is selected on the Bivariate Correlations dialog.
Spearman Correlation
The setting is available when Spearman is selected on the Bivariate Correlations dialog and
provides options for estimating the Spearman Correlation variance via the following methods:
• Fieller, Hartley and Pearson
• Bonett and Wright
• Coruso and Cliff
CORRELATIONS and NONPAR CORR Command Additional Features
The command syntax language also allows you to:
• Write a correlation matrix for Pearson correlations that can be used in place of raw data to obtain other
analyses such as factor analysis (with the MATRIX subcommand).
• Obtain correlations of each variable on a list with each variable on a second list (using the keyword
WITH on the VARIABLES subcommand).
See the Command Syntax Reference for complete syntax information.
Partial Correlations
The Partial Correlations procedure computes partial correlation coefficients that describe the linear
relationship between two variables while controlling for the effects of one or more additional variables.
Correlations are measures of linear association. Two variables can be perfectly related, but if the
relationship is not linear, a correlation coefficient is not an appropriate statistic for measuring their
association.
Example
Is there a relationship between healthcare funding and disease rates? Although you might expect any
such relationship to be a negative one, a study reports a significant positive correlation: as healthcare
funding increases, disease rates appear to increase. Controlling for the rate of visits to healthcare
providers, however, virtually eliminates the observed positive correlation. Healthcare funding and
disease rates only appear to be positively related because more people have access to healthcare
when funding increases, which leads to more reported diseases by doctors and hospitals.
Statistics
For each variable: number of cases with nonmissing values, mean, and standard deviation. Partial and
zero-order correlation matrices, with degrees of freedom and significance levels.
Data considerations
Data
Use symmetric, quantitative variables.
Assumptions
The Partial Correlations procedure assumes that each pair of variables is bivariate normal.
Obtaining Partial Correlations
1. From the menus choose:
Analyze > Correlate > Partial…
80 IBM SPSS Statistics Base V27
2. Select two or more numeric variables for which partial correlations are to be computed.
3. Select one or more numeric control variables.
The following options are also available:
Test of Significance
You can select two-tailed or one-tailed probabilities. If the direction of association is known in
advance, select One-tailed. Otherwise, select Two-tailed.
Display actual significance level
By default, the probability and degrees of freedom are shown for each correlation coefficient. If you
deselect this item, coefficients significant at the 0.05 level are identified with a single asterisk,
coefficients significant at the 0.01 level are identified with a double asterisk, and degrees of freedom
are suppressed. This setting affects both partial and zero-order correlation matrices.
Partial Correlations Options
Statistics. You can choose one or both of the following:
• Means and standard deviations. Displayed for each variable. The number of cases with nonmissing
values is also shown.
• Zero-order correlations. A matrix of simple correlations between all variables, including control
variables, is displayed.
Missing Values. You can choose one of the following alternatives:
• Exclude cases listwise. Cases having missing values for any variable, including a control variable, are
excluded from all computations.
• Exclude cases pairwise. For computation of the zero-order correlations on which the partial
correlations are based, a case having missing values for both or one of a pair of variables is not used.
Pairwise deletion uses as much of the data as possible. However, the number of cases may differ across
coefficients. When pairwise deletion is in effect, the degrees of freedom for a particular partial
coefficient are based on the smallest number of cases used in the calculation of any of the zero-order
correlations.
PARTIAL CORR Command Additional Features
The command syntax language also allows you to:
• Read a zero-order correlation matrix or write a partial correlation matrix (with the MATRIX
subcommand).
• Obtain partial correlations between two lists of variables (using the keyword WITH on the VARIABLES
subcommand).
• Obtain multiple analyses (with multiple VARIABLES subcommands).
• Specify order values to request (for example, both first- and second-order partial correlations) when
you have two control variables (with the VARIABLES subcommand).
• Suppress redundant coefficients (with the FORMAT subcommand).
• Display a matrix of simple correlations when some coefficients cannot be computed (with the
STATISTICS subcommand).
See the Command Syntax Reference for complete syntax information.
Distances
This procedure calculates any of a wide variety of statistics measuring either similarities or dissimilarities
(distances), either between pairs of variables or between pairs of cases. These similarity or distance
measures can then be used with other procedures, such as factor analysis, cluster analysis, or
multidimensional scaling, to help analyze complex datasets.
Chapter 1. Core features 81
Example. Is it possible to measure similarities between pairs of automobiles based on certain
characteristics, such as engine size, MPG, and horsepower? By computing similarities between autos, you
can gain a sense of which autos are similar to each other and which are different from each other. For a
more formal analysis, you might consider applying a hierarchical cluster analysis or multidimensional
scaling to the similarities to explore the underlying structure.
Statistics. Dissimilarity (distance) measures for interval data are Euclidean distance, squared Euclidean
distance, Chebychev, block, Minkowski, or customized; for count data, chi-square or phi-square; for
binary data, Euclidean distance, squared Euclidean distance, size difference, pattern difference, variance,
shape, or Lance and Williams. Similarity measures for interval data are Pearson correlation or cosine; for
binary data, Russel and Rao, simple matching, Jaccard, dice, Rogers and Tanimoto, Sokal and Sneath 1,
Sokal and Sneath 2, Sokal and Sneath 3, Kulczynski 1, Kulczynski 2, Sokal and Sneath 4, Hamann,
Lambda, Anderberg’s D, Yule’s Y, Yule’s Q, Ochiai, Sokal and Sneath 5, phi 4-point correlation, or
dispersion.
To Obtain Distance Matrices
1. From the menus choose:
Analyze > Correlate > Distances…
2. Select at least one numeric variable to compute distances between cases, or select at least two
numeric variables to compute distances between variables.
3. Select an alternative in the Compute Distances group to calculate proximities either between cases or
between variables.
Distances Dissimilarity Measures
From the Measure group, select the alternative that corresponds to your type of data (interval, count, or
binary); then, from the drop-down list, select one of the measures that corresponds to that type of data.
Available measures, by data type, are:
• Interval data. Euclidean distance, squared Euclidean distance, Chebychev, block, Minkowski, or
customized.
• Count data. Chi-square measure or phi-square measure.
• Binary data. Euclidean distance, squared Euclidean distance, size difference, pattern difference,
variance, shape, or Lance and Williams. (Enter values for Present and Absent to specify which two
values are meaningful; Distances will ignore all other values.)
The Transform Values group allows you to standardize data values for either cases or variables before
computing proximities. These transformations are not applicable to binary data. Available standardization
methods are z scores, range –1 to 1, range 0 to 1, maximum magnitude of 1, mean of 1, or standard
deviation of 1.
The Transform Measures group allows you to transform the values generated by the distance measure.
They are applied after the distance measure has been computed. Available options are absolute values,
change sign, and rescale to 0–1 range.
Distances Similarity Measures
From the Measure group, select the alternative that corresponds to your type of data (interval or binary);
then, from the drop-down list, select one of the measures that corresponds to that type of data. Available
measures, by data type, are:
• Interval data. Pearson correlation or cosine.
• Binary data. Russell and Rao, simple matching, Jaccard, Dice, Rogers and Tanimoto, Sokal and Sneath
1, Sokal and Sneath 2, Sokal and Sneath 3, Kulczynski 1, Kulczynski 2, Sokal and Sneath 4, Hamann,
Lambda, Anderberg’s D, Yule’s Y, Yule’s Q, Ochiai, Sokal and Sneath 5, phi 4-point correlation, or
dispersion. (Enter values for Present and Absent to specify which two values are meaningful; Distances
will ignore all other values.)
82 IBM SPSS Statistics Base V27
The Transform Values group allows you to standardize data values for either cases or variables before
computing proximities. These transformations are not applicable to binary data. Available standardization
methods are z scores, range –1 to 1, range 0 to 1, maximum magnitude of 1, mean of 1, and standard
deviation of 1.
The Transform Measures group allows you to transform the values generated by the distance measure.
They are applied after the distance measure has been computed. Available options are absolute values,
change sign, and rescale to 0–1 range.
PROXIMITIES Command Additional Features
The Distances procedure uses PROXIMITIES command syntax. The command syntax language also
allows you to:
• Specify any integer as the power for the Minkowski distance measure.
• Specify any integers as the power and root for a customized distance measure.
See the Command Syntax Reference for complete syntax information.
Linear models
Linear models predict a continuous target based on linear relationships between the target and one or
more predictors.
Linear models are relatively simple and give an easily interpreted mathematical formula for scoring. The
properties of these models are well understood and can typically be built very quickly compared to other
model types (such as neural networks or decision trees) on the same dataset.
Example. An insurance company with limited resources to investigate homeowners’ insurance claims
wants to build a model for estimating claims costs. By deploying this model to service centers,
representatives can enter claim information while on the phone with a customer and immediately obtain
the “expected” cost of the claim based on past data.
Field requirements. There must be a Target and at least one Input. By default, fields with predefined
roles of Both or None are not used. The target must be continuous (scale). There are no measurement
level restrictions on predictors (inputs); categorical (nominal, and ordinal) fields are used as factors in the
model and continuous fields are used as covariates.
Note: If a categorical field has more than 1000 categories, the procedure does not run and no model is
built.
To obtain a linear model
This feature requires the Statistics Base option.
From the menus choose:
Analyze > Regression > Automatic Linear Models…
1. Make sure there is at least one target and one input.
2. Click Build Options to specify optional build and model settings.
3. Click Model Options to save scores to the active dataset and export the model to an external file.
4. Click Run to run the procedure and create the Model objects.
Objectives
What is your main objective? Select the appropriate objective.
• Create a standard model. The method builds a single model to predict the target using the predictors.
Generally speaking, standard models are easier to interpret and can be faster to score than boosted,
bagged, or large dataset ensembles.
Chapter 1. Core features 83
• Enhance model accuracy (boosting). The method builds an ensemble model using boosting, which
generates a sequence of models to obtain more accurate predictions. Ensembles can take longer to
build and to score than a standard model.
Boosting produces a succession of “component models”, each of which is built on the entire dataset.
Prior to building each successive component model, the records are weighted based on the previous
component model’s residuals. Cases with large residuals are given relatively higher analysis weights so
that the next component model will focus on predicting these records well. Together these component
models form an ensemble model. The ensemble model scores new records using a combining rule; the
available rules depend upon the measurement level of the target.
• Enhance model stability (bagging). The method builds an ensemble model using bagging (bootstrap
aggregating), which generates multiple models to obtain more reliable predictions. Ensembles can take
longer to build and to score than a standard model.
Bootstrap aggregation (bagging) produces replicates of the training dataset by sampling with
replacement from the original dataset. This creates bootstrap samples of equal size to the original
dataset. Then a “component model” is built on each replicate. Together these component models form
an ensemble model. The ensemble model scores new records using a combining rule; the available
rules depend upon the measurement level of the target.
• Create a model for very large datasets (requires IBM SPSS Statistics Server). The method builds an
ensemble model by splitting the dataset into separate data blocks. Choose this option if your dataset is
too large to build any of the models above, or for incremental model building. This option can take less
time to build, but can take longer to score than a standard model. This option requires IBM SPSS
Statistics Server connectivity.
See “Ensembles ” on page 85 for settings related to boosting, bagging, and very large datasetsboosting
and bagging.
Basics
Automatically prepare data. This option allows the procedure to internally transform the target and
predictors in order to maximize the predictive power of the model; any transformations are saved with the
model and applied to new data for scoring. The original versions of transformed fields are excluded from
the model. By default, the following automatic data preparation are performed.
• Date and Time handling. Each date predictor is transformed into new a continuous predictor
containing the elapsed time since a reference date (1970-01-01). Each time predictor is transformed
into a new continuous predictor containing the time elapsed since a reference time (00:00:00).
• Adjust measurement level. Continuous predictors with less than 5 distinct values are recast as ordinal
predictors. Ordinal predictors with greater than 10 distinct values are recast as continuous predictors.
• Outlier handling. Values of continuous predictors that lie beyond a cutoff value (3 standard deviations
from the mean) are set to the cutoff value.
• Missing value handling. Missing values of nominal predictors are replaced with the mode of the
training partition. Missing values of ordinal predictors are replaced with the median of the training
partition. Missing values of continuous predictors are replaced with the mean of the training partition.
• Supervised merging. This makes a more parsimonious model by reducing the number of fields to be
processed in association with the target. Similar categories are identified based upon the relationship
between the input and the target. Categories that are not significantly different (that is, having a p-value
greater than 0.1) are merged. If all categories are merged into one, the original and derived versions of
the field are excluded from the model because they have no value as a predictor.
Confidence level. This is the level of confidence used to compute interval estimates of the model
coefficients in the Coefficients view. Specify a value greater than 0 and less than 100. The default is 95.
Model Selection
Model selection method. Choose one of the model selection methods (details below) or Include all
predictors, which simply enters all available predictors as main effects model terms. By default, Forward
stepwise is used.
84 IBM SPSS Statistics Base V27
Forward Stepwise Selection. This starts with no effects in the model and adds and removes effects one
step at a time until no more can be added or removed according to the stepwise criteria.
• Criteria for entry/removal. This is the statistic used to determine whether an effect should be added to
or removed from the model. Information Criterion (AICC) is based on the likelihood of the training set
given the model, and is adjusted to penalize overly complex models. F Statistics is based on a
statistical test of the improvement in model error. Adjusted R-squared is based on the fit of the training
set, and is adjusted to penalize overly complex models. Overfit Prevention Criterion (ASE) is based on
the fit (average squared error, or ASE) of the overfit prevention set. The overfit prevention set is a
random subsample of approximately 30% of the original dataset that is not used to train the model.
If any criterion other than F Statistics is chosen, then at each step the effect that corresponds to the
greatest positive increase in the criterion is added to the model. Any effects in the model that
correspond to a decrease in the criterion are removed.
If F Statistics is chosen as the criterion, then at each step the effect that has the smallest p-value less
than the specified threshold, Include effects with p-values less than, is added to the model. The
default is 0.05. Any effects in the model with a p-value greater than the specified threshold, Remove
effects with p-values greater than, are removed. The default is 0.10.
• Customize maximum number of effects in the final model. By default, all available effects can be
entered into the model. Alternatively, if the stepwise algorithm ends a step with the specified maximum
number of effects, the algorithm stops with the current set of effects.
• Customize maximum number of steps. The stepwise algorithm stops after a certain number of steps.
By default, this is 3 times the number of available effects. Alternatively, specify a positive integer
maximum number of steps.
Best Subsets Selection. This checks “all possible” models, or at least a larger subset of the possible
models than forward stepwise, to choose the best according to the best subsets criterion. Information
Criterion (AICC) is based on the likelihood of the training set given the model, and is adjusted to penalize
overly complex models. Adjusted R-squared is based on the fit of the training set, and is adjusted to
penalize overly complex models. Overfit Prevention Criterion (ASE) is based on the fit (average squared
error, or ASE) of the overfit prevention set. The overfit prevention set is a random subsample of
approximately 30% of the original dataset that is not used to train the model.
The model with the greatest value of the criterion is chosen as the best model.
Note: Best subsets selection is more computationally intensive than forward stepwise selection. When
best subsets is performed in conjunction with boosting, bagging, or very large datasets, it can take
considerably longer to build than a standard model built using forward stepwise selection.
Ensembles
These settings determine the behavior of ensembling that occurs when boosting, bagging, or very large
datasets are requested in Objectives. Options that do not apply to the selected objective are ignored.
Bagging and Very Large Datasets. When scoring an ensemble, this is the rule used to combine the
predicted values from the base models to compute the ensemble score value.
• Default combining rule for continuous targets. Ensemble predicted values for continuous targets can
be combined using the mean or median of the predicted values from the base models.
Note that when the objective is to enhance model accuracy, the combining rule selections are ignored.
Boosting always uses a weighted majority vote to score categorical targets and a weighted median to
score continuous targets.
Boosting and Bagging. Specify the number of base models to build when the objective is to enhance
model accuracy or stability; for bagging, this is the number of bootstrap samples. It should be a positive
integer.
Chapter 1. Core features 85
Advanced
Replicate results. Setting a random seed allows you to replicate analyses. The random number generator
is used to choose which records are in the overfit prevention set. Specify an integer or click Generate,
which will create a pseudo-random integer between 1 and 2147483647, inclusive. The default is
54752075.
Model Options
Save predicted values to the dataset. The default variable name is PredictedValue.
Export model. This writes the model to an external .zip file. You can use this model file to apply the
model information to other data files for scoring purposes. Specify a unique, valid file name. If the file
specification refers to an existing file, then the file is overwritten.
Model Summary
The Model Summary view is a snapshot, at-a-glance summary of the model and its fit.
Table. The table identifies some high-level model settings, including:
• The name of the target specified on the Fields tab,
• Whether automatic data preparation was performed as specified on the Basicssettings,
• The model selection method and selection criterion specified on the Model Selectionsettings. The value
of the selection criterion for the final model is also displayed, and is presented in smaller is better
format.
Chart. The chart displays the accuracy of the final model, which is presented in larger is better format.
The value is 100 × the adjusted R 2 for the final model.
Automatic Data Preparation
This view shows information about which fields were excluded and how transformed fields were derived
in the automatic data preparation (ADP) step. For each field that was transformed or excluded, the table
lists the field name, its role in the analysis, and the action taken by the ADP step. Fields are sorted by
ascending alphabetical order of field names. The possible actions taken for each field include:
• Derive duration: months computes the elapsed time in months from the values in a field containing
dates to the current system date.
• Derive duration: hours computes the elapsed time in hours from the values in a field containing times
to the current system time.
• Change measurement level from continuous to ordinal recasts continuous fields with less than 5
unique values as ordinal fields.
• Change measurement level from ordinal to continuous recasts ordinal fields with more than 10
unique values as continuous fields.
• Trim outliers sets values of continuous predictors that lie beyond a cutoff value (3 standard deviations
from the mean) to the cutoff value.
• Replace missing values replaces missing values of nominal fields with the mode, ordinal fields with the
median, and continuous fields with the mean.
• Merge categories to maximize association with target identifies “similar” predictor categories based
upon the relationship between the input and the target. Categories that are not significantly different
(that is, having a p-value greater than 0.05) are merged.
• Exclude constant predictor / after outlier handling / after merging of categories removes predictors
that have a single value, possibly after other ADP actions have been taken.
Predictor Importance
Typically, you will want to focus your modeling efforts on the predictor fields that matter most and
consider dropping or ignoring those that matter least. The predictor importance chart helps you do this by
86 IBM SPSS Statistics Base V27
indicating the relative importance of each predictor in estimating the model. Since the values are relative,
the sum of the values for all predictors on the display is 1.0. Predictor importance does not relate to
model accuracy. It just relates to the importance of each predictor in making a prediction, not whether or
not the prediction is accurate.
Predicted By Observed
This displays a binned scatterplot of the predicted values on the vertical axis by the observed values on
the horizontal axis. Ideally, the points should lie on a 45-degree line; this view can tell you whether any
records are predicted particularly badly by the model.
Residuals
This displays a diagnostic chart of model residuals.
Chart styles. There are different display styles, which are accessible from the Style dropdown list.
• Histogram. This is a binned histogram of the studentized residuals with an overlay of the normal
distribution. Linear models assume that the residuals have a normal distribution, so the histogram
should ideally closely approximate the smooth line.
• P-P Plot. This is a binned probability-probability plot comparing the studentized residuals to a normal
distribution. If the slope of the plotted points is less steep than the normal line, the residuals show
greater variability than a normal distribution; if the slope is steeper, the residuals show less variability
than a normal distribution. If the plotted points have an S-shaped curve, then the distribution of
residuals is skewed.
Outliers
This table lists records that exert undue influence upon the model, and displays the record ID (if specified
on the Fields tab), target value, and Cook’s distance. Cook’s distance is a measure of how much the
residuals of all records would change if a particular record were excluded from the calculation of the
model coefficients. A large Cook’s distance indicates that excluding a record from changes the
coefficients substantially, and should therefore be considered influential.
Influential records should be examined carefully to determine whether you can give them less weight in
estimating the model, or truncate the outlying values to some acceptable threshold, or remove the
influential records completely.
Effects
This view displays the size of each effect in the model.
Styles. There are different display styles, which are accessible from the Style dropdown list.
• Diagram. This is a chart in which effects are sorted from top to bottom by decreasing predictor
importance. Connecting lines in the diagram are weighted based on effect significance, with greater line
width corresponding to more significant effects (smaller p-values). Hovering over a connecting line
reveals a tooltip that shows the p-value and importance of the effect. This is the default.
• Table. This is an ANOVA table for the overall model and the individual model effects. The individual
effects are sorted from top to bottom by decreasing predictor importance. Note that by default, the
table is collapsed to only show the results for the overall model. To see the results for the individual
model effects, click the Corrected Model cell in the table.
Predictor importance. There is a Predictor Importance slider that controls which predictors are shown in
the view. This does not change the model, but simply allows you to focus on the most important
predictors. By default, the top 10 effects are displayed.
Significance. There is a Significance slider that further controls which effects are shown in the view,
beyond those shown based on predictor importance. Effects with significance values greater than the
slider value are hidden. This does not change the model, but simply allows you to focus on the most
important effects. By default the value is 1.00, so that no effects are filtered based on significance.
Chapter 1. Core features 87
Coefficients
This view displays the value of each coefficient in the model. Note that factors (categorical predictors) are
indicator-coded within the model, so that effects containing factors will generally have multiple
associated coefficients; one for each category except the category corresponding to the redundant
(reference) parameter.
Styles. There are different display styles, which are accessible from the Style dropdown list.
• Diagram. This is a chart which displays the intercept first, and then sorts effects from top to bottom by
decreasing predictor importance. Within effects containing factors, coefficients are sorted by ascending
order of data values. Connecting lines in the diagram are colored based on the sign of the coefficient
(see the diagram key) and weighted based on coefficient significance, with greater line width
corresponding to more significant coefficients (smaller p-values). Hovering over a connecting line
reveals a tooltip that shows the value of the coefficient, its p-value, and the importance of the effect the
parameter is associated with. This is the default style.
• Table. This shows the values, significance tests, and confidence intervals for the individual model
coefficients. After the intercept, the effects are sorted from top to bottom by decreasing predictor
importance. Within effects containing factors, coefficients are sorted by ascending order of data values.
Note that by default the table is collapsed to only show the coefficient, significance, and importance of
each model parameter. To see the standard error, t statistic, and confidence interval, click the
Coefficient cell in the table. Hovering over the name of a model parameter in the table reveals a tooltip
that shows the name of the parameter, the effect the parameter is associated with, and (for categorical
predictors), the value labels associated with the model parameter. This can be particularly useful to see
the new categories created when automatic data preparation merges similar categories of a categorical
predictor.
Predictor importance. There is a Predictor Importance slider that controls which predictors are shown in
the view. This does not change the model, but simply allows you to focus on the most important
predictors. By default, the top 10 effects are displayed.
Significance. There is a Significance slider that further controls which coefficients are shown in the view,
beyond those shown based on predictor importance. Coefficients with significance values greater than
the slider value are hidden. This does not change the model, but simply allows you to focus on the most
important coefficients. By default the value is 1.00, so that no coefficients are filtered based on
significance.
Estimated Means
These are charts displayed for significant predictors. The chart displays the model-estimated value of the
target on the vertical axis for each value of the predictor on the horizontal axis, holding all other
predictors constant. It provides a useful visualization of the effects of each predictor’s coefficients on the
target.
Note: if no predictors are significant, no estimated means are produced.
Model Building Summary
When a model selection algorithm other than None is chosen on the Model Selection settings, this
provides some details of the model building process.
Forward stepwise. When forward stepwise is the selection algorithm, the table displays the last 10 steps
in the stepwise algorithm. For each step, the value of the selection criterion and the effects in the model
at that step are shown. This gives you a sense of how much each step contributes to the model. Each
column allows you to sort the rows so that you can more easily see which effects are in the model at a
given step.
Best subsets. When best subsets is the selection algorithm, the table displays the top 10 models. For
each model, the value of the selection criterion and the effects in the model are shown. This gives you a
sense of the stability of the top models; if they tend to have many similar effects with a few differences,
then you can be fairly confident in the “top” model; if they tend to have very different effects, then some
88 IBM SPSS Statistics Base V27
of the effects may be too similar and should be combined (or one removed). Each column allows you to
sort the rows so that you can more easily see which effects are in the model at a given step.
Linear Regression
Linear Regression estimates the coefficients of the linear equation, involving one or more independent
variables, that best predict the value of the dependent variable. For example, you can try to predict a
salesperson’s total yearly sales (the dependent variable) from independent variables such as age,
education, and years of experience.
Example. Is the number of games won by a basketball team in a season related to the average number of
points the team scores per game? A scatterplot indicates that these variables are linearly related. The
number of games won and the average number of points scored by the opponent are also linearly related.
These variables have a negative relationship. As the number of games won increases, the average number
of points scored by the opponent decreases. With linear regression, you can model the relationship of
these variables. A good model can be used to predict how many games teams will win.
Statistics. For each variable: number of valid cases, mean, and standard deviation. For each model:
regression coefficients, correlation matrix, part and partial correlations, multiple R, R 2, adjusted R 2,
change in R 2, standard error of the estimate, analysis-of-variance table, predicted values, and residuals.
Also, 95%-confidence intervals for each regression coefficient, variance-covariance matrix, variance
inflation factor, tolerance, Durbin-Watson test, distance measures (Mahalanobis, Cook, and leverage
values), DfBeta, DfFit, prediction intervals, and casewise diagnostic information. Plots: scatterplots,
partial plots, histograms, and normal probability plots.
Linear Regression Data Considerations
Data. The dependent and independent variables should be quantitative. Categorical variables, such as
religion, major field of study, or region of residence, need to be recoded to binary (dummy) variables or
other types of contrast variables.
Assumptions. For each value of the independent variable, the distribution of the dependent variable must
be normal. The variance of the distribution of the dependent variable should be constant for all values of
the independent variable. The relationship between the dependent variable and each independent
variable should be linear, and all observations should be independent.
To Obtain a Linear Regression Analysis
1. From the menus choose:
Analyze > Regression > Linear…
2. In the Linear Regression dialog box, select a numeric dependent variable.
3. Select one or more numeric independent variables.
Optionally, you can:
• Group independent variables into blocks and specify different entry methods for different subsets of
variables.
• Choose a selection variable to limit the analysis to a subset of cases having a particular value(s) for this
variable.
• Select a case identification variable for identifying points on plots.
• Select a numeric WLS Weight variable for a weighted least squares analysis.
WLS. Allows you to obtain a weighted least-squares model. Data points are weighted by the reciprocal of
their variances. This means that observations with large variances have less impact on the analysis than
observations associated with small variances. If the value of the weighting variable is zero, negative, or
missing, the case is excluded from the analysis.
Linear Regression Variable Selection Methods
Method selection allows you to specify how independent variables are entered into the analysis. Using
different methods, you can construct a variety of regression models from the same set of variables.
Chapter 1. Core features 89
• Enter (Regression). A procedure for variable selection in which all variables in a block are entered in a
single step.
• Stepwise. At each step, the independent variable not in the equation that has the smallest probability of
F is entered, if that probability is sufficiently small. Variables already in the regression equation are
removed if their probability of F becomes sufficiently large. The method terminates when no more
variables are eligible for inclusion or removal.
• Remove. A procedure for variable selection in which all variables in a block are removed in a single step.
• Backward Elimination. A variable selection procedure in which all variables are entered into the
equation and then sequentially removed. The variable with the smallest partial correlation with the
dependent variable is considered first for removal. If it meets the criterion for elimination, it is removed.
After the first variable is removed, the variable remaining in the equation with the smallest partial
correlation is considered next. The procedure stops when there are no variables in the equation that
satisfy the removal criteria.
• Forward Selection. A stepwise variable selection procedure in which variables are sequentially entered
into the model. The first variable considered for entry into the equation is the one with the largest
positive or negative correlation with the dependent variable. This variable is entered into the equation
only if it satisfies the criterion for entry. If the first variable is entered, the independent variable not in
the equation that has the largest partial correlation is considered next. The procedure stops when there
are no variables that meet the entry criterion.
The significance values in your output are based on fitting a single model. Therefore, the significance
values are generally invalid when a stepwise method (stepwise, forward, or backward) is used.
All variables must pass the tolerance criterion to be entered in the equation, regardless of the entry
method specified. The default tolerance level is 0.0001. Also, a variable is not entered if it would cause
the tolerance of another variable already in the model to drop below the tolerance criterion.
All independent variables selected are added to a single regression model. However, you can specify
different entry methods for different subsets of variables. For example, you can enter one block of
variables into the regression model using stepwise selection and a second block using forward selection.
To add a second block of variables to the regression model, click Next.
Linear Regression Set Rule
Cases defined by the selection rule are included in the analysis. For example, if you select a variable,
choose equals, and type 5 for the value, then only cases for which the selected variable has a value equal
to 5 are included in the analysis. A string value is also permitted.
Linear Regression Plots
Plots can aid in the validation of the assumptions of normality, linearity, and equality of variances. Plots
are also useful for detecting outliers, unusual observations, and influential cases. After saving them as
new variables, predicted values, residuals, and other diagnostic information are available in the Data
Editor for constructing plots with the independent variables. The following plots are available:
Scatterplots. You can plot any two of the following: the dependent variable, standardized predicted
values, standardized residuals, deleted residuals, adjusted predicted values, Studentized residuals, or
Studentized deleted residuals. Plot the standardized residuals against the standardized predicted values
to check for linearity and equality of variances.
Source variable list. Lists the dependent variable (DEPENDNT) and the following predicted and residual
variables: Standardized predicted values (*ZPRED), Standardized residuals (*ZRESID), Deleted residuals
(*DRESID), Adjusted predicted values (*ADJPRED), Studentized residuals (*SRESID), Studentized deleted
residuals (*SDRESID).
Produce all partial plots. Displays scatterplots of residuals of each independent variable and the
residuals of the dependent variable when both variables are regressed separately on the rest of the
independent variables. At least two independent variables must be in the equation for a partial plot to be
produced.
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Standardized Residual Plots. You can obtain histograms of standardized residuals and normal
probability plots comparing the distribution of standardized residuals to a normal distribution.
If any plots are requested, summary statistics are displayed for standardized predicted values and
standardized residuals (*ZPRED and *ZRESID).
Linear Regression: Saving New Variables
You can save predicted values, residuals, and other statistics useful for diagnostic information. Each
selection adds one or more new variables to your active data file.
Predicted Values. Values that the regression model predicts for each case.
• Unstandardized. The value the model predicts for the dependent variable.
• Standardized. A transformation of each predicted value into its standardized form. That is, the mean
predicted value is subtracted from the predicted value, and the difference is divided by the standard
deviation of the predicted values. Standardized predicted values have a mean of 0 and a standard
deviation of 1.
• Adjusted. The predicted value for a case when that case is excluded from the calculation of the
regression coefficients.
• S.E. of mean predictions. Standard errors of the predicted values. An estimate of the standard deviation
of the average value of the dependent variable for cases that have the same values of the independent
variables.
Distances. Measures to identify cases with unusual combinations of values for the independent variables
and cases that may have a large impact on the regression model.
• Mahalanobis. A measure of how much a case’s values on the independent variables differ from the
average of all cases. A large Mahalanobis distance identifies a case as having extreme values on one or
more of the independent variables.
• Cook’s. A measure of how much the residuals of all cases would change if a particular case were
excluded from the calculation of the regression coefficients. A large Cook’s D indicates that excluding a
case from computation of the regression statistics changes the coefficients substantially.
• Leverage values. Measures the influence of a point on the fit of the regression. The centered leverage
ranges from 0 (no influence on the fit) to (N-1)/N.
Prediction Intervals. The upper and lower bounds for both mean and individual prediction intervals.
• Mean. Lower and upper bounds (two variables) for the prediction interval of the mean predicted
response.
• Individual. Lower and upper bounds (two variables) for the prediction interval of the dependent variable
for a single case.
• Confidence Interval. Enter a value between 1 and 99.99 to specify the confidence level for the two
Prediction Intervals. Mean or Individual must be selected before entering this value. Typical confidence
interval values are 90, 95, and 99.
Residuals. The actual value of the dependent variable minus the value predicted by the regression
equation.
• Unstandardized. The difference between an observed value and the value predicted by the model.
• Standardized. The residual divided by an estimate of its standard deviation. Standardized residuals,
which are also known as Pearson residuals, have a mean of 0 and a standard deviation of 1.
• Studentized. The residual divided by an estimate of its standard deviation that varies from case to case,
depending on the distance of each case’s values on the independent variables from the means of the
independent variables.
• Deleted. The residual for a case when that case is excluded from the calculation of the regression
coefficients. It is the difference between the value of the dependent variable and the adjusted predicted
value.
Chapter 1. Core features 91
• Studentized deleted. The deleted residual for a case divided by its standard error. The difference
between a Studentized deleted residual and its associated Studentized residual indicates how much
difference eliminating a case makes on its own prediction.
Influence Statistics. The change in the regression coefficients (DfBeta[s]) and predicted values (DfFit)
that results from the exclusion of a particular case. Standardized DfBetas and DfFit values are also
available along with the covariance ratio.
• DfBeta(s). The difference in beta value is the change in the regression coefficient that results from the
exclusion of a particular case. A value is computed for each term in the model, including the constant.
• Standardized DfBeta. Standardized difference in beta value. The change in the regression coefficient
that results from the exclusion of a particular case. You may want to examine cases with absolute
values greater than 2 divided by the square root of N, where N is the number of cases. A value is
computed for each term in the model, including the constant.
• DfFit. The difference in fit value is the change in the predicted value that results from the exclusion of a
particular case.
• Standardized DfFit. Standardized difference in fit value. The change in the predicted value that results
from the exclusion of a particular case. You may want to examine standardized values which in absolute
value exceed 2 times the square root of p/N, where p is the number of parameters in the model and N is
the number of cases.
• Covariance ratio. The ratio of the determinant of the covariance matrix with a particular case excluded
from the calculation of the regression coefficients to the determinant of the covariance matrix with all
cases included. If the ratio is close to 1, the case does not significantly alter the covariance matrix.
Coefficient Statistics. Saves regression coefficients to a dataset or a data file. Datasets are available for
subsequent use in the same session but are not saved as files unless explicitly saved prior to the end of
the session. Dataset names must conform to variable naming rules.
Export model information to XML file. Parameter estimates and (optionally) their covariances are
exported to the specified file in XML (PMML) format. You can use this model file to apply the model
information to other data files for scoring purposes.
Linear Regression Statistics
The following statistics are available:
Regression Coefficients. Estimates displays Regression coefficient B, standard error of B, standardized
coefficient beta, t value for B, and two-tailed significance level of t. Confidence intervals displays
confidence intervals with the specified level of confidence for each regression coefficient or a covariance
matrix. Covariance matrix displays a variance-covariance matrix of regression coefficients with
covariances off the diagonal and variances on the diagonal. A correlation matrix is also displayed.
Model fit. The variables entered and removed from the model are listed, and the following goodness-of-
fit statistics are displayed: multiple R, R 2 and adjusted R 2, standard error of the estimate, and an
analysis-of-variance table.
R squared change. The change in the R 2 statistic that is produced by adding or deleting an independent
variable. If the R 2 change associated with a variable is large, that means that the variable is a good
predictor of the dependent variable.
Descriptives. Provides the number of valid cases, the mean, and the standard deviation for each variable
in the analysis. A correlation matrix with a one-tailed significance level and the number of cases for each
correlation are also displayed.
Partial Correlation. The correlation that remains between two variables after removing the correlation that
is due to their mutual association with the other variables. The correlation between the dependent
variable and an independent variable when the linear effects of the other independent variables in the
model have been removed from both.
Part Correlation. The correlation between the dependent variable and an independent variable when the
linear effects of the other independent variables in the model have been removed from the independent
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variable. It is related to the change in R-squared when a variable is added to an equation. Sometimes
called the semipartial correlation.
Collinearity diagnostics. Collinearity (or multicollinearity) is the undesirable situation when one
independent variable is a linear function of other independent variables. Eigenvalues of the scaled and
uncentered cross-products matrix, condition indices, and variance-decomposition proportions are
displayed along with variance inflation factors (VIF) and tolerances for individual variables.
Residuals. Displays the Durbin-Watson test for serial correlation of the residuals and casewise diagnostic
information for the cases meeting the selection criterion (outliers above n standard deviations).
Linear Regression Options
The following options are available:
Stepping Method Criteria. These options apply when either the forward, backward, or stepwise variable
selection method has been specified. Variables can be entered or removed from the model depending on
either the significance (probability) of the F value or the F value itself.
• Use Probability of F. A variable is entered into the model if the significance level of its F value is less than
the Entry value and is removed if the significance level is greater than the Removal value. Entry must be
less than Removal, and both values must be positive. To enter more variables into the model, increase
the Entry value. To remove more variables from the model, lower the Removal value.
• Use F Value. A variable is entered into the model if its F value is greater than the Entry value and is
removed if the F value is less than the Removal value. Entry must be greater than Removal, and both
values must be positive. To enter more variables into the model, lower the Entry value. To remove more
variables from the model, increase the Removal value.
Include constant in equation. By default, the regression model includes a constant term. Deselecting
this option forces regression through the origin, which is rarely done. Some results of regression through
the origin are not comparable to results of regression that do include a constant. For example, R 2 cannot
be interpreted in the usual way.
Missing Values. You can choose one of the following:
• Exclude cases listwise. Only cases with valid values for all variables are included in the analyses.
• Exclude cases pairwise. Cases with complete data for the pair of variables being correlated are used to
compute the correlation coefficient on which the regression analysis is based. Degrees of freedom are
based on the minimum pairwise N.
• Replace with mean. All cases are used for computations, with the mean of the variable substituted for
missing observations.
REGRESSION Command Additional Features
The command syntax language also allows you to:
• Write a correlation matrix or read a matrix in place of raw data to obtain your regression analysis (with
the MATRIX subcommand).
• Specify tolerance levels (with the CRITERIA subcommand).
• Obtain multiple models for the same or different dependent variables (with the METHOD and
DEPENDENT subcommands).
• Obtain additional statistics (with the DESCRIPTIVES and STATISTICS subcommands).
See the Command Syntax Reference for complete syntax information.
Ordinal Regression
Ordinal Regression allows you to model the dependence of a polytomous ordinal response on a set of
predictors, which can be factors or covariates. The design of Ordinal Regression is based on the
methodology of McCullagh (1980, 1998), and the procedure is referred to as PLUM in the syntax.
Chapter 1. Core features 93
Standard linear regression analysis involves minimizing the sum-of-squared differences between a
response (dependent) variable and a weighted combination of predictor (independent) variables. The
estimated coefficients reflect how changes in the predictors affect the response. The response is
assumed to be numerical, in the sense that changes in the level of the response are equivalent
throughout the range of the response. For example, the difference in height between a person who is 150
cm tall and a person who is 140 cm tall is 10 cm, which has the same meaning as the difference in height
between a person who is 210 cm tall and a person who is 200 cm tall. These relationships do not
necessarily hold for ordinal variables, in which the choice and number of response categories can be quite
arbitrary.
Example. Ordinal Regression could be used to study patient reaction to drug dosage. The possible
reactions may be classified as none, mild, moderate, or severe. The difference between a mild and
moderate reaction is difficult or impossible to quantify and is based on perception. Moreover, the
difference between a mild and moderate response may be greater or less than the difference between a
moderate and severe response.
Statistics and plots. Observed and expected frequencies and cumulative frequencies, Pearson residuals
for frequencies and cumulative frequencies, observed and expected probabilities, observed and expected
cumulative probabilities of each response category by covariate pattern, asymptotic correlation and
covariance matrices of parameter estimates, Pearson’s chi-square and likelihood-ratio chi-square,
goodness-of-fit statistics, iteration history, test of parallel lines assumption, parameter estimates,
standard errors, confidence intervals, and Cox and Snell’s, Nagelkerke’s, and McFadden’s R 2 statistics.
Ordinal Regression Data Considerations
Data. The dependent variable is assumed to be ordinal and can be numeric or string. The ordering is
determined by sorting the values of the dependent variable in ascending order. The lowest value defines
the first category. Factor variables are assumed to be categorical. Covariate variables must be numeric.
Note that using more than one continuous covariate can easily result in the creation of a very large cell
probabilities table.
Assumptions. Only one response variable is allowed, and it must be specified. Also, for each distinct
pattern of values across the independent variables, the responses are assumed to be independent
multinomial variables.
Related procedures. Nominal logistic regression uses similar models for nominal dependent variables.
Obtaining an Ordinal Regression
1. From the menus choose:
Analyze > Regression > Ordinal…
2. Select one dependent variable.
3. Click OK.
Ordinal Regression Options
The Options dialog box allows you to adjust parameters used in the iterative estimation algorithm, choose
a level of confidence for your parameter estimates, and select a link function.
Iterations. You can customize the iterative algorithm.
• Maximum iterations. Specify a non-negative integer. If 0 is specified, the procedure returns the initial
estimates.
• Maximum step-halving. Specify a positive integer.
• Log-likelihood convergence. The algorithm stops if the absolute or relative change in the log-likelihood
is less than this value. The criterion is not used if 0 is specified.
• Parameter convergence. The algorithm stops if the absolute or relative change in each of the
parameter estimates is less than this value. The criterion is not used if 0 is specified.
Confidence interval. Specify a value greater than or equal to 0 and less than 100.
Delta. The value added to zero cell frequencies. Specify a non-negative value less than 1.
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Singularity tolerance. Used for checking for highly dependent predictors. Select a value from the list of
options.
Link function. The link function is a transformation of the cumulative probabilities that allows estimation
of the model. The following five link functions are available.
• Logit. f(x)=log(x/(1−x) ). Typically used for evenly distributed categories.
• Complementary log-log. f(x)=log(−log(1−x)). Typically used when higher categories are more probable.
• Negative log-log. f(x)=−log(−log(x)). Typically used when lower categories are more probable.
• Probit. f(x)=Φ−1(x). Typically used when the latent variable is normally distributed.
• Cauchit (inverse Cauchy). f(x)=tan(π(x−0.5)). Typically used when the latent variable has many
extreme values.
Ordinal Regression Output
The Output dialog box allows you to produce tables for display in the Viewer and save variables to the
working file.
Display. Produces tables for:
• Print iteration history for every n step(s). The log-likelihood and parameter estimates are printed for
the print iteration frequency specified. The first and last iterations are always printed.
• Goodness of fit statistics. The Pearson and likelihood-ratio chi-square statistics. They are computed
based on the classification specified in the variable list.
• Summary statistics. Cox and Snell’s, Nagelkerke’s, and McFadden’s R 2 statistics.
• Parameter estimates. Parameter estimates, standard errors, and confidence intervals.
• Asymptotic correlation of parameter estimates. Matrix of parameter estimate correlations.
• Asymptotic covariance of parameter estimates. Matrix of parameter estimate covariances.
• Cell information. Observed and expected frequencies and cumulative frequencies, Pearson residuals
for frequencies and cumulative frequencies, observed and expected probabilities, and observed and
expected cumulative probabilities of each response category by covariate pattern. Note that for models
with many covariate patterns (for example, models with continuous covariates), this option can
generate a very large, unwieldy table.
• Test of parallel lines. Test of the hypothesis that the location parameters are equivalent across the
levels of the dependent variable. This is available only for the location-only model.
Saved Variables. Saves the following variables to the working file:
• Estimated response probabilities. Model-estimated probabilities of classifying a factor/covariate
pattern into the response categories. There are as many probabilities as the number of response
categories.
• Predicted category. The response category that has the maximum estimated probability for a factor/
covariate pattern.
• Predicted category probability. Estimated probability of classifying a factor/covariate pattern into the
predicted category. This probability is also the maximum of the estimated probabilities of the factor/
covariate pattern.
• Actual category probability. Estimated probability of classifying a factor/covariate pattern into the
actual category.
Print Log-Likelihood. Controls the display of the log-likelihood. Including multinomial constant gives
you the full value of the likelihood. To compare your results across products that do not include the
constant, you can choose to exclude it.
Ordinal Regression Location Model
The Location dialog box allows you to specify the location model for your analysis.
Chapter 1. Core features 95
Specify model. A main-effects model contains the covariate and factor main effects but no interaction
effects. You can create a custom model to specify subsets of factor interactions or covariate interactions.
Factors/covariates. The factors and covariates are listed.
Location model. The model depends on the main effects and interaction effects that you select.
For the selected factors and covariates:
Interaction
Creates the highest-level interaction term of all selected variables. This is the default.
Main effects
Creates a main-effects term for each variable selected.
All 2-way
Creates all possible two-way interactions of the selected variables.
All 3-way
Creates all possible three-way interactions of the selected variables.
All 4-way
Creates all possible four-way interactions of the selected variables.
All 5-way
Creates all possible five-way interactions of the selected variables.
Build Terms and Custom Terms
Build terms
Use this choice when you want to include non-nested terms of a certain type (such as main effects)
for all combinations of a selected set of factors and covariates.
Build custom terms
Use this choice when you want to include nested terms or when you want to explicitly build any term
variable by variable. Building a nested term involves the following steps:
Ordinal Regression Scale Model
The Scale dialog box allows you to specify the scale model for your analysis.
Factors/covariates. The factors and covariates are listed.
Scale model. The model depends on the main and interaction effects that you select.
For the selected factors and covariates:
Interaction
Creates the highest-level interaction term of all selected variables. This is the default.
Main effects
Creates a main-effects term for each variable selected.
All 2-way
Creates all possible two-way interactions of the selected variables.
All 3-way
Creates all possible three-way interactions of the selected variables.
All 4-way
Creates all possible four-way interactions of the selected variables.
All 5-way
Creates all possible five-way interactions of the selected variables.
Build Terms and Custom Terms
Build terms
Use this choice when you want to include non-nested terms of a certain type (such as main effects)
for all combinations of a selected set of factors and covariates.
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Build custom terms
Use this choice when you want to include nested terms or when you want to explicitly build any term
variable by variable. Building a nested term involves the following steps:
PLUM Command Additional Features
You can customize your Ordinal Regression if you paste your selections into a syntax window and edit the
resulting PLUM command syntax. The command syntax language also allows you to:
• Create customized hypothesis tests by specifying null hypotheses as linear combinations of
parameters.
See the Command Syntax Reference for complete syntax information.
Curve Estimation
The Curve Estimation procedure produces curve estimation regression statistics and related plots for 11
different curve estimation regression models. A separate model is produced for each dependent variable.
You can also save predicted values, residuals, and prediction intervals as new variables.
Example. An Internet service provider tracks the percentage of virus-infected e-mail traffic on its
networks over time. A scatterplot reveals that the relationship is nonlinear. You might fit a quadratic or
cubic model to the data and check the validity of assumptions and the goodness of fit of the model.
Statistics. For each model: regression coefficients, multiple R, R 2, adjusted R 2, standard error of the
estimate, analysis-of-variance table, predicted values, residuals, and prediction intervals. Models: linear,
logarithmic, inverse, quadratic, cubic, power, compound, S-curve, logistic, growth, and exponential.
Curve Estimation Data Considerations
Data. The dependent and independent variables should be quantitative. If you select Time from the
active dataset as the independent variable (instead of selecting a variable), the Curve Estimation
procedure generates a time variable where the length of time between cases is uniform. If Time is
selected, the dependent variable should be a time-series measure. Time-series analysis requires a data
file structure in which each case (row) represents a set of observations at a different time and the length
of time between cases is uniform.
Assumptions. Screen your data graphically to determine how the independent and dependent variables
are related (linearly, exponentially, etc.). The residuals of a good model should be randomly distributed
and normal. If a linear model is used, the following assumptions should be met: For each value of the
independent variable, the distribution of the dependent variable must be normal. The variance of the
distribution of the dependent variable should be constant for all values of the independent variable. The
relationship between the dependent variable and the independent variable should be linear, and all
observations should be independent.
To Obtain a Curve Estimation
1. From the menus choose:
Analyze > Regression > Curve Estimation…
2. Select one or more dependent variables. A separate model is produced for each dependent variable.
3. Select an independent variable (either select a variable in the active dataset or select Time).
4. Optionally:
• Select a variable for labeling cases in scatterplots. For each point in the scatterplot, you can use the
Point Selection tool to display the value of the Case Label variable.
• Click Save to save predicted values, residuals, and prediction intervals as new variables.
The following options are also available:
• Include constant in equation. Estimates a constant term in the regression equation. The constant is
included by default.
Chapter 1. Core features 97
• Plot models. Plots the values of the dependent variable and each selected model against the
independent variable. A separate chart is produced for each dependent variable.
• Display ANOVA table. Displays a summary analysis-of-variance table for each selected model.
Curve Estimation Models
You can choose one or more curve estimation regression models. To determine which model to use, plot
your data. If your variables appear to be related linearly, use a simple linear regression model. When your
variables are not linearly related, try transforming your data. When a transformation does not help, you
may need a more complicated model. View a scatterplot of your data; if the plot resembles a
mathematical function you recognize, fit your data to that type of model. For example, if your data
resemble an exponential function, use an exponential model.
Linear. Model whose equation is Y = b0 + (b1 * t). The series values are modeled as a linear function of
time.
Logarithmic. Model whose equation is Y = b0 + (b1 * ln(t)).
Inverse. Model whose equation is Y = b0 + (b1 / t).
Quadratic. Model whose equation is Y = b0 + (b1 * t) + (b2 * t**2). The quadratic model can be used to
model a series that “takes off” or a series that dampens.
Cubic. Model that is defined by the equation Y = b0 + (b1 * t) + (b2 * t**2) + (b3 * t**3).
Power. Model whose equation is Y = b0 * (t**b1) or ln(Y) = ln(b0) + (b1 * ln(t)).
Compound. Model whose equation is Y = b0 * (b1**t) or ln(Y) = ln(b0) + (ln(b1) * t).
S-curve. Model whose equation is Y = e**(b0 + (b1/t)) or ln(Y) = b0 + (b1/t).
Logistic. Model whose equation is Y = 1 / (1/u + (b0 * (b1**t))) or ln(1/y-1/u) = ln (b0) + (ln(b1) * t) where u
is the upper boundary value. After selecting Logistic, specify the upper boundary value to use in the
regression equation. The value must be a positive number that is greater than the largest dependent
variable value.
Growth. Model whose equation is Y = e**(b0 + (b1 * t)) or ln(Y) = b0 + (b1 * t).
Exponential. Model whose equation is Y = b0 * (e**(b1 * t)) or ln(Y) = ln(b0) + (b1 * t).
Curve Estimation Save
Save Variables. For each selected model, you can save predicted values, residuals (observed value of the
dependent variable minus the model predicted value), and prediction intervals (upper and lower bounds).
The new variable names and descriptive labels are displayed in a table in the output window.
Predict Cases. In the active dataset, if you select Time instead of a variable as the independent variable,
you can specify a forecast period beyond the end of the time series. You can choose one of the following
alternatives:
• Predict from estimation period through last case. Predicts values for all cases in the file, based on the
cases in the estimation period. The estimation period, displayed at the bottom of the dialog box, is
defined with the Range subdialog box of the Select Cases option on the Data menu. If no estimation
period has been defined, all cases are used to predict values.
• Predict through. Predicts values through the specified date, time, or observation number, based on the
cases in the estimation period. This feature can be used to forecast values beyond the last case in the
time series. The currently defined date variables determine what text boxes are available for specifying
the end of the prediction period. If there are no defined date variables, you can specify the ending
observation (case) number.
Use the Define Dates option on the Data menu to create date variables.
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Partial Least Squares Regression
The Partial Least Squares Regression procedure estimates partial least squares (PLS, also known as
“projection to latent structure”) regression models. PLS is a predictive technique that is an alternative to
ordinary least squares (OLS) regression, canonical correlation, or structural equation modeling, and it is
particularly useful when predictor variables are highly correlated or when the number of predictors
exceeds the number of cases.
PLS combines features of principal components analysis and multiple regression. It first extracts a set of
latent factors that explain as much of the covariance as possible between the independent and
dependent variables. Then a regression step predicts values of the dependent variables using the
decomposition of the independent variables.
Tables
Proportion of variance explained (by latent factor), latent factor weights, latent factor loadings,
independent variable importance in projection (VIP), and regression parameter estimates (by
dependent variable) are all produced by default.
Charts
Variable importance in projection (VIP), factor scores, factor weights for the first three latent factors,
and distance to the model are all produced from the Options tab.
Data considerations
Measurement level
The dependent and independent (predictor) variables can be scale, nominal, or ordinal. The
procedure assumes that the appropriate measurement level has been assigned to all variables,
although you can temporarily change the measurement level for a variable by right-clicking the
variable in the source variable list and selecting a measurement level from the pop-up menu.
Categorical (nominal or ordinal) variables are treated equivalently by the procedure.
Categorical variable coding
The procedure temporarily recodes categorical dependent variables using one-of-c coding for the
duration of the procedure. If there are c categories of a variable, then the variable is stored as c
vectors, with the first category denoted (1,0,…,0), the next category (0,1,0,…,0), …, and the final
category (0,0,…,0,1). Categorical dependent variables are represented using dummy coding; that is,
simply omit the indicator corresponding to the reference category.
Frequency weights
Weight values are rounded to the nearest whole number before use. Cases with missing weights or
weights less than 0.5 are not used in the analyses.
Missing values
User- and system-missing values are treated as invalid.
Rescaling
All model variables are centered and standardized, including indicator variables representing
categorical variables.
Obtaining Partial Least Squares Regression
From the menus choose:
Analyze > Regression > Partial Least Squares…
1. Select at least one dependent variable.
2. Select at least one independent variable.
Optionally, you can:
• Specify a reference category for categorical (nominal or ordinal) dependent variables.
• Specify a variable to be used as a unique identifier for casewise output and saved datasets.
• Specify an upper limit on the number of latent factors to be extracted.
Chapter 1. Core features 99
Prerequisites
The Partial Least Squares Regression procedure is a Python extension command and requires IBM SPSS
Statistics – Essentials for Python, which is installed by default with your IBM SPSS Statistics product. It
also requires the NumPy and SciPy Python libraries, which are freely available.
Note: For users working in distributed analysis mode (requires IBM SPSS Statistics Server), NumPy and
SciPy must be installed on the server. Contact your system administrator for assistance.
Windows and Mac Users
For Windows and Mac, NumPy and SciPy must be installed to a separate version of Python 3.8 from
the version that is installed with IBM SPSS Statistics. If you do not have a separate version of Python
3.8, you can download it from http://www.python.org. Then, install NumPy and SciPy for Python
version 3.8. The installers are available from http://www.scipy.org/Download.
To enable use of NumPy and SciPy, you must set your Python location to the version of Python 3.8
where you installed NumPy and SciPy. The Python location is set from the File Locations tab in the
Options dialog (Edit > Options).
Linux Users
We suggest that you download the source and build NumPy and SciPy yourself. The source is
available from http://www.scipy.org/Download. You can install NumPy and SciPy to the version of
Python 3.8 that is installed with IBM SPSS Statistics. It is in the Python directory under the location
where IBM SPSS Statistics is installed.
If you choose to install NumPy and SciPy to a version of Python 3.8 other than the version that is
installed with IBM SPSS Statistics, then you must set your Python location to point to that version. The
Python location is set from the File Locations tab in the Options dialog (Edit > Options).
Windows and Unix Server
NumPy and SciPy must be installed, on the server, to a separate version of Python 3.8 from the
version that is installed with IBM SPSS Statistics. If there is not a separate version of Python 3.8 on
the server, then it can be downloaded from http://www.python.org. NumPy and SciPy for Python 3.8
are available from http://www.scipy.org/Download. To enable use of NumPy and SciPy, the Python
location for the server must be set to the version of Python 3.8 where NumPy and SciPy are installed.
The Python location is set from the IBM SPSS Statistics Administration Console.
Model
Specify Model Effects. A main-effects model contains all factor and covariate main effects. Select
Custom to specify interactions. You must indicate all of the terms to be included in the model.
Factors and Covariates. The factors and covariates are listed.
Model. The model depends on the nature of your data. After selecting Custom, you can select the main
effects and interactions that are of interest in your analysis.
Build Terms
For the selected factors and covariates:
Interaction. Creates the highest-level interaction term of all selected variables. This is the default.
Main effects. Creates a main-effects term for each variable selected.
All 2-way. Creates all possible two-way interactions of the selected variables.
All 3-way. Creates all possible three-way interactions of the selected variables.
All 4-way. Creates all possible four-way interactions of the selected variables.
All 5-way. Creates all possible five-way interactions of the selected variables.
100 IBM SPSS Statistics Base V27
http://www.python.org
http://www.scipy.org/Download
http://www.scipy.org/Download
http://www.python.org
http://www.scipy.org/Download
Options
The Options tab allows the user to save and plot model estimates for individual cases, latent factors, and
predictors.
For each type of data, specify the name of a dataset. The dataset names must be unique. If you specify
the name of an existing dataset, its contents are replaced; otherwise, a new dataset is created.
• Save estimates for individual cases. Saves the following casewise model estimates: predicted values,
residuals, distance to latent factor model, and latent factor scores. It also plots latent factor scores.
• Save estimates for latent factors. Saves latent factor loadings and latent factor weights. It also plots
latent factor weights.
• Save estimates for independent variables. Saves regression parameter estimates and variable
importance to projection (VIP). It also plots VIP by latent factor.
Nearest Neighbor Analysis
Nearest Neighbor Analysis is a method for classifying cases based on their similarity to other cases. In
machine learning, it was developed as a way to recognize patterns of data without requiring an exact
match to any stored patterns, or cases. Similar cases are near each other and dissimilar cases are distant
from each other. Thus, the distance between two cases is a measure of their dissimilarity.
Cases that are near each other are said to be “neighbors.” When a new case (holdout) is presented, its
distance from each of the cases in the model is computed. The classifications of the most similar cases –
the nearest neighbors – are tallied and the new case is placed into the category that contains the greatest
number of nearest neighbors.
You can specify the number of nearest neighbors to examine; this value is called k.
Nearest neighbor analysis can also be used to compute values for a continuous target. In this situation,
the average or median target value of the nearest neighbors is used to obtain the predicted value for the
new case.
Nearest Neighbor Analysis Data Considerations
Target and features. The target and features can be:
• Nominal. A variable can be treated as nominal when its values represent categories with no intrinsic
ranking (for example, the department of the company in which an employee works). Examples of
nominal variables include region, postal code, and religious affiliation.
• Ordinal. A variable can be treated as ordinal when its values represent categories with some intrinsic
ranking (for example, levels of service satisfaction from highly dissatisfied to highly satisfied). Examples
of ordinal variables include attitude scores representing degree of satisfaction or confidence and
preference rating scores.
• Scale. A variable can be treated as scale (continuous) when its values represent ordered categories with
a meaningful metric, so that distance comparisons between values are appropriate. Examples of scale
variables include age in years and income in thousands of dollars.
Nominal and Ordinal variables are treated equivalently by Nearest Neighbor Analysis. The procedure
assumes that the appropriate measurement level has been assigned to each variable; however, you can
temporarily change the measurement level for a variable by right-clicking the variable in the source
variable list and selecting a measurement level from the pop-up menu.
An icon next to each variable in the variable list identifies the measurement level and data type:
Table 1. Measurement level icons
Numeric String Date Time
Scale (Continuous) n/a
Chapter 1. Core features 101
Table 1. Measurement level icons (continued)
Numeric String Date Time
Ordinal
Nominal
Categorical variable coding. The procedure temporarily recodes categorical predictors and dependent
variables using one-of-c coding for the duration of the procedure. If there are c categories of a variable,
then the variable is stored as c vectors, with the first category denoted (1,0,…,0), the next category
(0,1,0,…,0), …, and the final category (0,0,…,0,1).
This coding scheme increases the dimensionality of the feature space. In particular, the total number of
dimensions is the number of scale predictors plus the number of categories across all categorical
predictors. As a result, this coding scheme can lead to slower training. If your nearest neighbors training
is proceeding very slowly, you might try reducing the number of categories in your categorical predictors
by combining similar categories or dropping cases that have extremely rare categories before running the
procedure.
All one-of-c coding is based on the training data, even if a holdout sample is defined (see “Partitions ” on
page 104). Thus, if the holdout sample contains cases with predictor categories that are not present in
the training data, then those cases are not scored. If the holdout sample contains cases with dependent
variable categories that are not present in the training data, then those cases are scored.
Rescaling. Scale features are normalized by default. All rescaling is performed based on the training data,
even if a holdout sample is defined (see “Partitions ” on page 104). If you specify a variable to define
partitions, it is important that the features have similar distributions across the training and holdout
samples. Use, for example, the Explore procedure to examine the distributions across partitions.
Frequency weights. Frequency weights are ignored by this procedure.
Replicating results. The procedure uses random number generation during random assignment of
partitions and cross-validation folds. If you want to replicate your results exactly, in addition to using the
same procedure settings, set a seed for the Mersenne Twister (see “Partitions ” on page 104), or use
variables to define partitions and cross-validation folds.
To obtain a nearest neighbor analysis
From the menus choose:
Analyze > Classify > Nearest Neighbor…
1. Specify one or more features, which can be thought of independent variables or predictors if there is a
target.
Target (optional). If no target (dependent variable or response) is specified, then the procedure finds
the k nearest neighbors only – no classification or prediction is done.
Normalize scale features. Normalized features have the same range of values, which can improve the
performance of the estimation algorithm. Adjusted normalization, [2*(x−min)/(max−min)]−1, is used.
Adjusted normalized values fall between −1 and 1.
Focal case identifier (optional). This allows you to mark cases of particular interest. For example, a
researcher wants to determine whether the test scores from one school district – the focal case – are
comparable to those from similar school districts. He uses nearest neighbor analysis to find the school
districts that are most similar with respect to a given set of features. Then he compares the test scores
from the focal school district to those from the nearest neighbors.
Focal cases could also be used in clinical studies to select control cases that are similar to clinical
cases. Focal cases are displayed in the k nearest neighbors and distances table, feature space chart,
102 IBM SPSS Statistics Base V27
peers chart, and quadrant map. Information on focal cases is saved to the files specified on the Output
tab.
Cases with a positive value on the specified variable are treated as focal cases. It is invalid to specify a
variable with no positive values.
Case label (optional). Cases are labeled using these values in the feature space chart, peers chart, and
quadrant map.
Fields with unknown measurement level
The Measurement Level alert is displayed when the measurement level for one or more variables (fields)
in the dataset is unknown. Since measurement level affects the computation of results for this procedure,
all variables must have a defined measurement level.
Scan Data. Reads the data in the active dataset and assigns default measurement level to any fields with
a currently unknown measurement level. If the dataset is large, that may take some time.
Assign Manually. Opens a dialog that lists all fields with an unknown measurement level. You can use
this dialog to assign measurement level to those fields. You can also assign measurement level in Variable
View of the Data Editor.
Since measurement level is important for this procedure, you cannot access the dialog to run this
procedure until all fields have a defined measurement level.
Neighbors
Number of Nearest Neighbors (k). Specify the number of nearest neighbors. Note that using a greater
number of neighbors will not necessarily result in a more accurate model.
If a target is specified on the Variables tab, you can alternatively specify a range of values and allow the
procedure to choose the “best” number of neighbors within that range. The method for determining the
number of nearest neighbors depends upon whether feature selection is requested on the Features tab.
• If feature selection is in effect, then feature selection is performed for each value of k in the requested
range, and the k, and accompanying feature set, with the lowest error rate (or the lowest sum-of-
squares error if the target is scale) is selected.
• If feature selection is not in effect, then V-fold cross-validation is used to select the “best” number of
neighbors. See the Partition tab for control over assignment of folds.
Distance Computation. This is the metric used to specify the distance metric used to measure the
similarity of cases.
• Euclidean metric. The distance between two cases, x and y, is the square root of the sum, over all
dimensions, of the squared differences between the values for the cases.
• City block metric. The distance between two cases is the sum, over all dimensions, of the absolute
differences between the values for the cases. Also called Manhattan distance.
Optionally, if a target is specified on the Variables tab, you can choose to weight features by their
normalized importance when computing distances. Feature importance for a predictor is calculated by
the ratio of the error rate or sum-of-squares error of the model with the predictor removed from the
model to the error rate or sum-of-squares error for the full model. Normalized importance is calculated by
reweighting the feature importance values so that they sum to 1.
Predictions for Scale Target. If a scale target is specified on the Variables tab, this specifies whether the
predicted value is computed based upon the mean or the median value of the nearest neighbors.
Features
The Features tab allows you to request and specify options for feature selection when a target is specified
on the Variables tab. By default, all features are considered for feature selection, but you can optionally
select a subset of features to force into the model.
Chapter 1. Core features 103
Stopping Criterion. At each step, the feature whose addition to the model results in the smallest error
(computed as the error rate for a categorical target and sum of squares error for a scale target) is
considered for inclusion in the model set. Forward selection continues until the specified condition is met.
• Specified number of features. The algorithm adds a fixed number of features in addition to those
forced into the model. Specify a positive integer. Decreasing values of the number to select creates a
more parsimonious model, at the risk of missing important features. Increasing values of the number to
select will capture all the important features, at the risk of eventually adding features that actually
increase the model error.
• Minimum change in absolute error ratio. The algorithm stops when the change in the absolute error
ratio indicates that the model cannot be further improved by adding more features. Specify a positive
number. Decreasing values of the minimum change will tend to include more features, at the risk of
including features that don’t add much value to the model. Increasing the value of the minimum change
will tend to exclude more features, at the risk of losing features that are important to the model. The
“optimal” value of the minimum change will depend upon your data and application. See the Feature
Selection Error Log in the output to help you assess which features are most important. See the topic
“Feature selection error log ” on page 108 for more information.
Partitions
The Partitions tab allows you to divide the dataset into training and holdout sets and, when applicable,
assign cases into cross-validation folds
Training and Holdout Partitions. This group specifies the method of partitioning the active dataset into
training and holdout samples. The training sample comprises the data records used to train the nearest
neighbor model; some percentage of cases in the dataset must be assigned to the training sample in
order to obtain a model. The holdout sample is an independent set of data records used to assess the
final model; the error for the holdout sample gives an “honest” estimate of the predictive ability of the
model because the holdout cases were not used to build the model.
• Randomly assign cases to partitions. Specify the percentage of cases to assign to the training sample.
The rest are assigned to the holdout sample.
• Use variable to assign cases. Specify a numeric variable that assigns each case in the active dataset to
the training or holdout sample. Cases with a positive value on the variable are assigned to the training
sample, cases with a value of 0 or a negative value, to the holdout sample. Cases with a system-missing
value are excluded from the analysis. Any user-missing values for the partition variable are always
treated as valid.
Cross-Validation Folds. V-fold cross-validation is used to determine the “best” number of neighbors. It is
not available in conjunction with feature selection for performance reasons.
Cross-validation divides the sample into a number of subsamples, or folds. Nearest neighbor models are
then generated, excluding the data from each subsample in turn. The first model is based on all of the
cases except those in the first sample fold, the second model is based on all of the cases except those in
the second sample fold, and so on. For each model, the error is estimated by applying the model to the
subsample excluded in generating it. The “best” number of nearest neighbors is the one which produces
the lowest error across folds.
• Randomly assign cases to folds. Specify the number of folds that should be used for cross-validation.
The procedure randomly assigns cases to folds, numbered from 1 to V, the number of folds.
• Use variable to assign cases. Specify a numeric variable that assigns each case in the active dataset to
a fold. The variable must be numeric and take values from 1 to V. If any values in this range are missing,
and on any splits if split files are in effect, this will cause an error.
Set seed for Mersenne Twister. Setting a seed allows you to replicate analyses. Using this control is
similar to setting the Mersenne Twister as the active generator and specifying a fixed starting point on the
Random Number Generators dialog, with the important difference that setting the seed in this dialog will
preserve the current state of the random number generator and restore that state after the analysis is
complete.
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Save
Names of Saved Variables. Automatic name generation ensures that you keep all of your work. Custom
names allow you to discard/replace results from previous runs without first deleting the saved variables in
the Data Editor.
Variables to Save
• Predicted value or category. This saves the predicted value for a scale target or the predicted category
for a categorical target.
• Predicted probability. This saves the predicted probabilities for a categorical target. A separate
variable is saved for each of the first n categories, where n is specified in the Maximum categories to
save for categorical target control.
• Training/Holdout partition variables. If cases are randomly assigned to the training and holdout
samples on the Partitions tab, this saves the value of the partition (training or holdout) to which the case
was assigned.
• Cross-validation fold variable. If cases are randomly assigned to cross-validation folds on the
Partitions tab, this saves the value of the fold to which the case was assigned.
Output
Viewer Output
• Case processing summary. Displays the case processing summary table, which summarizes the
number of cases included and excluded in the analysis, in total and by training and holdout samples.
• Charts and tables. Displays model-related output, including tables and charts. Tables in the model
view include k nearest neighbors and distances for focal cases, classification of categorical response
variables, and an error summary. Graphical output in the model view includes a selection error log,
feature importance chart, feature space chart, peers chart, and quadrant map. See the topic “Model
View ” on page 105 for more information.
Files
• Export model to XML. You can use this model file to apply the model information to other data files for
scoring purposes. This option is not available if split files have been defined.
• Export distances between focal cases and k nearest neighbors. For each focal case, a separate
variable is created for each of the focal case’s k nearest neighbors (from the training sample) and the
corresponding k nearest distances.
Options
User-Missing Values. Categorical variables must have valid values for a case to be included in the
analysis. These controls allow you to decide whether user-missing values are treated as valid among
categorical variables.
System-missing values and missing values for scale variables are always treated as invalid.
Model View
When you select Charts and tables in the Output tab, the procedure creates a Nearest Neighbor Model
object in the Viewer. By activating (double-clicking) this object, you gain an interactive view of the model.
The model view has a 2-panel window:
• The first panel displays an overview of the model called the main view.
• The second panel displays one of two types of views:
An auxiliary model view shows more information about the model, but is not focused on the model
itself.
A linked view is a view that shows details about one feature of the model when the user drills down on
part of the main view.
Chapter 1. Core features 105
By default, the first panel shows the feature space and the second panel shows the variable importance
chart. If the variable importance chart is not available; that is, when Weight features by importance was
not selected on the Features tab, the first available view in the View dropdown is shown.
When a view has no available information, its item text in the View dropdown is disabled.
Feature Space
The feature space chart is an interactive graph of the feature space (or a subspace, if there are more than
3 features). Each axis represents a feature in the model, and the location of points in the chart show the
values of these features for cases in the training and holdout partitions.
Keys. In addition to the feature values, points in the plot convey other information.
• Shape indicates the partition to which a point belongs, either Training or Holdout.
• The color/shading of a point indicates the value of the target for that case; with distinct color values
equal to the categories of a categorical target, and shades indicating the range of values of a continuous
target. The indicated value for the training partition is the observed value; for the holdout partition, it is
the predicted value. If no target is specified, this key is not shown.
• Heavier outlines indicate a case is focal. Focal cases are shown linked to their k nearest neighbors.
Controls and Interactivity. A number of controls in the chart allow you explore the Feature Space.
• You can choose which subset of features to show in the chart and change which features are
represented on the dimensions.
• “Focal cases” are simply points selected in the Feature Space chart. If you specified a focal case
variable, the points representing the focal cases will initially be selected. However, any point can
temporarily become a focal case if you select it. The “usual” controls for point selection apply; clicking
on a point selects that point and deselects all others; Control-clicking on a point adds it to the set of
selected points. Linked views, such as the Peers Chart, will automatically update based upon the cases
selected in the Feature Space.
• You can change the number of nearest neighbors (k) to display for focal cases.
• Hovering over a point in the chart displays a tooltip with the value of the case label, or case number if
case labels are not defined, and the observed and predicted target values.
• A “Reset” button allows you to return the Feature Space to its original state.
Adding and removing fields/variables
You can add new fields/variables to the feature space or remove the ones that are currently displayed.
Variables Palette
The Variables palette must be displayed before you can add and remove variables. To display the
Variables palette, the Model Viewer must be in Edit mode and a case must be selected in the feature
space.
1. To put the Model Viewer in Edit mode, from the menus choose:
View > Edit Mode
2. Once in Edit Mode, click any case in the feature space.
3. To display the Variables palette, from the menus choose:
View > Palettes > Variables
The Variables palette lists all of the variables in the feature space. The icon next to the variable name
indicates the variable’s measurement level.
4. To temporarily change a variable’s measurement level, right click the variable in the variables palette
and choose an option.
Variable Zones
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Variables are added to “zones” in the feature space. To display the zones, start dragging a variable from
the Variables palette or select Show zones.
The feature space has zones for the x, y, and z axes.
Moving Variables into Zones
Here are some general rules for and tips for moving variables into zones:
• To move a variable into a zone, click and drag the variable from the Variables palette and drop it into the
zone. If you choose Show zones, you can also right-click a zone and select a variable that you want to
add to the zone.
• If you drag a variable from the Variables palette to a zone already occupied by another variable, the old
variable is replaced with the new.
• If you drag a variable from one zone to a zone already occupied by another variable, the variables swap
positions.
• Clicking the X in a zone removes the variable from that zone.
• If there are multiple graphic elements in the visualization, each graphic element can have its own
associated variable zones. First select the graphic element.
Variable Importance
Typically, you will want to focus your modeling efforts on the variables that matter most and consider
dropping or ignoring those that matter least. The variable importance chart helps you do this by indicating
the relative importance of each variable in estimating the model. Since the values are relative, the sum of
the values for all variables on the display is 1.0. Variable importance does not relate to model accuracy. It
just relates to the importance of each variable in making a prediction, not whether or not the prediction is
accurate.
Peers
This chart displays the focal cases and their k nearest neighbors on each feature and on the target. It is
available if a focal case is selected in the Feature Space.
Linking behavior. The Peers chart is linked to the Feature Space in two ways.
• Cases selected (focal) in the Feature Space are displayed in the Peers chart, along with their k nearest
neighbors.
• The value of k selected in the Feature Space is used in the Peers chart.
Nearest Neighbor Distances
This table displays the k nearest neighbors and distances for focal cases only. It is available if a focal case
identifier is specified on the Variables tab, and only displays focal cases identified by this variable.
Each row of:
• The Focal Case column contains the value of the case labeling variable for the focal case; if case labels
are not defined, this column contains the case number of the focal case.
• The ith column under the Nearest Neighbors group contains the value of the case labeling variable for
the ith nearest neighbor of the focal case; if case labels are not defined, this column contains the case
number of the ith nearest neighbor of the focal case.
• The ith column under the Nearest Distances group contains the distance of the ith nearest neighbor to
the focal case
Quadrant map
This chart displays the focal cases and their k nearest neighbors on a scatterplot (or dotplot, depending
upon the measurement level of the target) with the target on the y-axis and a scale feature on the x-axis,
paneled by features. It is available if there is a target and if a focal case is selected in the Feature Space.
• Reference lines are drawn for continuous variables, at the variable means in the training partition.
Chapter 1. Core features 107
Feature selection error log
Points on the chart display the error (either the error rate or sum-of-squares error, depending upon the
measurement level of the target) on the y-axis for the model with the feature listed on the x-axis (plus all
features to the left on the x-axis). This chart is available if there is a target and feature selection is in
effect.
k selection error log
Points on the chart display the error (either the error rate or sum-of-squares error, depending upon the
measurement level of the target) on the y-axis for the model with the number of nearest neighbors (k) on
the x-axis. This chart is available if there is a target and k selection is in effect.
k and Feature Selection Error Log
These are feature selection charts (see “Feature selection error log ” on page 108), paneled by k. This
chart is available if there is a target and k and feature selection are both in effect.
Classification Table
This table displays the cross-classification of observed versus predicted values of the target, by partition.
It is available if there is a target and it is categorical.
• The (Missing) row in the Holdout partition contains holdout cases with missing values on the target.
These cases contribute to the Holdout Sample: Overall Percent values but not to the Percent Correct
values.
Error Summary
This table is available if there is a target variable. It displays the error associated with the model; sum-of-
squares for a continuous target and the error rate (100% − overall percent correct) for a categorical
target.
Discriminant Analysis
Discriminant analysis builds a predictive model for group membership. The model is composed of a
discriminant function (or, for more than two groups, a set of discriminant functions) based on linear
combinations of the predictor variables that provide the best discrimination between the groups. The
functions are generated from a sample of cases for which group membership is known; the functions can
then be applied to new cases that have measurements for the predictor variables but have unknown
group membership.
Note: The grouping variable can have more than two values. The codes for the grouping variable must be
integers, however, and you need to specify their minimum and maximum values. Cases with values
outside of these bounds are excluded from the analysis.
Example. On average, people in temperate zone countries consume more calories per day than people in
the tropics, and a greater proportion of the people in the temperate zones are city dwellers. A researcher
wants to combine this information into a function to determine how well an individual can discriminate
between the two groups of countries. The researcher thinks that population size and economic
information may also be important. Discriminant analysis allows you to estimate coefficients of the linear
discriminant function, which looks like the right side of a multiple linear regression equation. That is,
using coefficients a, b, c, and d, the function is:
D = a * climate + b * urban + c * population + d * gross domestic product per capita
If these variables are useful for discriminating between the two climate zones, the values of D will differ
for the temperate and tropic countries. If you use a stepwise variable selection method, you may find that
you do not need to include all four variables in the function.
Statistics. For each variable: means, standard deviations, univariate ANOVA. For each analysis: Box’s M,
within-groups correlation matrix, within-groups covariance matrix, separate-groups covariance matrix,
total covariance matrix. For each canonical discriminant function: eigenvalue, percentage of variance,
108 IBM SPSS Statistics Base V27
canonical correlation, Wilks’ lambda, chi-square. For each step: prior probabilities, Fisher’s function
coefficients, unstandardized function coefficients, Wilks’ lambda for each canonical function.
Discriminant Analysis Data Considerations
Data. The grouping variable must have a limited number of distinct categories, coded as integers.
Independent variables that are nominal must be recoded to dummy or contrast variables.
Assumptions. Cases should be independent. Predictor variables should have a multivariate normal
distribution, and within-group variance-covariance matrices should be equal across groups. Group
membership is assumed to be mutually exclusive (that is, no case belongs to more than one group) and
collectively exhaustive (that is, all cases are members of a group). The procedure is most effective when
group membership is a truly categorical variable; if group membership is based on values of a continuous
variable (for example, high IQ versus low IQ), consider using linear regression to take advantage of the
richer information that is offered by the continuous variable itself.
To Obtain a Discriminant Analysis
1. From the menus choose:
Analyze > Classify > Discriminant…
2. Select an integer-valued grouping variable and click Define Range to specify the categories of interest.
3. Select the independent, or predictor, variables. (If your grouping variable does not have integer values,
Automatic Recode on the Transform menu will create a variable that does.)
4. Select the method for entering the independent variables.
• Enter independents together. Simultaneously enters all independent variables that satisfy
tolerance criteria.
• Use stepwise method. Uses stepwise analysis to control variable entry and removal.
5. Optionally, select cases with a selection variable.
Discriminant Analysis Define Range
Specify the minimum and maximum value of the grouping variable for the analysis. Cases with values
outside of this range are not used in the discriminant analysis but are classified into one of the existing
groups based on the results of the analysis. The minimum and maximum values must be integers.
Discriminant Analysis Select Cases
To select cases for your analysis:
1. In the Discriminant Analysis dialog box, choose a selection variable.
2. Click Value to enter an integer as the selection value.
Only cases with the specified value for the selection variable are used to derive the discriminant
functions. Statistics and classification results are generated for both selected and unselected cases. This
process provides a mechanism for classifying new cases based on previously existing data or for
partitioning your data into training and testing subsets to perform validation on the model generated.
Discriminant Analysis Statistics
Descriptives. Available options are means (including standard deviations), univariate ANOVAs, and Box’s
M test.
• Means. Displays total and group means, as well as standard deviations for the independent variables.
• Univariate ANOVAs. Performs a one-way analysis-of-variance test for equality of group means for each
independent variable.
• Box’s M. A test for the equality of the group covariance matrices. For sufficiently large samples, a
nonsignificant p value means there is insufficient evidence that the matrices differ. The test is sensitive
to departures from multivariate normality.
Chapter 1. Core features 109
Function Coefficients. Available options are Fisher’s classification coefficients and unstandardized
coefficients.
• Fisher’s. Displays Fisher’s classification function coefficients that can be used directly for classification.
A separate set of classification function coefficients is obtained for each group, and a case is assigned
to the group for which it has the largest discriminant score (classification function value).
• Unstandardized. Displays the unstandardized discriminant function coefficients.
Matrices. Available matrices of coefficients for independent variables are within-groups correlation
matrix, within-groups covariance matrix, separate-groups covariance matrix, and total covariance matrix.
• Within-groups correlation. Displays a pooled within-groups correlation matrix that is obtained by
averaging the separate covariance matrices for all groups before computing the correlations.
• Within-groups covariance. Displays a pooled within-groups covariance matrix, which may differ from the
total covariance matrix. The matrix is obtained by averaging the separate covariance matrices for all
groups.
• Separate-groups covariance. Displays separate covariance matrices for each group.
• Total covariance. Displays a covariance matrix from all cases as if they were from a single sample.
Discriminant Analysis Stepwise Method
Method. Select the statistic to be used for entering or removing new variables. Available alternatives are
Wilks’ lambda, unexplained variance, Mahalanobis distance, smallest F ratio, and Rao’s V. With Rao’s V,
you can specify the minimum increase in V for a variable to enter.
• Wilks’ lambda. A variable selection method for stepwise discriminant analysis that chooses variables for
entry into the equation on the basis of how much they lower Wilks’ lambda. At each step, the variable
that minimizes the overall Wilks’ lambda is entered.
• Unexplained variance. At each step, the variable that minimizes the sum of the unexplained variation
between groups is entered.
• Mahalanobis distance. A measure of how much a case’s values on the independent variables differ from
the average of all cases. A large Mahalanobis distance identifies a case as having extreme values on one
or more of the independent variables.
• Smallest F ratio. A method of variable selection in stepwise analysis based on maximizing an F ratio
computed from the Mahalanobis distance between groups.
• Rao’s V. A measure of the differences between group means. Also called the Lawley-Hotelling trace. At
each step, the variable that maximizes the increase in Rao’s V is entered. After selecting this option,
enter the minimum value a variable must have to enter the analysis.
Criteria. Available alternatives are Use F value and Use probability of F. Enter values for entering and
removing variables.
• Use F value. A variable is entered into the model if its F value is greater than the Entry value and is
removed if the F value is less than the Removal value. Entry must be greater than Removal, and both
values must be positive. To enter more variables into the model, lower the Entry value. To remove more
variables from the model, increase the Removal value.
• Use probability of F. A variable is entered into the model if the significance level of its F value is less than
the Entry value and is removed if the significance level is greater than the Removal value. Entry must be
less than Removal, and both values must be positive. To enter more variables into the model, increase
the Entry value. To remove more variables from the model, lower the Removal value.
Display. Summary of steps displays statistics for all variables after each step; F for pairwise distances
displays a matrix of pairwise F ratios for each pair of groups.
Discriminant Analysis Classification
Prior Probabilities. This option determines whether the classification coefficients are adjusted for a priori
knowledge of group membership.
110 IBM SPSS Statistics Base V27
• All groups equal. Equal prior probabilities are assumed for all groups; this has no effect on the
coefficients.
• Compute from group sizes. The observed group sizes in your sample determine the prior probabilities
of group membership. For example, if 50% of the observations included in the analysis fall into the first
group, 25% in the second, and 25% in the third, the classification coefficients are adjusted to increase
the likelihood of membership in the first group relative to the other two.
Display. Available display options are casewise results, summary table, and leave-one-out classification.
• Casewise results. Codes for actual group, predicted group, posterior probabilities, and discriminant
scores are displayed for each case.
• Summary table. The number of cases correctly and incorrectly assigned to each of the groups based on
the discriminant analysis. Sometimes called the “Confusion Matrix.”
• Leave-one-out classification. Each case in the analysis is classified by the functions derived from all
cases other than that case. It is also known as the “U-method.”
Replace missing values with mean. Select this option to substitute the mean of an independent variable
for a missing value during the classification phase only.
Use Covariance Matrix. You can choose to classify cases using a within-groups covariance matrix or a
separate-groups covariance matrix.
• Within-groups. The pooled within-groups covariance matrix is used to classify cases.
• Separate-groups. Separate-groups covariance matrices are used for classification. Because
classification is based on the discriminant functions (not based on the original variables), this option is
not always equivalent to quadratic discrimination.
Plots. Available plot options are combined-groups, separate-groups, and territorial map.
• Combined-groups. Creates an all-groups scatterplot of the first two discriminant function values. If
there is only one function, a histogram is displayed instead.
• Separate-groups. Creates separate-group scatterplots of the first two discriminant function values. If
there is only one function, histograms are displayed instead.
• Territorial map. A plot of the boundaries used to classify cases into groups based on function values.
The numbers correspond to groups into which cases are classified. The mean for each group is
indicated by an asterisk within its boundaries. The map is not displayed if there is only one discriminant
function.
Discriminant Analysis Save
You can add new variables to your active data file. Available options are predicted group membership (a
single variable), discriminant scores (one variable for each discriminant function in the solution), and
probabilities of group membership given the discriminant scores (one variable for each group).
You can also export model information to the specified file in XML format. You can use this model file to
apply the model information to other data files for scoring purposes.
DISCRIMINANT Command Additional Features
The command syntax language also allows you to:
• Perform multiple discriminant analyses (with one command) and control the order in which variables
are entered (with the ANALYSIS subcommand).
• Specify prior probabilities for classification (with the PRIORS subcommand).
• Display rotated pattern and structure matrices (with the ROTATE subcommand).
• Limit the number of extracted discriminant functions (with the FUNCTIONS subcommand).
• Restrict classification to the cases that are selected (or unselected) for the analysis (with the SELECT
subcommand).
• Read and analyze a correlation matrix (with the MATRIX subcommand).
Chapter 1. Core features 111
• Write a correlation matrix for later analysis (with the MATRIX subcommand).
See the Command Syntax Reference for complete syntax information.
Factor Analysis
Factor analysis attempts to identify underlying variables, or factors, that explain the pattern of
correlations within a set of observed variables. Factor analysis is often used in data reduction to identify a
small number of factors that explain most of the variance that is observed in a much larger number of
manifest variables. Factor analysis can also be used to generate hypotheses regarding causal
mechanisms or to screen variables for subsequent analysis (for example, to identify collinearity prior to
performing a linear regression analysis).
The factor analysis procedure offers a high degree of flexibility:
• Seven methods of factor extraction are available.
• Five methods of rotation are available, including direct oblimin and promax for nonorthogonal rotations.
• Three methods of computing factor scores are available, and scores can be saved as variables for
further analysis.
Example. What underlying attitudes lead people to respond to the questions on a political survey as they
do? Examining the correlations among the survey items reveals that there is significant overlap among
various subgroups of items–questions about taxes tend to correlate with each other, questions about
military issues correlate with each other, and so on. With factor analysis, you can investigate the number
of underlying factors and, in many cases, identify what the factors represent conceptually. Additionally,
you can compute factor scores for each respondent, which can then be used in subsequent analyses. For
example, you might build a logistic regression model to predict voting behavior based on factor scores.
Statistics. For each variable: number of valid cases, mean, and standard deviation. For each factor
analysis: correlation matrix of variables, including significance levels, determinant, and inverse;
reproduced correlation matrix, including anti-image; initial solution (communalities, eigenvalues, and
percentage of variance explained); Kaiser-Meyer-Olkin measure of sampling adequacy and Bartlett’s test
of sphericity; unrotated solution, including factor loadings, communalities, and eigenvalues; and rotated
solution, including rotated pattern matrix and transformation matrix. For oblique rotations: rotated
pattern and structure matrices; factor score coefficient matrix and factor covariance matrix. Plots: scree
plot of eigenvalues and loading plot of first two or three factors.
Factor Analysis Data Considerations
Data. The variables should be quantitative at the interval or ratio level. Categorical data (such as religion
or country of origin) are not suitable for factor analysis. Data for which Pearson correlation coefficients
can sensibly be calculated should be suitable for factor analysis.
Assumptions. The data should have a bivariate normal distribution for each pair of variables, and
observations should be independent. The factor analysis model specifies that variables are determined by
common factors (the factors estimated by the model) and unique factors (which do not overlap between
observed variables); the computed estimates are based on the assumption that all unique factors are
uncorrelated with each other and with the common factors.
To Obtain a Factor Analysis
1. From the menus choose:
Analyze > Dimension Reduction > Factor…
2. Select the variables for the factor analysis.
Factor Analysis Select Cases
To select cases for your analysis:
1. Choose a selection variable.
2. Click Value to enter an integer as the selection value.
112 IBM SPSS Statistics Base V27
Only cases with that value for the selection variable are used in the factor analysis.
Factor Analysis Descriptives
Statistics. Univariate descriptives includes the mean, standard deviation, and number of valid cases for
each variable. Initial solution displays initial communalities, eigenvalues, and the percentage of variance
explained.
Correlation Matrix. The available options are coefficients, significance levels, determinant, KMO and
Bartlett’s test of sphericity, inverse, reproduced, and anti-image.
• KMO and Bartlett’s Test of Sphericity. The Kaiser-Meyer-Olkin measure of sampling adequacy tests
whether the partial correlations among variables are small. Bartlett’s test of sphericity tests whether
the correlation matrix is an identity matrix, which would indicate that the factor model is inappropriate.
• Reproduced. The estimated correlation matrix from the factor solution. Residuals (difference between
estimated and observed correlations) are also displayed.
• Anti-image. The anti-image correlation matrix contains the negatives of the partial correlation
coefficients, and the anti-image covariance matrix contains the negatives of the partial covariances. In a
good factor model, most of the off-diagonal elements will be small. The measure of sampling adequacy
for a variable is displayed on the diagonal of the anti-image correlation matrix.
Factor Analysis Extraction
Method. Allows you to specify the method of factor extraction. Available methods are principal
components, unweighted least squares, generalized least squares, maximum likelihood, principal axis
factoring, alpha factoring, and image factoring.
• Principal Components Analysis. A factor extraction method used to form uncorrelated linear
combinations of the observed variables. The first component has maximum variance. Successive
components explain progressively smaller portions of the variance and are all uncorrelated with each
other. Principal components analysis is used to obtain the initial factor solution. It can be used when a
correlation matrix is singular.
• Unweighted Least-Squares Method. A factor extraction method that minimizes the sum of the squared
differences between the observed and reproduced correlation matrices (ignoring the diagonals).
• Generalized Least-Squares Method. A factor extraction method that minimizes the sum of the squared
differences between the observed and reproduced correlation matrices. Correlations are weighted by
the inverse of their uniqueness, so that variables with high uniqueness are given less weight than those
with low uniqueness.
• Maximum-Likelihood Method. A factor extraction method that produces parameter estimates that are
most likely to have produced the observed correlation matrix if the sample is from a multivariate normal
distribution. The correlations are weighted by the inverse of the uniqueness of the variables, and an
iterative algorithm is employed.
• Principal Axis Factoring. A method of extracting factors from the original correlation matrix, with
squared multiple correlation coefficients placed in the diagonal as initial estimates of the
communalities. These factor loadings are used to estimate new communalities that replace the old
communality estimates in the diagonal. Iterations continue until the changes in the communalities from
one iteration to the next satisfy the convergence criterion for extraction.
• Alpha Factoring. A factor extraction method that considers the variables in the analysis to be a sample
from the universe of potential variables. This method maximizes the alpha reliability of the factors.
• Image Factoring. A factor extraction method developed by Guttman and based on image theory. The
common part of the variable, called the partial image, is defined as its linear regression on remaining
variables, rather than a function of hypothetical factors.
Analyze. Allows you to specify either a correlation matrix or a covariance matrix.
• Correlation matrix. Useful if variables in your analysis are measured on different scales.
• Covariance matrix. Useful when you want to apply your factor analysis to multiple groups with different
variances for each variable.
Chapter 1. Core features 113
Extract. You can either retain all factors whose eigenvalues exceed a specified value, or you can retain a
specific number of factors.
Display. Allows you to request the unrotated factor solution and a scree plot of the eigenvalues.
• Unrotated Factor Solution. Displays unrotated factor loadings (factor pattern matrix), communalities,
and eigenvalues for the factor solution.
• Scree plot. A plot of the variance that is associated with each factor. This plot is used to determine how
many factors should be kept. Typically the plot shows a distinct break between the steep slope of the
large factors and the gradual trailing of the rest (the scree).
Maximum Iterations for Convergence. Allows you to specify the maximum number of steps that the
algorithm can take to estimate the solution.
Factor Analysis Rotation
Method. Allows you to select the method of factor rotation. Available methods are varimax, direct
oblimin, quartimax, equamax, or promax.
• Varimax Method. An orthogonal rotation method that minimizes the number of variables that have high
loadings on each factor. This method simplifies the interpretation of the factors.
• Direct Oblimin Method. A method for oblique (nonorthogonal) rotation. When delta equals 0 (the
default), solutions are most oblique. As delta becomes more negative, the factors become less oblique.
To override the default delta of 0, enter a number less than or equal to 0.8.
• Quartimax Method. A rotation method that minimizes the number of factors needed to explain each
variable. This method simplifies the interpretation of the observed variables.
• Equamax Method. A rotation method that is a combination of the varimax method, which simplifies the
factors, and the quartimax method, which simplifies the variables. The number of variables that load
highly on a factor and the number of factors needed to explain a variable are minimized.
• Promax Rotation. An oblique rotation, which allows factors to be correlated. This rotation can be
calculated more quickly than a direct oblimin rotation, so it is useful for large datasets.
Display. Allows you to include output on the rotated solution, as well as loading plots for the first two or
three factors.
• Rotated Solution. A rotation method must be selected to obtain a rotated solution. For orthogonal
rotations, the rotated pattern matrix and factor transformation matrix are displayed. For oblique
rotations, the pattern, structure, and factor correlation matrices are displayed.
• Factor Loading Plot. Three-dimensional factor loading plot of the first three factors. For a two-factor
solution, a two-dimensional plot is shown. The plot is not displayed if only one factor is extracted. Plots
display rotated solutions if rotation is requested.
Maximum Iterations for Convergence. Allows you to specify the maximum number of steps that the
algorithm can take to perform the rotation.
Factor Analysis Scores
Save as variables. Creates one new variable for each factor in the final solution.
Method. The alternative methods for calculating factor scores are regression, Bartlett, and Anderson-
Rubin.
• Regression Method. A method for estimating factor score coefficients. The scores that are produced
have a mean of 0 and a variance equal to the squared multiple correlation between the estimated factor
scores and the true factor values. The scores may be correlated even when factors are orthogonal.
• Bartlett Scores. A method of estimating factor score coefficients. The scores that are produced have a
mean of 0. The sum of squares of the unique factors over the range of variables is minimized.
• Anderson-Rubin Method. A method of estimating factor score coefficients; a modification of the Bartlett
method which ensures orthogonality of the estimated factors. The scores that are produced have a
mean of 0, have a standard deviation of 1, and are uncorrelated.
114 IBM SPSS Statistics Base V27
Display factor score coefficient matrix. Shows the coefficients by which variables are multiplied to
obtain factor scores. Also shows the correlations between factor scores.
Factor Analysis Options
Missing Values. Allows you to specify how missing values are handled. The available choices are to
exclude cases listwise, exclude cases pairwise, or replace with mean.
Coefficient Display Format. Allows you to control aspects of the output matrices. You sort coefficients by
size and suppress coefficients with absolute values that are less than the specified value.
FACTOR Command Additional Features
The command syntax language also allows you to:
• Specify convergence criteria for iteration during extraction and rotation.
• Specify individual rotated-factor plots.
• Specify how many factor scores to save.
• Specify diagonal values for the principal axis factoring method.
• Write correlation matrices or factor-loading matrices to disk for later analysis.
• Read and analyze correlation matrices or factor-loading matrices.
See the Command Syntax Reference for complete syntax information.
Choosing a Procedure for Clustering
Cluster analyses can be performed using the TwoStep, Hierarchical, or K-Means Cluster Analysis
procedure. Each procedure employs a different algorithm for creating clusters, and each has options not
available in the others.
TwoStep Cluster Analysis. For many applications, the TwoStep Cluster Analysis procedure will be the
method of choice. It provides the following unique features:
• Automatic selection of the best number of clusters, in addition to measures for choosing between
cluster models.
• Ability to create cluster models simultaneously based on categorical and continuous variables.
• Ability to save the cluster model to an external XML file and then read that file and update the cluster
model using newer data.
Additionally, the TwoStep Cluster Analysis procedure can analyze large data files.
Hierarchical Cluster Analysis. The Hierarchical Cluster Analysis procedure is limited to smaller data files
(hundreds of objects to be clustered) but has the following unique features:
• Ability to cluster cases or variables.
• Ability to compute a range of possible solutions and save cluster memberships for each of those
solutions.
• Several methods for cluster formation, variable transformation, and measuring the dissimilarity
between clusters.
As long as all the variables are of the same type, the Hierarchical Cluster Analysis procedure can analyze
interval (continuous), count, or binary variables.
K-Means Cluster Analysis. The K-Means Cluster Analysis procedure is limited to continuous data and
requires you to specify the number of clusters in advance, but it has the following unique features:
• Ability to save distances from cluster centers for each object.
• Ability to read initial cluster centers from and save final cluster centers to an external IBM SPSS
Statistics file.
Additionally, the K-Means Cluster Analysis procedure can analyze large data files.
Chapter 1. Core features 115
TwoStep Cluster Analysis
The TwoStep Cluster Analysis procedure is an exploratory tool designed to reveal natural groupings (or
clusters) within a dataset that would otherwise not be apparent. The algorithm employed by this
procedure has several desirable features that differentiate it from traditional clustering techniques:
• Handling of categorical and continuous variables. By assuming variables to be independent, a joint
multinomial-normal distribution can be placed on categorical and continuous variables.
• Automatic selection of number of clusters. By comparing the values of a model-choice criterion
across different clustering solutions, the procedure can automatically determine the optimal number of
clusters.
• Scalability. By constructing a cluster features (CF) tree that summarizes the records, the TwoStep
algorithm allows you to analyze large data files.
Example. Retail and consumer product companies regularly apply clustering techniques to data that
describe their customers’ buying habits, gender, age, income level, etc. These companies tailor their
marketing and product development strategies to each consumer group to increase sales and build brand
loyalty.
Distance Measure. This selection determines how the similarity between two clusters is computed.
• Log-likelihood. The likelihood measure places a probability distribution on the variables. Continuous
variables are assumed to be normally distributed, while categorical variables are assumed to be
multinomial. All variables are assumed to be independent.
• Euclidean. The Euclidean measure is the “straight line” distance between two clusters. It can be used
only when all of the variables are continuous.
Number of Clusters. This selection allows you to specify how the number of clusters is to be determined.
• Determine automatically. The procedure will automatically determine the “best” number of clusters,
using the criterion specified in the Clustering Criterion group. Optionally, enter a positive integer
specifying the maximum number of clusters that the procedure should consider.
• Specify fixed. Allows you to fix the number of clusters in the solution. Enter a positive integer.
Count of Continuous Variables. This group provides a summary of the continuous variable
standardization specifications made in the Options dialog box. See the topic “TwoStep Cluster Analysis
Options” on page 117 for more information.
Clustering Criterion. This selection determines how the automatic clustering algorithm determines the
number of clusters. Either the Bayesian Information Criterion (BIC) or the Akaike Information Criterion
(AIC) can be specified.
TwoStep Cluster Analysis Data Considerations
Data. This procedure works with both continuous and categorical variables. Cases represent objects to be
clustered, and the variables represent attributes upon which the clustering is based.
Case Order. Note that the cluster features tree and the final solution may depend on the order of cases.
To minimize order effects, randomly order the cases. You may want to obtain several different solutions
with cases sorted in different random orders to verify the stability of a given solution. In situations where
this is difficult due to extremely large file sizes, multiple runs with a sample of cases sorted in different
random orders might be substituted.
Assumptions. The likelihood distance measure assumes that variables in the cluster model are
independent. Further, each continuous variable is assumed to have a normal (Gaussian) distribution, and
each categorical variable is assumed to have a multinomial distribution. Empirical internal testing
indicates that the procedure is fairly robust to violations of both the assumption of independence and the
distributional assumptions, but you should try to be aware of how well these assumptions are met.
Use the Bivariate Correlations procedure to test the independence of two continuous variables. Use the
Crosstabs procedure to test the independence of two categorical variables. Use the Means procedure to
test the independence between a continuous variable and categorical variable. Use the Explore procedure
116 IBM SPSS Statistics Base V27
to test the normality of a continuous variable. Use the Chi-Square Test procedure to test whether a
categorical variable has a specified multinomial distribution.
To Obtain a TwoStep Cluster Analysis
1. From the menus choose:
Analyze > Classify > TwoStep Cluster…
2. Select one or more categorical or continuous variables.
Optionally, you can:
• Adjust the criteria by which clusters are constructed.
• Select settings for noise handling, memory allocation, variable standardization, and cluster model input.
• Request model viewer output.
• Save model results to the working file or to an external XML file.
TwoStep Cluster Analysis Options
Outlier Treatment. This group allows you to treat outliers specially during clustering if the cluster
features (CF) tree fills. The CF tree is full if it cannot accept any more cases in a leaf node and no leaf node
can be split.
• If you select noise handling and the CF tree fills, it will be regrown after placing cases in sparse leaves
into a “noise” leaf. A leaf is considered sparse if it contains fewer than the specified percentage of cases
of the maximum leaf size. After the tree is regrown, the outliers will be placed in the CF tree if possible.
If not, the outliers are discarded.
• If you do not select noise handling and the CF tree fills, it will be regrown using a larger distance change
threshold. After final clustering, values that cannot be assigned to a cluster are labeled outliers. The
outlier cluster is given an identification number of –1 and is not included in the count of the number of
clusters.
Memory Allocation. This group allows you to specify the maximum amount of memory in megabytes
(MB) that the cluster algorithm should use. If the procedure exceeds this maximum, it will use the disk to
store information that will not fit in memory. Specify a number greater than or equal to 4.
• Consult your system administrator for the largest value that you can specify on your system.
• The algorithm may fail to find the correct or specified number of clusters if this value is too low.
Variable standardization. The clustering algorithm works with standardized continuous variables. Any
continuous variables that are not standardized should be left as variables in the To be Standardized list.
To save some time and computational effort, you can select any continuous variables that you have
already standardized as variables in the Assumed Standardized list.
Advanced Options
CF Tree Tuning Criteria. The following clustering algorithm settings apply specifically to the cluster
features (CF) tree and should be changed with care:
• Initial Distance Change Threshold. This is the initial threshold used to grow the CF tree. If inserting a
given case into a leaf of the CF tree would yield tightness less than the threshold, the leaf is not split. If
the tightness exceeds the threshold, the leaf is split.
• Maximum Branches (per leaf node). The maximum number of child nodes that a leaf node can have.
• Maximum Tree Depth. The maximum number of levels that the CF tree can have.
• Maximum Number of Nodes Possible. This indicates the maximum number of CF tree nodes that could
potentially be generated by the procedure, based on the function (b d+1 – 1) / (b – 1), where b is the
maximum branches and d is the maximum tree depth. Be aware that an overly large CF tree can be a
drain on system resources and can adversely affect the performance of the procedure. At a minimum,
each node requires 16 bytes.
Chapter 1. Core features 117
Cluster Model Update. This group allows you to import and update a cluster model generated in a prior
analysis. The input file contains the CF tree in XML format. The model will then be updated with the data
in the active file. You must select the variable names in the main dialog box in the same order in which
they were specified in the prior analysis. The XML file remains unaltered, unless you specifically write the
new model information to the same filename. See the topic “TwoStep Cluster Analysis Output” on page
118 for more information.
If a cluster model update is specified, the options pertaining to generation of the CF tree that were
specified for the original model are used. More specifically, the distance measure, noise handling,
memory allocation, or CF tree tuning criteria settings for the saved model are used, and any settings for
these options in the dialog boxes are ignored.
Note: When performing a cluster model update, the procedure assumes that none of the selected cases in
the active dataset were used to create the original cluster model. The procedure also assumes that the
cases used in the model update come from the same population as the cases used to create the original
model; that is, the means and variances of continuous variables and levels of categorical variables are
assumed to be the same across both sets of cases. If your “new” and “old” sets of cases come from
heterogeneous populations, you should run the TwoStep Cluster Analysis procedure on the combined
sets of cases for the best results.
TwoStep Cluster Analysis Output
Output. This group provides options for displaying the clustering results.
• Pivot tables. Results are displayed in pivot tables.
• Charts and tables in Model Viewer. Results are displayed in the Model Viewer.
• Evaluation fields. This calculates cluster data for variables that were not used in cluster creation.
Evaluation fields can be displayed along with the input features in the model viewer by selecting them in
the Display subdialog. Fields with missing values are ignored.
Working Data File. This group allows you to save variables to the active dataset.
• Create cluster membership variable. This variable contains a cluster identification number for each
case. The name of this variable is tsc_n, where n is a positive integer indicating the ordinal of the active
dataset save operation completed by this procedure in a given session.
XML Files. The final cluster model and CF tree are two types of output files that can be exported in XML
format.
• Export final model. The final cluster model is exported to the specified file in XML (PMML) format. You
can use this model file to apply the model information to other data files for scoring purposes.
• Export CF tree. This option allows you to save the current state of the cluster tree and update it later
using newer data.
The Cluster Viewer
Cluster models are typically used to find groups (or clusters) of similar records based on the variables
examined, where the similarity between members of the same group is high and the similarity between
members of different groups is low. The results can be used to identify associations that would otherwise
not be apparent. For example, through cluster analysis of customer preferences, income level, and buying
habits, it may be possible to identify the types of customers who are more likely to respond to a particular
marketing campaign.
There are two approaches to interpreting the results in a cluster display:
• Examine clusters to determine characteristics unique to that cluster. Does one cluster contain all the
high-income borrowers? Does this cluster contain more records than the others?
• Examine fields across clusters to determine how values are distributed among clusters. Does one’s level
of education determine membership in a cluster? Does a high credit score distinguish between
membership in one cluster or another?
118 IBM SPSS Statistics Base V27
Using the main views and the various linked views in the Cluster Viewer, you can gain insight to help you
answer these questions.
To see information about the cluster model, activate (double-click) the Model Viewer object in the Viewer.
Cluster Viewer
The Cluster Viewer is made up of two panels, the main view on the left and the linked, or auxiliary, view on
the right. There are two main views:
• Model Summary (the default). See the topic “Model Summary View” on page 119 for more information.
• Clusters. See the topic “Clusters View” on page 119 for more information.
There are four linked/auxiliary views:
• Predictor Importance. See the topic “Cluster Predictor Importance View” on page 121 for more
information.
• Cluster Sizes (the default). See the topic “Cluster Sizes View” on page 121 for more information.
• Cell Distribution. See the topic “Cell Distribution View” on page 121 for more information.
• Cluster Comparison. See the topic “Cluster Comparison View” on page 121 for more information.
Model Summary View
The Model Summary view shows a snapshot, or summary, of the cluster model, including a Silhouette
measure of cluster cohesion and separation that is shaded to indicate poor, fair, or good results. This
snapshot enables you to quickly check if the quality is poor, in which case you may decide to return to the
modeling node to amend the cluster model settings to produce a better result.
The results of poor, fair, and good are based on the work of Kaufman and Rousseeuw (1990) regarding
interpretation of cluster structures. In the Model Summary view, a good result equates to data that
reflects Kaufman and Rousseeuw’s rating as either reasonable or strong evidence of cluster structure, fair
reflects their rating of weak evidence, and poor reflects their rating of no significant evidence.
The silhouette measure averages, over all records, (B−A) / max(A,B), where A is the record’s distance to
its cluster center and B is the record’s distance to the nearest cluster center that it doesn’t belong to. A
silhouette coefficient of 1 would mean that all cases are located directly on their cluster centers. A value
of −1 would mean all cases are located on the cluster centers of some other cluster. A value of 0 means,
on average, cases are equidistant between their own cluster center and the nearest other cluster.
The summary includes a table that contains the following information:
• Algorithm. The clustering algorithm used, for example, “TwoStep”.
• Input Features. The number of fields, also known as inputs or predictors.
• Clusters. The number of clusters in the solution.
Clusters View
The Clusters view contains a cluster-by-features grid that includes cluster names, sizes, and profiles for
each cluster.
The columns in the grid contain the following information:
• Cluster. The cluster numbers created by the algorithm.
• Label. Any labels applied to each cluster (this is blank by default). Double-click in the cell to enter a
label that describes the cluster contents; for example, “Luxury car buyers”.
• Description. Any description of the cluster contents (this is blank by default). Double-click in the cell to
enter a description of the cluster; for example, “55+ years of age, professionals, earning over
$100,000”.
• Size. The size of each cluster as a percentage of the overall cluster sample. Each size cell within the grid
displays a vertical bar that shows the size percentage within the cluster, a size percentage in numeric
format, and the cluster case counts.
Chapter 1. Core features 119
• Features. The individual inputs or predictors, sorted by overall importance by default. If any columns
have equal sizes they are shown in ascending sort order of the cluster numbers.
Overall feature importance is indicated by the color of the cell background shading; the most important
feature is darkest; the least important feature is unshaded. A guide above the table indicates the
importance attached to each feature cell color.
When you hover your mouse over a cell, the full name/label of the feature and the importance value for
the cell is displayed. Further information may be displayed, depending on the view and feature type. In
the Cluster Centers view, this includes the cell statistic and the cell value; for example: “Mean: 4.32”. For
categorical features the cell shows the name of the most frequent (modal) category and its percentage.
Within the Clusters view, you can select various ways to display the cluster information:
• Transpose clusters and features. See the topic “Transpose Clusters and Features” on page 120 for
more information.
• Sort features. See the topic “Sort Features” on page 120 for more information.
• Sort clusters. See the topic “Sort Clusters” on page 120 for more information.
• Select cell contents. See the topic “Cell Contents” on page 120 for more information.
Transpose Clusters and Features
By default, clusters are displayed as columns and features are displayed as rows. To reverse this display,
click the Transpose Clusters and Features button to the left of the Sort Features By buttons. For
example you may want to do this when you have many clusters displayed, to reduce the amount of
horizontal scrolling required to see the data.
Sort Features
The Sort Features By buttons enable you to select how feature cells are displayed:
• Overall Importance. This is the default sort order. Features are sorted in descending order of overall
importance, and sort order is the same across clusters. If any features have tied importance values, the
tied features are listed in ascending sort order of the feature names.
• Within-Cluster Importance. Features are sorted with respect to their importance for each cluster. If
any features have tied importance values, the tied features are listed in ascending sort order of the
feature names. When this option is chosen the sort order usually varies across clusters.
• Name. Features are sorted by name in alphabetical order.
• Data order. Features are sorted by their order in the dataset.
Sort Clusters
By default clusters are sorted in descending order of size. The Sort Clusters By buttons enable you to
sort them by name in alphabetical order, or, if you have created unique labels, in alphanumeric label order
instead.
Features that have the same label are sorted by cluster name. If clusters are sorted by label and you edit
the label of a cluster, the sort order is automatically updated.
Cell Contents
The Cells buttons enable you to change the display of the cell contents for features and evaluation fields.
• Cluster Centers. By default, cells display feature names/labels and the central tendency for each
cluster/feature combination. The mean is shown for continuous fields and the mode (most frequently
occurring category) with category percentage for categorical fields.
• Absolute Distributions. Shows feature names/labels and absolute distributions of the features within
each cluster. For categorical features, the display shows bar charts overlaid with categories ordered in
ascending order of the data values. For continuous features, the display shows a smooth density plot
which use the same endpoints and intervals for each cluster.
120 IBM SPSS Statistics Base V27
The solid red colored display shows the cluster distribution, whilst the paler display represents the
overall data.
• Relative Distributions. Shows feature names/labels and relative distributions in the cells. In general
the displays are similar to those shown for absolute distributions, except that relative distributions are
displayed instead.
The solid red colored display shows the cluster distribution, while the paler display represents the
overall data.
• Basic View. Where there are a lot of clusters, it can be difficult to see all the detail without scrolling. To
reduce the amount of scrolling, select this view to change the display to a more compact version of the
table.
Cluster Predictor Importance View
The Predictor Importance view shows the relative importance of each field in estimating the model.
Cluster Sizes View
The Cluster Sizes view shows a pie chart that contains each cluster. The percentage size of each cluster is
shown on each slice; hover the mouse over each slice to display the count in that slice.
Below the chart, a table lists the following size information:
• The size of the smallest cluster (both a count and percentage of the whole).
• The size of the largest cluster (both a count and percentage of the whole).
• The ratio of size of the largest cluster to the smallest cluster.
Cell Distribution View
The Cell Distribution view shows an expanded, more detailed, plot of the distribution of the data for any
feature cell you select in the table in the Clusters main panel.
Cluster Comparison View
The Cluster Comparison view consists of a grid-style layout, with features in the rows and selected
clusters in the columns. This view helps you to better understand the factors that make up the clusters; it
also enables you to see differences between clusters not only as compared with the overall data, but with
each other.
To select clusters for display, click on the top of the cluster column in the Clusters main panel. Use either
Ctrl-click or Shift-click to select or deselect more than one cluster for comparison.
Note: You can select up to five clusters for display.
Clusters are shown in the order in which they were selected, while the order of fields is determined by the
Sort Features By option. When you select Within-Cluster Importance, fields are always sorted by
overall importance .
The background plots show the overall distributions of each features:
• Categorical features are shown as dot plots, where the size of the dot indicates the most frequent/
modal category for each cluster (by feature).
• Continuous features are displayed as boxplots, which show overall medians and the interquartile
ranges.
Overlaid on these background views are boxplots for selected clusters:
• For continuous features, square point markers and horizontal lines indicate the median and
interquartile range for each cluster.
• Each cluster is represented by a different color, shown at the top of the view.
Chapter 1. Core features 121
Navigating the Cluster Viewer
The Cluster Viewer is an interactive display. You can:
• Select a field or cluster to view more details.
• Compare clusters to select items of interest.
• Alter the display.
• Transpose axes.
Using the Toolbars
You control the information shown in both the left and right panels by using the toolbar options. You can
change the orientation of the display (top-down, left-to-right, or right-to-left) using the toolbar controls.
In addition, you can also reset the viewer to the default settings, and open a dialog box to specify the
contents of the Clusters view in the main panel.
The Sort Features By, Sort Clusters By, Cells, and Display options are only available when you select the
Clusters view in the main panel. See the topic “Clusters View” on page 119 for more information.
Table 2. Toolbar icons
Icon Topic
See Transpose Clusters and Features
See Sort Features By
See Sort Clusters By
See Cells
Control Cluster View Display
To control what is shown in the Clusters view on the main panel, click the Display button; the Display
dialog opens.
Features. Selected by default. To hide all input features, deselect the check box.
Evaluation Fields. Choose the evaluation fields (fields not used to create the cluster model, but sent to
the model viewer to evaluate the clusters) to display; none are shown by default. Note The evaluation field
must be a string with more than one value. This check box is unavailable if no evaluation fields are
available.
Cluster Descriptions. Selected by default. To hide all cluster description cells, deselect the check box.
Cluster Sizes. Selected by default. To hide all cluster size cells, deselect the check box.
Maximum Number of Categories. Specify the maximum number of categories to display in charts of
categorical features; the default is 20.
Filtering Records
If you want to know more about the cases in a particular cluster or group of clusters, you can select a
subset of records for further analysis based on the selected clusters.
1. Select the clusters in the Cluster view of the Cluster Viewer. To select multiple clusters, use Ctrl-click.
2. From the menus choose:
Generate > Filter Records…
3. Enter a filter variable name. Records from the selected clusters will receive a value of 1 for this field.
All other records will receive a value of 0 and will be excluded from subsequent analyses until you
change the filter status.
122 IBM SPSS Statistics Base V27
4. Click OK.
Hierarchical Cluster Analysis
This procedure attempts to identify relatively homogeneous groups of cases (or variables) based on
selected characteristics, using an algorithm that starts with each case (or variable) in a separate cluster
and combines clusters until only one is left. You can analyze raw variables, or you can choose from a
variety of standardizing transformations. Distance or similarity measures are generated by the Proximities
procedure. Statistics are displayed at each stage to help you select the best solution.
Example. Are there identifiable groups of television shows that attract similar audiences within each
group? With hierarchical cluster analysis, you could cluster television shows (cases) into homogeneous
groups based on viewer characteristics. This can be used to identify segments for marketing. Or you can
cluster cities (cases) into homogeneous groups so that comparable cities can be selected to test various
marketing strategies.
Statistics. Agglomeration schedule, distance (or similarity) matrix, and cluster membership for a single
solution or a range of solutions. Plots: dendrograms and icicle plots.
Hierarchical Cluster Analysis Data Considerations
Data. The variables can be quantitative, binary, or count data. Scaling of variables is an important issue–
differences in scaling may affect your cluster solution(s). If your variables have large differences in scaling
(for example, one variable is measured in dollars and the other is measured in years), you should consider
standardizing them (this can be done automatically by the Hierarchical Cluster Analysis procedure).
Case order. If tied distances or similarities exist in the input data or occur among updated clusters during
joining, the resulting cluster solution may depend on the order of cases in the file. You may want to obtain
several different solutions with cases sorted in different random orders to verify the stability of a given
solution.
Assumptions. The distance or similarity measures used should be appropriate for the data analyzed (see
the Proximities procedure for more information on choices of distance and similarity measures). Also, you
should include all relevant variables in your analysis. Omission of influential variables can result in a
misleading solution. Because hierarchical cluster analysis is an exploratory method, results should be
treated as tentative until they are confirmed with an independent sample.
To Obtain a Hierarchical Cluster Analysis
1. From the menus choose:
Analyze > Classify > Hierarchical Cluster…
2. If you are clustering cases, select at least one numeric variable. If you are clustering variables, select
at least three numeric variables.
Optionally, you can select an identification variable to label cases.
Hierarchical Cluster Analysis Method
Cluster Method. Available alternatives are between-groups linkage, within-groups linkage, nearest
neighbor, furthest neighbor, centroid clustering, median clustering, and Ward’s method.
Measure. Allows you to specify the distance or similarity measure to be used in clustering. Select the type
of data and the appropriate distance or similarity measure:
• Interval. Available alternatives are Euclidean distance, squared Euclidean distance, cosine, Pearson
correlation, Chebychev, block, Minkowski, and customized.
• Counts. Available alternatives are chi-square measure and phi-square measure.
• Binary. Available alternatives are Euclidean distance, squared Euclidean distance, size difference,
pattern difference, variance, dispersion, shape, simple matching, phi 4-point correlation, lambda,
Anderberg’s D, dice, Hamann, Jaccard, Kulczynski 1, Kulczynski 2, Lance and Williams, Ochiai, Rogers
and Tanimoto, Russel and Rao, Sokal and Sneath 1, Sokal and Sneath 2, Sokal and Sneath 3, Sokal and
Sneath 4, Sokal and Sneath 5, Yule’s Y, and Yule’s Q.
Chapter 1. Core features 123
Transform Values. Allows you to standardize data values for either cases or values before computing
proximities (not available for binary data). Available standardization methods are z scores, range −1 to 1,
range 0 to 1, maximum magnitude of 1, mean of 1, and standard deviation of 1.
Transform Measures. Allows you to transform the values generated by the distance measure. They are
applied after the distance measure has been computed. Available alternatives are absolute values,
change sign, and rescale to 0–1 range.
Hierarchical Cluster Analysis Statistics
Agglomeration schedule. Displays the cases or clusters combined at each stage, the distances between
the cases or clusters being combined, and the last cluster level at which a case (or variable) joined the
cluster.
Proximity matrix. Gives the distances or similarities between items.
Cluster Membership. Displays the cluster to which each case is assigned at one or more stages in the
combination of clusters. Available options are single solution and range of solutions.
Hierarchical Cluster Analysis Plots
Dendrogram. Displays a dendrogram. Dendrograms can be used to assess the cohesiveness of the
clusters formed and can provide information about the appropriate number of clusters to keep.
Icicle. Displays an icicle plot, including all clusters or a specified range of clusters. Icicle plots display
information about how cases are combined into clusters at each iteration of the analysis. Orientation
allows you to select a vertical or horizontal plot.
Hierarchical Cluster Analysis Save New Variables
Cluster Membership. Allows you to save cluster memberships for a single solution or a range of
solutions. Saved variables can then be used in subsequent analyses to explore other differences between
groups.
CLUSTER Command Syntax Additional Features
The Hierarchical Cluster procedure uses CLUSTER command syntax. The command syntax language also
allows you to:
• Use several clustering methods in a single analysis.
• Read and analyze a proximity matrix.
• Write a proximity matrix to disk for later analysis.
• Specify any values for power and root in the customized (Power) distance measure.
• Specify names for saved variables.
See the Command Syntax Reference for complete syntax information.
K-Means Cluster Analysis
This procedure attempts to identify relatively homogeneous groups of cases based on selected
characteristics, using an algorithm that can handle large numbers of cases. However, the algorithm
requires you to specify the number of clusters. You can specify initial cluster centers if you know this
information. You can select one of two methods for classifying cases, either updating cluster centers
iteratively or classifying only. You can save cluster membership, distance information, and final cluster
centers. Optionally, you can specify a variable whose values are used to label casewise output. You can
also request analysis of variance F statistics. While these statistics are opportunistic (the procedure tries
to form groups that do differ), the relative size of the statistics provides information about each variable’s
contribution to the separation of the groups.
Example. What are some identifiable groups of television shows that attract similar audiences within
each group? With k-means cluster analysis, you could cluster television shows (cases) into k
124 IBM SPSS Statistics Base V27
homogeneous groups based on viewer characteristics. This process can be used to identify segments for
marketing. Or you can cluster cities (cases) into homogeneous groups so that comparable cities can be
selected to test various marketing strategies.
Statistics. Complete solution: initial cluster centers, ANOVA table. Each case: cluster information,
distance from cluster center.
K-Means Cluster Analysis Data Considerations
Data. Variables should be quantitative at the interval or ratio level. If your variables are binary or counts,
use the Hierarchical Cluster Analysis procedure.
Case and initial cluster center order. The default algorithm for choosing initial cluster centers is not
invariant to case ordering. The Use running means option in the Iterate dialog box makes the resulting
solution potentially dependent on case order, regardless of how initial cluster centers are chosen. If you
are using either of these methods, you may want to obtain several different solutions with cases sorted in
different random orders to verify the stability of a given solution. Specifying initial cluster centers and not
using the Use running means option will avoid issues related to case order. However, ordering of the
initial cluster centers may affect the solution if there are tied distances from cases to cluster centers. To
assess the stability of a given solution, you can compare results from analyses with different
permutations of the initial center values.
Assumptions. Distances are computed using simple Euclidean distance. If you want to use another
distance or similarity measure, use the Hierarchical Cluster Analysis procedure. Scaling of variables is an
important consideration. If your variables are measured on different scales (for example, one variable is
expressed in dollars and another variable is expressed in years), your results may be misleading. In such
cases, you should consider standardizing your variables before you perform the k-means cluster analysis
(this task can be done in the Descriptives procedure). The procedure assumes that you have selected the
appropriate number of clusters and that you have included all relevant variables. If you have chosen an
inappropriate number of clusters or omitted important variables, your results may be misleading.
To Obtain a K-Means Cluster Analysis
1. From the menus choose:
Analyze > Classify > K-Means Cluster…
2. Select the variables to be used in the cluster analysis.
3. Specify the number of clusters. (The number of clusters must be at least 2 and must not be greater
than the number of cases in the data file.)
4. Select either Iterate and classify or Classify only.
5. Optionally, select an identification variable to label cases.
K-Means Cluster Analysis Efficiency
The k-means cluster analysis command is efficient primarily because it does not compute the distances
between all pairs of cases, as do many clustering algorithms, including the algorithm that is used by the
hierarchical clustering command.
For maximum efficiency, take a sample of cases and select the Iterate and classify method to determine
cluster centers. Select Write final as. Then restore the entire data file and select Classify only as the
method and select Read initial from to classify the entire file using the centers that are estimated from
the sample. You can write to and read from a file or a dataset. Datasets are available for subsequent use
in the same session but are not saved as files unless explicitly saved prior to the end of the session.
Dataset names must conform to variable-naming rules. See the topic for more information.
K-Means Cluster Analysis Iterate
Note: These options are available only if you select the Iterate and classify method from the K-Means
Cluster Analysis dialog box.
Chapter 1. Core features 125
Maximum Iterations. Limits the number of iterations in the k-means algorithm. Iteration stops after this
many iterations even if the convergence criterion is not satisfied. This number must be between 1 and
999.
To reproduce the algorithm used by the Quick Cluster command prior to version 5.0, set Maximum
Iterations to 1.
Convergence Criterion. Determines when iteration ceases. It represents a proportion of the minimum
distance between initial cluster centers, so it must be greater than 0 but not greater than 1. If the
criterion equals 0.02, for example, iteration ceases when a complete iteration does not move any of the
cluster centers by a distance of more than 2% of the smallest distance between any initial cluster
centers.
Use running means. Allows you to request that cluster centers be updated after each case is assigned. If
you do not select this option, new cluster centers are calculated after all cases have been assigned.
K-Means Cluster Analysis Save
You can save information about the solution as new variables to be used in subsequent analyses:
Cluster membership. Creates a new variable indicating the final cluster membership of each case. Values
of the new variable range from 1 to the number of clusters.
Distance from cluster center. Creates a new variable indicating the Euclidean distance between each
case and its classification center.
K-Means Cluster Analysis Options
Statistics. You can select the following statistics: initial cluster centers, ANOVA table, and cluster
information for each case.
• Initial cluster centers. First estimate of the variable means for each of the clusters. By default, a number
of well-spaced cases equal to the number of clusters is selected from the data. Initial cluster centers
are used for a first round of classification and are then updated.
• ANOVA table. Displays an analysis-of-variance table which includes univariate F tests for each
clustering variable. The F tests are only descriptive and the resulting probabilities should not be
interpreted. The ANOVA table is not displayed if all cases are assigned to a single cluster.
• Cluster information for each case. Displays for each case the final cluster assignment and the Euclidean
distance between the case and the cluster center used to classify the case. Also displays Euclidean
distance between final cluster centers.
Missing Values. Available options are Exclude cases listwise or Exclude cases pairwise.
• Exclude cases listwise. Excludes cases with missing values for any clustering variable from the
analysis.
• Exclude cases pairwise. Assigns cases to clusters based on distances that are computed from all
variables with nonmissing values.
QUICK CLUSTER Command Additional Features
The K-Means Cluster procedure uses QUICK CLUSTER command syntax. The command syntax language
also allows you to:
• Accept the first k cases as initial cluster centers, thereby avoiding the data pass that is normally used to
estimate them.
• Specify initial cluster centers directly as a part of the command syntax.
• Specify names for saved variables.
See the Command Syntax Reference for complete syntax information.
126 IBM SPSS Statistics Base V27
Nonparametric Tests
Nonparametric tests make minimal assumptions about the underlying distribution of the data. The tests
that are available in these dialogs can be grouped into three broad categories based on how the data are
organized:
• A one-sample test analyzes one field.
• A test for related samples compares two or more fields for the same set of cases.
• An independent-samples test analyzes one field that is grouped by categories of another field.
One-Sample Nonparametric Tests
One-sample nonparametric tests identify differences in single fields using one or more nonparametric
tests. Nonparametric tests do not assume your data follow the normal distribution.
What is your objective? The objectives allow you to quickly specify different but commonly used test
settings.
• Automatically compare observed data to hypothesized. This objective applies the Binomial test to
categorical fields with only two categories, the Chi-Square test to all other categorical fields, and the
Kolmogorov-Smirnov test to continuous fields.
• Test sequence for randomness. This objective uses the Runs test to test the observed sequence of
data values for randomness.
• Custom analysis. When you want to manually amend the test settings on the Settings tab, select this
option. Note that this setting is automatically selected if you subsequently make changes to options on
the Settings tab that are incompatible with the currently selected objective.
Obtaining One-Sample Nonparametric Tests
From the menus choose:
Analyze > Nonparametric Tests > One Sample…
1. Click Run.
Optionally, you can:
• Specify an objective on the Objective tab.
• Specify field assignments on the Fields tab.
• Specify expert settings on the Settings tab.
Fields Tab
The Fields tab specifies which fields should be tested.
Use predefined roles. This option uses existing field information. All fields with a predefined role as
Input, Target, or Both will be used as test fields. At least one test field is required.
Use custom field assignments. This option allows you to override field roles. After selecting this option,
specify the fields below:
• Test Fields. Select one or more fields.
Settings Tab
The Settings tab comprises several different groups of settings that you can modify to fine-tune how the
algorithm processes your data. If you make any changes to the default settings that are incompatible with
the currently selected objective, the Objective tab is automatically updated to select the Customize
analysis option.
Choose Tests
These settings specify the tests to be performed on the fields specified on the Fields tab.
Chapter 1. Core features 127
Automatically choose the tests based on the data. This setting applies the Binomial test to categorical
fields with only two valid (non-missing) categories, the Chi-Square test to all other categorical fields, and
the Kolmogorov-Smirnov test to continuous fields.
Customize tests. This setting allows you to choose specific tests to be performed.
• Compare observed binary probability to hypothesized (Binomial test). The Binomial test can be
applied to all fields. This produces a one-sample test that tests whether the observed distribution of a
flag field (a categorical field with only two categories) is the same as what is expected from a specified
binomial distribution. In addition, you can request confidence intervals. See “Binomial Test Options ” on
page 128 for details on the test settings.
• Compare observed probabilities to hypothesized (Chi-Square test). The Chi-Square test is applied to
nominal and ordinal fields. This produces a one-sample test that computes a chi-square statistic based
on the differences between the observed and expected frequencies of categories of a field. See “Chi-
Square Test Options ” on page 129 for details on the test settings.
• Test observed distribution against hypothesized (Kolmogorov-Smirnov test). The Kolmogorov-
Smirnov test is applied to continuous and ordinal fields. This produces a one-sample test of whether the
sample cumulative distribution function for a field is homogenous with a uniform, normal, Poisson, or
exponential distribution. See “Kolmogorov-Smirnov Options ” on page 129 for details on the test
settings.
• Compare median to hypothesized (Wilcoxon signed-rank test). The Wilcoxon signed-rank test is
applied to continuous and ordinal fields. This produces a one-sample test of median value of a field.
Specify a number as the hypothesized median.
• Test sequence for randomness (Runs test). The Runs test is applied to all fields. This produces a one-
sample test of whether the sequence of values of a dichotomized field is random. See “Runs Test
Options ” on page 129 for details on the test settings.
Binomial Test Options
The binomial test is intended for flag fields (categorical fields with only two categories), but is applied to
all fields by using rules for defining “success”.
Hypothesized proportion. This specifies the expected proportion of records defined as “successes”, or p.
Specify a value greater than 0 and less than 1. The default is 0.5.
Confidence Interval. The following methods for computing confidence intervals for binary data are
available:
• Clopper-Pearson (exact). An exact interval based on the cumulative binomial distribution.
• Jeffreys. A Bayesian interval based on the posterior distribution of p using the Jeffreys prior.
• Likelihood ratio. An interval based on the likelihood function for p.
Define Success for Categorical Fields. This specifies how “success”, the data value(s) tested against the
hypothesized proportion, is defined for categorical fields.
• Use first category found in data performs the binomial test using the first value found in the sample to
define “success”. This option is only applicable to nominal or ordinal fields with only two values; all
other categorical fields specified on the Fields tab where this option is used will not be tested. This is
the default.
• Specify success values performs the binomial test using the specified list of values to define “success”.
Specify a list of string or numeric values. The values in the list do not need to be present in the sample.
Define Success for Continuous Fields. This specifies how “success”, the data value(s) tested against the
test value, is defined for continuous fields. Success is defined as values equal to or less than a cut point.
• Sample midpoint sets the cut point at the average of the minimum and maximum values.
• Custom cutpoint allows you to specify a value for the cut point.
128 IBM SPSS Statistics Base V27
Chi-Square Test Options
All categories have equal probability. This produces equal frequencies among all categories in the
sample. This is the default.
Customize expected probability. This allows you to specify unequal frequencies for a specified list of
categories. Specify a list of string or numeric values. The values in the list do not need to be present in the
sample. In the Category column, specify category values. In the Relative Frequency column, specify a
value greater than 0 for each category. Custom frequencies are treated as ratios so that, for example,
specifying frequencies 1, 2, and 3 is equivalent to specifying frequencies 10, 20, and 30, and both specify
that 1/6 of the records are expected to fall into the first category, 1/3 into the second, and 1/2 into the
third. When custom expected probabilities are specified, the custom category values must include all the
field values in the data; otherwise the test is not performed for that field.
Kolmogorov-Smirnov Options
This dialog specifies which distributions should be tested and the parameters of the hypothesized
distributions.
When certain parameters of the distribution have to be estimated from the sample, the Kolmogorov-
Smirnov test no longer applies. In these instances, the Lilliefors test statistic can be used to estimate the
p-value by using the Monte Carlo sampling for testing normality with mean and variance unknown. The
Lilliefors test applies to the three continuous distributions (Normal, Exponential, and Uniform). Note that
the test does not apply if the underlying distribution is discrete (Poisson). The test is only defined for one-
sample inference when the corresponding distribution parameters are not specified.
Normal
Use sample data uses the observed mean and standard deviation and provides options for selecting
the existing Asymptotic test results, or use Lilliefors test based on the Monte Carlo sampling.
Custom allows you to specify values.
Uniform
Use sample data uses the observed minimum and maximum and uses Lilliefors test based on the
Monte Carlo sampling. Custom allows you to specify minimum and maximum values.
Exponential
Sample mean uses the observed mean and uses Lilliefors test based on the Monte Carlo sampling.
Custom allows you to specify an observed mean value.
Poisson
Mean allows you to specify an observed mean value.
Runs Test Options
The runs test is intended for flag fields (categorical fields with only two categories), but can be applied to
all fields by using rules for defining the groups.
Define Groups for Categorical Fields. The following options are available:
• There are only 2 categories in the sample performs the runs test using the values found in the sample
to define the groups. This option is only applicable to nominal or ordinal fields with only two values; all
other categorical fields specified on the Fields tab where this option is used will not be tested.
• Recode data into 2 categories performs the runs test using the specified list of values to define one of
the groups. All other values in the sample define the other group. The values in the list do not all need to
be present in the sample, but at least one record must be in each group.
Define Cut Point for Continuous Fields. This specifies how groups are defined for continuous fields. The
first group is defined as values equal to or less than a cut point.
• Sample median sets the cut point at the sample median.
• Sample mean sets the cut point at the sample mean.
• Custom allows you to specify a value for the cut point.
Chapter 1. Core features 129
Test Options
Significance level
This specifies the significance level (alpha) for all tests. Specify a numeric value between 0 and 1.
0.05 is the default.
Confidence interval (%)
This specifies the confidence level for all confidence intervals produced. Specify a numeric value
between 0 and 100. 95 is the default.
Excluded Cases
This specifies how to determine the case basis for tests.
Exclude cases test by test
Records with missing values for a field that is used for a specific test are omitted from that test.
When several tests are specified in the analysis, each test is evaluated separately.
Exclude cases listwise
Records with missing values for any field that is named on the Fields tab are excluded from all
analyses.
Monte Carlo Sampling
When certain parameters of the distribution have to be estimated from the sample, the Kolmogorov-
Smirnov test no longer applies. In these instances, the Lilliefors test statistic can be used to estimate
the p-value by using the Monte Carlo sampling for testing normality with mean and variance unknown.
The Lilliefors test applies to the three continuous distributions (Normal, Exponential, and Uniform).
Note that the test does not apply if the underlying distribution is discrete (Poisson). The test is only
defined for one-sample inference when the corresponding distribution parameters are not specified.
Set custom seed
When enabled, this setting provides the option of resetting the random Seed value that is used for
Monte Carlo sampling. The value must be a single integer between 1 and 2,147,483,647. The
default value is 2,000,000.
Number of samples
Resets the number of Monte Carlo sampling replicates that are used by the Lilliefors test. The
value must be a single integer between 100 and the largest integer. The default value is 10,000.
Simulation confidence level (%)
Resets the Kolmogorov-Smirnov test’s estimated confidence interval level. The value must be a
single value between 0 and 100. The default value is 99.
User-Missing Values
User-Missing Values for Categorical Fields. Categorical fields must have valid values for a record to be
included in the analysis. These controls allow you to decide whether user-missing values are treated as
valid among categorical fields. System-missing values and missing values for continuous fields are always
treated as invalid.
NPTESTS command additional features
The command syntax language also allows you to:
• Specify one-sample, independent-samples, and related-samples tests in a single run of the procedure.
See the Command Syntax Reference for complete syntax information.
Independent-Samples Nonparametric Tests
Independent-samples nonparametric tests identify differences between two or more groups using one or
more nonparametric tests. Nonparametric tests do not assume your data follow the normal distribution.
What is your objective? The objectives allow you to quickly specify different but commonly used test
settings.
130 IBM SPSS Statistics Base V27
• Automatically compare distributions across groups. This objective applies the Mann-Whitney U test
to data with 2 groups, or the Kruskal-Wallis 1-way ANOVA to data with k groups.
• Compare medians across groups. This objective uses the Median test to compare the observed
medians across groups.
• Custom analysis. When you want to manually amend the test settings on the Settings tab, select this
option. Note that this setting is automatically selected if you subsequently make changes to options on
the Settings tab that are incompatible with the currently selected objective.
To Obtain Independent-Samples Nonparametric Tests
From the menus choose:
Analyze > Nonparametric Tests > Independent Samples…
1. Click Run.
Optionally, you can:
• Specify an objective on the Objective tab.
• Specify field assignments on the Fields tab.
• Specify expert settings on the Settings tab.
Fields Tab
The Fields tab specifies which fields should be tested and the field used to define groups.
Use predefined roles. This option uses existing field information. All continuous and ordinal fields with a
predefined role as Target or Both will be used as test fields. If there is a single categorical field with a
predefined role as Input, it will be used as a grouping field. Otherwise no grouping field is used by default
and you must use custom field assignments. At least one test field and a grouping field is required.
Use custom field assignments. This option allows you to override field roles. After selecting this option,
specify the fields below:
• Test Fields. Select one or more continuous or ordinal fields.
• Groups. Select a categorical field.
Settings Tab
The Settings tab comprises several different groups of settings that you can modify to fine tune how the
algorithm processes your data. If you make any changes to the default settings that are incompatible with
the currently selected objective, the Objective tab is automatically updated to select the Customize
analysis option.
Choose Tests
These settings specify the tests to be performed on the fields specified on the Fields tab.
Automatically choose the tests based on the data. This setting applies the Mann-Whitney U test to data
with 2 groups, or the Kruskal-Wallis 1-way ANOVA to data with k groups.
Customize tests. This setting allows you to choose specific tests to be performed.
• Compare Distributions across Groups. These produce independent-samples tests of whether the
samples are from the same population.
Mann-Whitney U (2 samples) uses the rank of each case to test whether the groups are drawn from the
same population. The first value in ascending order of the grouping field defines the first group and the
second defines the second group. If the grouping field has more than two values, this test is not
produced.
Kolmogorov-Smirnov (2 samples) is sensitive to any difference in median, dispersion, skewness, and
so forth, between the two distributions. If the grouping field has more than two values, this test is not
produced.
Chapter 1. Core features 131
Test sequence for randomness (Wald-Wolfowitz for 2 samples) produces a runs test with group
membership as the criterion. If the grouping field has more than two values, this test is not produced.
Kruskal-Wallis 1-way ANOVA (k samples) is an extension of the Mann-Whitney U test and the
nonparametric analog of one-way analysis of variance. You can optionally request multiple comparisons
of the k samples, either all pairwise multiple comparisons or stepwise step-down comparisons.
Test for ordered alternatives (Jonckheere-Terpstra for k samples) is a more powerful alternative to
Kruskal-Wallis when the k samples have a natural ordering. For example, the k populations might
represent k increasing temperatures. The hypothesis that different temperatures produce the same
response distribution is tested against the alternative that as the temperature increases, the magnitude
of the response increases. Here, the alternative hypothesis is ordered; therefore, Jonckheere-Terpstra
is the most appropriate test to use. Smallest to largest specifies the alternative hypothesis that the
location parameter of the first group is less than or equal to the second, which is less than or equal to
the third, and so on. Largest to smallest specifies the alternative hypothesis that the location
parameter of the first group is greater than or equal to the second, which is greater than or equal to the
third, and so on. For both options, the alternative hypothesis also assumes that the locations are not all
equal. You can optionally request multiple comparisons of the k samples, either All pairwise multiple
comparisons or Stepwise step-down comparisons.
• Compare Ranges across Groups. This produces an independent-samples tests of whether the samples
have the same range. Moses extreme reaction (2 samples) tests a control group versus a comparison
group. The first value in ascending order of the grouping field defines the control group and the second
defines the comparison group. If the grouping field has more than two values, this test is not produced.
• Compare Medians across Groups. This produces an independent-samples tests of whether the
samples have the same median. Median test (k samples) can use either the pooled sample median
(calculated across all records in the dataset) or a custom value as the hypothesized median. You can
optionally request multiple comparisons of the k samples, either All pairwise multiple comparisons or
Stepwise step-down comparisons.
• Estimate Confidence Intervals across Groups. Hodges-Lehman estimate (2 samples) produces an
independent samples estimate and confidence interval for the difference in the medians of two groups.
If the grouping field has more than two values, this test is not produced.
Test Options
Significance level. This specifies the significance level (alpha) for all tests. Specify a numeric value
between 0 and 1. 0.05 is the default.
Confidence interval (%). This specifies the confidence level for all confidence intervals produced. Specify
a numeric value between 0 and 100. 95 is the default.
Excluded Cases. This specifies how to determine the case basis for tests. Exclude cases listwise means
that records with missing values for any field that is named on any subcommand are excluded from all
analyses. Exclude cases test by test means that records with missing values for a field that is used for a
specific test are omitted from that test. When several tests are specified in the analysis, each test is
evaluated separately.
User-Missing Values
User-Missing Values for Categorical Fields. Categorical fields must have valid values for a record to be
included in the analysis. These controls allow you to decide whether user-missing values are treated as
valid among categorical fields. System-missing values and missing values for continuous fields are always
treated as invalid.
NPTESTS command additional features
The command syntax language also allows you to:
• Specify one-sample, independent-samples, and related-samples tests in a single run of the procedure.
See the Command Syntax Reference for complete syntax information.
132 IBM SPSS Statistics Base V27
Related-Samples Nonparametric Tests
Identifies differences between two or more related fields using one or more nonparametric tests.
Nonparametric tests do not assume your data follow the normal distribution.
Data Considerations. Each record corresponds to a given subject for which two or more related
measurements are stored in separate fields in the dataset. For example, a study concerning the
effectiveness of a dieting plan can be analyzed using related-samples nonparametric tests if each
subject’s weight is measured at regular intervals and stored in fields like Pre-diet weight, Interim weight,
and Post-diet weight. These fields are “related”.
What is your objective? The objectives allow you to quickly specify different but commonly used test
settings.
• Automatically compare observed data to hypothesized data. This objective applies McNemar’s Test
to categorical data when 2 fields are specified, Cochran’s Q to categorical data when more than 2 fields
are specified, the Wilcoxon Matched-Pair Signed-Rank test to continuous data when 2 fields are
specified, and Friedman’s 2-Way ANOVA by Ranks to continuous data when more than 2 fields are
specified.
• Custom analysis. When you want to manually amend the test settings on the Settings tab, select this
option. Note that this setting is automatically selected if you subsequently make changes to options on
the Settings tab that are incompatible with the currently selected objective.
When fields of differing measurement level are specified, they are first separated by measurement level
and then the appropriate test is applied to each group. For example, if you choose Automatically
compare observed data to hypothesized data as your objective and specify 3 continuous fields and 2
nominal fields, then Friedman’s test is applied to the continuous fields and McNemar’s test is applied to
the nominal fields.
To Obtain Related-Samples Nonparametric Tests
From the menus choose:
Analyze > Nonparametric Tests > Related Samples…
1. Click Run.
Optionally, you can:
• Specify an objective on the Objective tab.
• Specify field assignments on the Fields tab.
• Specify expert settings on the Settings tab.
Fields Tab
The Fields tab specifies which fields should be tested.
Use predefined roles. This option uses existing field information. All fields with a predefined role as
Target or Both will be used as test fields. At least two test fields are required.
Use custom field assignments. This option allows you to override field roles. After selecting this option,
specify the fields below:
• Test Fields. Select two or more fields. Each field corresponds to a separate related sample.
Settings Tab
The Settings tab comprises several different groups of settings that you can modify to fine tune how the
procedure processes your data. If you make any changes to the default settings that are incompatible
with the other objectives, the Objective tab is automatically updated to select the Customize analysis
option.
Choose Tests
These settings specify the tests to be performed on the fields specified on the Fields tab.
Chapter 1. Core features 133
Automatically choose the tests based on the data. This setting applies McNemar’s Test to categorical
data when 2 fields are specified, Cochran’s Q to categorical data when more than 2 fields are specified,
the Wilcoxon Matched-Pair Signed-Rank test to continuous data when 2 fields are specified, and
Friedman’s 2-Way ANOVA by Ranks to continuous data when more than 2 fields are specified.
Customize tests. This setting allows you to choose specific tests to be performed.
• Test for Change in Binary Data. McNemar’s test (2 samples) can be applied to categorical fields. This
produces a related-samples test of whether combinations of values between two flag fields (categorical
fields with only two values) are equally likely. If there are more than two fields specified on the Fields
tab, this test is not performed. See “McNemar’s Test: Define Success ” on page 134 for details on the
test settings. Cochran’s Q (k samples) can be applied to categorical fields. This produces a related-
samples test of whether combinations of values between k flag fields (categorical fields with only two
values) are equally likely. You can optionally request multiple comparisons of the k samples, either all
pairwise multiple comparisons or stepwise step-down comparisons. See “Cochran’s Q: Define
Success ” on page 134 for details on the test settings.
• Test for Changes in Multinomial Data. Marginal homogeneity test (2 samples) produces a related
samples test of whether combinations of values between two paired ordinal fields are equally likely.
The marginal homogeneity test is typically used in repeated measures situations. This test is an
extension of the McNemar test from binary response to multinomial response. If there are more than
two fields specified on the Fields tab, this test is not performed.
• Compare Median Difference to Hypothesized. These tests each produce a related-samples test of
whether the median difference between two fields is different from 0. The test applies to continuous
and ordinal fields. If there are more than two fields specified on the Fields tab, these tests are not
performed.
• Estimate Confidence Interval. This produces a related samples estimate and confidence interval for
the median difference between two paired fields. The test applies to continuous and ordinal fields. If
there are more than two fields specified on the Fields tab, this test is not performed.
• Quantify Associations. Kendall’s coefficient of concordance (k samples) produces a measure of
agreement among judges or raters, where each record is one judge’s rating of several items (fields). You
can optionally request multiple comparisons of the k samples, either All pairwise multiple comparisons
or Stepwise step-down comparisons.
• Compare Distributions. Friedman’s 2-way ANOVA by ranks (k samples) produces a related samples
test of whether k related samples have been drawn from the same population. You can optionally
request multiple comparisons of the k samples, either All pairwise multiple comparisons or Stepwise
step-down comparisons.
McNemar’s Test: Define Success
McNemar’s test is intended for flag fields (categorical fields with only two categories), but is applied to all
categorical fields by using rules for defining “success”.
Define Success for Categorical Fields. This specifies how “success” is defined for categorical fields.
• Use first category found in data performs the test using the first value found in the sample to define
“success”. This option is only applicable to nominal or ordinal fields with only two values; all other
categorical fields specified on the Fields tab where this option is used will not be tested. This is the
default.
• Specify success values performs the test using the specified list of values to define “success”. Specify
a list of string or numeric values. The values in the list do not need to be present in the sample.
Cochran’s Q: Define Success
Cochran’s Q test is intended for flag fields (categorical fields with only two categories), but is applied to all
categorical fields by using rules for defining “success”.
Define Success for Categorical Fields. This specifies how “success” is defined for categorical fields.
• Use first category found in data performs the test using the first value found in the sample to define
“success”. This option is only applicable to nominal or ordinal fields with only two values; all other
134 IBM SPSS Statistics Base V27
categorical fields specified on the Fields tab where this option is used will not be tested. This is the
default.
• Specify success values performs the test using the specified list of values to define “success”. Specify
a list of string or numeric values. The values in the list do not need to be present in the sample.
Test Options
Significance level. This specifies the significance level (alpha) for all tests. Specify a numeric value
between 0 and 1. 0.05 is the default.
Confidence interval (%). This specifies the confidence level for all confidence intervals produced. Specify
a numeric value between 0 and 100. 95 is the default.
Excluded Cases. This specifies how to determine the case basis for tests.
• Exclude cases listwise means that records with missing values for any field that is named on any
subcommand are excluded from all analyses.
• Exclude cases test by test means that records with missing values for a field that is used for a specific
test are omitted from that test. When several tests are specified in the analysis, each test is evaluated
separately.
User-Missing Values
User-Missing Values for Categorical Fields. Categorical fields must have valid values for a record to be
included in the analysis. These controls allow you to decide whether user-missing values are treated as
valid among categorical fields. System-missing values and missing values for continuous fields are always
treated as invalid.
NPTESTS command additional features
The command syntax language also allows you to:
• Specify one-sample, independent-samples, and related-samples tests in a single run of the procedure.
See the Command Syntax Reference for complete syntax information.
Model View
Model View
The procedure creates a Model Viewer object in the Viewer. By activating (double-clicking) this object,
you gain an interactive view of the model. The model view has a 2-panel window, the main view on the
left and the linked, or auxiliary, view on the right.
There are two main views:
• Hypothesis Summary. This is the default view.See the topic “Hypothesis Summary ” on page 136 for
more information.
• Confidence Interval Summary. See the topic “Confidence Interval Summary ” on page 136 for more
information.
There are seven linked/auxiliary views:
• One Sample Test. This is the default view if one-sample tests were requested. See the topic “One
Sample Test ” on page 136 for more information.
• Related Samples Test. This is the default view if related samples tests and no one-sample tests were
requested. See the topic “Related Samples Test ” on page 137 for more information.
• Independent Samples Test. This is the default view if no related samples tests or one-sample tests
were requested. See the topic “Independent Samples Test ” on page 138 for more information.
• Categorical Field Information. See the topic “Categorical Field Information ” on page 139 for more
information.
Chapter 1. Core features 135
• Continuous Field Information. See the topic “Continuous Field Information ” on page 139 for more
information.
• Pairwise Comparisons. See the topic “Pairwise Comparisons ” on page 139 for more information.
• Homogenous Subsets. See the topic “Homogeneous Subsets ” on page 139 for more information.
Hypothesis Summary
The Model Summary view is a snapshot, at-a-glance summary of the nonparametric tests. It emphasizes
null hypotheses and decisions, drawing attention to significant p-values.
• Each row corresponds to a separate test. Clicking on a row shows additional information about the test
in the linked view.
• Clicking on any column header sorts the rows by values in that column.
• The Reset button allows you to return the Model Viewer to its original state.
• The Field Filter dropdown list allows you to display only the tests that involve the selected field.
Confidence Interval Summary
The Confidence Interval Summary shows any confidence intervals produced by the nonparametric tests.
• Each row corresponds to a separate confidence interval.
• Clicking on any column header sorts the rows by values in that column.
One Sample Test
The One Sample Test view shows details related to any requested one-sample nonparametric tests. The
information shown depends upon the selected test.
• The Test dropdown allows you to select a given type of one-sample test.
• The Field(s) dropdown allows you to select a field that was tested using the selected test in the Test
dropdown.
Binomial Test
The Binomial Test shows a stacked bar chart and a test table.
• The stacked bar chart displays the observed and hypothesized frequencies for the “success” and
“failure” categories of the test field, with “failures” stacked on top of “successes”. Hovering over a bar
shows the category percentages in a tooltip. Visible differences in the bars indicate that the test field
may not have the hypothesized binomial distribution.
• The table shows details of the test.
Chi-Square Test
The Chi-Square Test view shows a clustered bar chart and a test table.
• The clustered bar chart displays the observed and hypothesized frequencies for each category of the
test field. Hovering over a bar shows the observed and hypothesized frequencies and their difference
(residual) in a tooltip. Visible differences in the observed versus hypothesized bars indicate that the test
field may not have the hypothesized distribution.
• The table shows details of the test.
Wilcoxon Signed Ranks
The Wilcoxon Signed Ranks Test view shows a histogram and a test table.
• The histogram includes vertical lines showing the observed and hypothetical medians.
• The table shows details of the test.
Runs Test
The Runs Test view shows a chart and a test table.
136 IBM SPSS Statistics Base V27
• The chart displays a normal distribution with the observed number of runs marked with a vertical line.
Note that when the exact test is performed, the test is not based on the normal distribution.
• The table shows details of the test.
Kolmogorov-Smirnov Test
The Kolmogorov-Smirnov Test view shows a histogram and a test table.
• The histogram includes an overlay of the probability density function for the hypothesized uniform,
normal, Poisson, or exponential distribution. Note that the test is based on cumulative distributions, and
the Most Extreme Differences reported in the table should be interpreted with respect to cumulative
distributions.
• The table shows details of the test.
Related Samples Test
The One Sample Test view shows details related to any requested one-sample nonparametric tests. The
information shown depends upon the selected test.
• The Test dropdown allows you to select a given type of one-sample test.
• The Field(s) dropdown allows you to select a field that was tested using the selected test in the Test
dropdown.
McNemar Test
The McNemar Test view shows a clustered bar chart and a test table.
• The clustered bar chart displays the observed and hypothesized frequencies for the off-diagonal cells of
the 2×2 table defined by the test fields.
• The table shows details of the test.
Sign Test
The Sign Test view shows a stacked histogram and a test table.
• The stacked histogram displays the differences between the fields, using the sign of the difference as
the stacking field.
• The table shows details of the test.
Wilcoxon Signed Ranks Test
The Wilcoxon Signed Ranks Test view shows a stacked histogram and a test table.
• The stacked histogram displays the differences between the fields, using the sign of the difference as
the stacking field.
• The table shows details of the test.
Marginal Homogeneity Test
The Marginal Homogeneity Test view shows a clustered bar chart and a test table.
• The clustered bar chart displays the observed frequencies for the off-diagonal cells of the table defined
by the test fields.
• The table shows details of the test.
Cochran’s Q Test
The Cochran’s Q Test view shows a stacked bar chart and a test table.
• The stacked bar chart displays the observed frequencies for the “success” and “failure” categories of
the test fields, with “failures” stacked on top of “successes”. Hovering over a bar shows the category
percentages in a tooltip.
• The table shows details of the test.
Friedman’s Two-Way Analysis of Variance by Ranks
Chapter 1. Core features 137
The Friedman’s Two-Way Analysis of Variance by Ranks view shows paneled histograms and a test table.
• The histograms display the observed distribution of ranks, paneled by the test fields.
• The table shows details of the test.
Kendall’s Coefficient of Concordance
The Kendall’s Coefficient of Concordance view shows paneled histograms and a test table.
• The histograms display the observed distribution of ranks, paneled by the test fields.
• The table shows details of the test.
Independent Samples Test
The Independent Samples Test view shows details related to any requested independent samples
nonparametric tests. The information shown depends upon the selected test.
• The Test dropdown allows you to select a given type of independent samples test.
• The Field(s) dropdown allows you to select a test and grouping field combination that was tested using
the selected test in the Test dropdown.
Mann-Whitney Test
The Mann-Whitney Test view shows a population pyramid chart and a test table.
• The population pyramid chart displays back-to-back histograms by the categories of the grouping field,
noting the number of records in each group and the mean rank of the group.
• The table shows details of the test.
Kolmogorov-Smirnov Test
The Kolmogorov-Smirnov Test view shows a population pyramid chart and a test table.
• The population pyramid chart displays back-to-back histograms by the categories of the grouping field,
noting the number of records in each group. The observed cumulative distribution lines can be
displayed or hidden by clicking the Cumulative button.
• The table shows details of the test.
Wald-Wolfowitz Runs Test
The Wald-Wolfowitz Runs Test view shows a stacked bar chart and a test table.
• The population pyramid chart displays back-to-back histograms by the categories of the grouping field,
noting the number of records in each group.
• The table shows details of the test.
Kruskal-Wallis Test
The Kruskal-Wallis Test view shows boxplots and a test table.
• Separate boxplots are displayed for each category of the grouping field. Hovering over a box shows the
mean rank in a tooltip.
• The table shows details of the test.
Jonckheere-Terpstra Test
The Jonckheere-Terpstra Test view shows box plots and a test table.
• Separate box plots are displayed for each category of the grouping field.
• The table shows details of the test.
Moses Test of Extreme Reaction
The Moses Test of Extreme Reaction view shows boxplots and a test table.
• Separate boxplots are displayed for each category of the grouping field. The point labels can be
displayed or hidden by clicking the Record ID button.
138 IBM SPSS Statistics Base V27
• The table shows details of the test.
Median Test
The Median Test view shows box plots and a test table.
• Separate box plots are displayed for each category of the grouping field.
• The table shows details of the test.
Categorical Field Information
The Categorical Field Information view displays a bar chart for the categorical field selected on the
Field(s) dropdown. The list of available fields is restricted to the categorical fields used in the currently
selected test in the Hypothesis Summary view.
• Hovering over a bar gives the category percentages in a tooltip.
Continuous Field Information
The Continuous Field Information view displays a histogram for the continuous field selected on the
Field(s) dropdown. The list of available fields is restricted to the continuous fields used in the currently
selected test in the Hypothesis Summary view.
Pairwise Comparisons
The Pairwise Comparisons view shows a distance network chart and comparisons table produced by k-
sample nonparametric tests when pairwise multiple comparisons are requested.
• The distance network chart is a graphical representation of the comparisons table in which the
distances between nodes in the network correspond to differences between samples. Yellow lines
correspond to statistically significant differences; black lines correspond to non-significant differences.
Hovering over a line in the network displays a tooltip with the adjusted significance of the difference
between the nodes connected by the line.
• The comparison table shows the numerical results of all pairwise comparisons. Each row corresponds
to a separate pairwise comparison. Clicking on a column header sorts the rows by values in that column.
Homogeneous Subsets
The Homogeneous Subsets view shows a comparisons table produced by k-sample nonparametric tests
when stepwise stepdown multiple comparisons are requested.
• Each row in the Sample group corresponds to a separate related sample (represented in the data by
separate fields). Samples that are not statistically significantly different are grouped into same-colored
subsets; there is a separate column for each identified subset. When all samples are statistically
significantly different, there is a separate subset for each sample. When none of the samples are
statistically significantly different, there is a single subset.
• A test statistic, significance value, and adjusted significance value are computed for each subset
containing more than one sample.
NPTESTS command additional features
The command syntax language also allows you to:
• Specify one-sample, independent-samples, and related-samples tests in a single run of the procedure.
See the Command Syntax Reference for complete syntax information.
Legacy Dialogs
There are a number of “legacy” dialogs that also perform nonparametric tests. These dialogs support the
functionality provided by the Exact Tests option.
Chi-Square Test. Tabulates a variable into categories and computes a chi-square statistic based on the
differences between observed and expected frequencies.
Chapter 1. Core features 139
Binomial Test. Compares the observed frequency in each category of a dichotomous variable with
expected frequencies from the binomial distribution.
Runs Test. Tests whether the order of occurrence of two values of a variable is random.
One-Sample Kolmogorov-Smirnov Test. Compares the observed cumulative distribution function for a
variable with a specified theoretical distribution, which may be normal, uniform, exponential, or Poisson.
Two-Independent-Samples Tests. Compares two groups of cases on one variable. The Mann-Whitney U
test, two-sample Kolmogorov-Smirnov test, Moses test of extreme reactions, and Wald-Wolfowitz runs
test are available.
Two-Related-Samples Tests. Compares the distributions of two variables. The Wilcoxon signed-rank
test, the sign test, and the McNemar test are available.
Tests for Several Independent Samples. Compares two or more groups of cases on one variable. The
Kruskal-Wallis test, the Median test, and the Jonckheere-Terpstra test are available.
Tests for Several Related Samples. Compares the distributions of two or more variables. Friedman’s
test, Kendall’s W, and Cochran’s Q are available.
Quartiles and the mean, standard deviation, minimum, maximum, and number of nonmissing cases are
available for all of the above tests.
Chi-Square Test
The Chi-Square Test procedure tabulates a variable into categories and computes a chi-square statistic.
This goodness-of-fit test compares the observed and expected frequencies in each category to test that
all categories contain the same proportion of values or test that each category contains a user-specified
proportion of values.
Examples. The chi-square test could be used to determine whether a bag of jelly beans contains equal
proportions of blue, brown, green, orange, red, and yellow candies. You could also test to see whether a
bag of jelly beans contains 5% blue, 30% brown, 10% green, 20% orange, 15% red, and 15% yellow
candies.
Statistics. Mean, standard deviation, minimum, maximum, and quartiles. The number and the percentage
of nonmissing and missing cases; the number of cases observed and expected for each category;
residuals; and the chi-square statistic.
Chi-Square Test Data Considerations
Data. Use ordered or unordered numeric categorical variables (ordinal or nominal levels of
measurement). To convert string variables to numeric variables, use the Automatic Recode procedure,
which is available on the Transform menu.
Assumptions. Nonparametric tests do not require assumptions about the shape of the underlying
distribution. The data are assumed to be a random sample. The expected frequencies for each category
should be at least 1. No more than 20% of the categories should have expected frequencies of less than
5.
To Obtain a Chi-Square Test
1. From the menus choose:
Analyze > Nonparametric Tests > Legacy Dialogs > Chi-Square…
2. Select one or more test variables. Each variable produces a separate test.
3. Optionally, click Options for descriptive statistics, quartiles, and control of the treatment of missing
data.
Chi-Square Test Expected Range and Expected Values
Expected Range. By default, each distinct value of the variable is defined as a category. To establish
categories within a specific range, select Use specified range and enter integer values for lower and
upper bounds. Categories are established for each integer value within the inclusive range, and cases with
140 IBM SPSS Statistics Base V27
values outside of the bounds are excluded. For example, if you specify a value of 1 for Lower and a value
of 4 for Upper, only the integer values of 1 through 4 are used for the chi-square test.
Expected Values. By default, all categories have equal expected values. Categories can have user-
specified expected proportions. Select Values, enter a value that is greater than 0 for each category of the
test variable, and then click Add. Each time you add a value, it appears at the bottom of the value list. The
order of the values is important; it corresponds to the ascending order of the category values of the test
variable. The first value of the list corresponds to the lowest group value of the test variable, and the last
value corresponds to the highest value. Elements of the value list are summed, and then each value is
divided by this sum to calculate the proportion of cases expected in the corresponding category. For
example, a value list of 3, 4, 5, 4 specifies expected proportions of 3/16, 4/16, 5/16, and 4/16.
Chi-Square Test Options
Statistics. You can choose one or both summary statistics.
• Descriptive. Displays the mean, standard deviation, minimum, maximum, and number of nonmissing
cases.
• Quartiles. Displays values corresponding to the 25th, 50th, and 75th percentiles.
Missing Values. Controls the treatment of missing values.
• Exclude cases test-by-test. When several tests are specified, each test is evaluated separately for
missing values.
• Exclude cases listwise. Cases with missing values for any variable are excluded from all analyses.
NPAR TESTS Command Additional Features (Chi-Square Test)
The command syntax language also allows you to:
• Specify different minimum and maximum values or expected frequencies for different variables (with
the CHISQUARE subcommand).
• Test the same variable against different expected frequencies or use different ranges (with the
EXPECTED subcommand).
See the Command Syntax Reference for complete syntax information.
Binomial Test
The Binomial Test procedure compares the observed frequencies of the two categories of a dichotomous
variable to the frequencies that are expected under a binomial distribution with a specified probability
parameter. By default, the probability parameter for both groups is 0.5. To change the probabilities, you
can enter a test proportion for the first group. The probability for the second group will be 1 minus the
specified probability for the first group.
Example. When you toss a dime, the probability of a head equals 1/2. Based on this hypothesis, a dime is
tossed 40 times, and the outcomes are recorded (heads or tails). From the binomial test, you might find
that 3/4 of the tosses were heads and that the observed significance level is small (0.0027). These results
indicate that it is not likely that the probability of a head equals 1/2; the coin is probably biased.
Statistics. Mean, standard deviation, minimum, maximum, number of nonmissing cases, and quartiles.
Binomial Test Data Considerations
Data. The variables that are tested should be numeric and dichotomous. To convert string variables to
numeric variables, use the Automatic Recode procedure, which is available on the Transform menu. A
dichotomous variable is a variable that can take only two possible values: yes or no, true or false, 0 or 1,
and so on. The first value encountered in the dataset defines the first group, and the other value defines
the second group. If the variables are not dichotomous, you must specify a cut point. The cut point
assigns cases with values that are less than or equal to the cut point to the first group and assigns the rest
of the cases to the second group.
Assumptions. Nonparametric tests do not require assumptions about the shape of the underlying
distribution. The data are assumed to be a random sample.
Chapter 1. Core features 141
To Obtain a Binomial Test
1. From the menus choose:
Analyze > Nonparametric Tests > Legacy Dialogs > Binomial…
2. Select one or more numeric test variables.
3. Optionally, click Options for descriptive statistics, quartiles, and control of the treatment of missing
data.
Binomial Test Options
Statistics. You can choose one or both summary statistics.
• Descriptive. Displays the mean, standard deviation, minimum, maximum, and number of nonmissing
cases.
• Quartiles. Displays values corresponding to the 25th, 50th, and 75th percentiles.
Missing Values. Controls the treatment of missing values.
• Exclude cases test-by-test. When several tests are specified, each test is evaluated separately for
missing values.
• Exclude cases listwise. Cases with missing values for any variable that is tested are excluded from all
analyses.
NPAR TESTS Command Additional Features (Binomial Test)
The command syntax language also allows you to:
• Select specific groups (and exclude other groups) when a variable has more than two categories (with
the BINOMIAL subcommand).
• Specify different cut points or probabilities for different variables (with the BINOMIAL subcommand).
• Test the same variable against different cut points or probabilities (with the EXPECTED subcommand).
See the Command Syntax Reference for complete syntax information.
Runs Test
The Runs Test procedure tests whether the order of occurrence of two values of a variable is random. A
run is a sequence of like observations. A sample with too many or too few runs suggests that the sample
is not random.
Examples. Suppose that 20 people are polled to find out whether they would purchase a product. The
assumed randomness of the sample would be seriously questioned if all 20 people were of the same
gender. The runs test can be used to determine whether the sample was drawn at random.
Statistics. Mean, standard deviation, minimum, maximum, number of nonmissing cases, and quartiles.
Runs Test Data Considerations
Data. The variables must be numeric. To convert string variables to numeric variables, use the Automatic
Recode procedure, which is available on the Transform menu.
Assumptions. Nonparametric tests do not require assumptions about the shape of the underlying
distribution. Use samples from continuous probability distributions.
To Obtain a Runs Test
1. From the menus choose:
Analyze > Nonparametric Tests > Legacy Dialogs > Runs…
2. Select one or more numeric test variables.
3. Optionally, click Options for descriptive statistics, quartiles, and control of the treatment of missing
data.
142 IBM SPSS Statistics Base V27
Runs Test Cut Point
Cut Point. Specifies a cut point to dichotomize the variables that you have chosen. You can use the
observed mean, median, or mode, or you can use a specified value as a cut point. Cases with values that
are less than the cut point are assigned to one group, and cases with values that are greater than or equal
to the cut point are assigned to another group. One test is performed for each chosen cut point.
Runs Test Options
Statistics. You can choose one or both summary statistics.
• Descriptive. Displays the mean, standard deviation, minimum, maximum, and number of nonmissing
cases.
• Quartiles. Displays values corresponding to the 25th, 50th, and 75th percentiles.
Missing Values. Controls the treatment of missing values.
• Exclude cases test-by-test. When several tests are specified, each test is evaluated separately for
missing values.
• Exclude cases listwise. Cases with missing values for any variable are excluded from all analyses.
NPAR TESTS Command Additional Features (Runs Test)
The command syntax language also allows you to:
• Specify different cut points for different variables (with the RUNS subcommand).
• Test the same variable against different custom cut points (with the RUNS subcommand).
See the Command Syntax Reference for complete syntax information.
One-Sample Kolmogorov-Smirnov Test
The One-Sample Kolmogorov-Smirnov Test procedure compares the observed cumulative distribution
function for a variable with a specified theoretical distribution, which may be normal, uniform, Poisson, or
exponential. The Kolmogorov-Smirnov Z is computed from the largest difference (in absolute value)
between the observed and theoretical cumulative distribution functions. This goodness-of-fit test tests
whether the observations could reasonably have come from the specified distribution.
Starting with version 27.0, the Lilliefors test statistic can be used to estimate the p-value by using the
Monte Carlo sampling for testing against a normal distribution with estimated parameters (this
functionality was previously possible only through the Explore procedure).
Example
Many parametric tests require normally distributed variables. The one-sample Kolmogorov-Smirnov
test can be used to test that a variable (for example, income) is normally distributed.
Statistics
Mean, standard deviation, minimum, maximum, number of non-missing cases, quartiles, Lilliefors
test, and Monte Carlo simulation.
One-Sample Kolmogorov-Smirnov test data considerations
Data
Use quantitative variables (interval or ratio level of measurement).
Assumptions
The Kolmogorov-Smirnov test assumes that the parameters of the test distribution are specified in
advance. This procedure estimates the parameters from the sample. The sample mean and sample
standard deviation are the parameters for a normal distribution, the sample minimum and maximum
values define the range of the uniform distribution, the sample mean is the parameter for the Poisson
distribution, and the sample mean is the parameter for the exponential distribution. The power of the
test to detect departures from the hypothesized distribution may be seriously diminished.
When certain parameters of the distribution have to be estimated from the sample, the Kolmogorov-
Smirnov test no longer applies. In these instances, the Lilliefors test statistic can be used to estimate
Chapter 1. Core features 143
the p-value by using the Monte Carlo sampling for testing normality with mean and variance unknown.
The Lilliefors test applies to the three continuous distributions (Normal, Exponential, and Uniform).
Note that the test does not apply if the underlying distribution is discrete (Poisson). The test is only
defined for one-sample inference when the corresponding distribution parameters are not specified.
Obtaining a One-Sample Kolmogorov-Smirnov test
1. From the menus choose:
Analyze > Nonparametric Tests > Legacy Dialogs > 1-Sample K-S…
2. Select one or more numeric test variables. Each variable produces a separate test.
3. Optionally, select a test distribution method:
Normal
When selected, you can specify whether distribution parameter(s) are estimated from sample data
(the default setting) or from custom settings. When Use sample data is selected, both the existing
asymptotic results and Lilliefors significance correction based on the Monte Carlo sampling are
used. When Custom is selected, provide values for both Mean and Std Dev.
Uniform
When selected, you can specify whether distribution parameter(s) are estimated from sample data
(the default setting) or from custom settings. When Use sample data is selected, the Lilliefors test
is used. When Custom is selected, provide values for both Min and Max.
Poisson
When selected, specify a Mean parameter value.
Exponential
When selected, you can specify whether distribution parameter(s) are estimated from the sample
mean (the default setting) or from custom settings. When Use sample data is selected, the
Lilliefors test is used. When Custom is selected, provide a Mean parameter value.
4. Optionally, click Simulation to specify Monte Carlo simulation parameters, click Exact to specify exact
test parameters, or click Options for descriptive statistics, quartiles, and control of the treatment of
missing data.
One-Sample Kolmogorov-Smirnov Test: Simulation
When certain parameters of the distribution have to be estimated from the sample, the Kolmogorov-
Smirnov test no longer applies. In these instances, the Lilliefors test statistic can be used to estimate the
p-value by using the Monte Carlo sampling for testing normality with mean and variance unknown. The
Lilliefors test applies to the three continuous distributions (Normal, Exponential, and Uniform). Note that
the test does not apply if the underlying distribution is discrete (Poisson). The test is only defined for one-
sample inference when the corresponding distribution parameters are not specified.
Monte Carlo Simulation Parameters
Confidence level
This optional setting resets the confidence interval level that is estimated by the Kolmogorov-
Smirnov test when using the Monte Carlo simulations. The value must be between 0 and 100. The
default setting is 99.
Number of samples
This optional setting resets the number of replicates that the Lilliefors test uses for the Monte
Carlo sampling. The value must be a single integer between 10000 and the largest number of
samples value. The default value is 10000.
Suppress the Monte Carlo results for the normal distribution
This optional setting suppresses the Monte Carlo sampling for the normal distribution results. By
default, the setting is not selected (which means both the existing asymptotic results and the
Lilliefors test results, that are based on the Monte Carlo sampling, are presented).
144 IBM SPSS Statistics Base V27
One-Sample Kolmogorov-Smirnov Test: Options
Statistics
You can choose one or both summary statistics.
Descriptive
Displays the mean, standard deviation, minimum, maximum, and number of nonmissing cases.
Quartiles
Displays values corresponding to the 25th, 50th, and 75th percentiles.
Missing Values
Controls the treatment of missing values.
Exclude cases test-by-test
When several tests are specified, each test is evaluated separately for missing values.
Exclude cases listwise
Cases with missing values for any variable are excluded from all analyses.
NPAR TESTS Command Additional Features (One-Sample Kolmogorov-Smirnov Test)
The command syntax language also allows you to specify the parameters of the test distribution (with the
K-S subcommand).
See the Command Syntax Reference for complete syntax information.
Two-Independent-Samples Tests
The Two-Independent-Samples Tests procedure compares two groups of cases on one variable.
Example. New dental braces have been developed that are intended to be more comfortable, to look
better, and to provide more rapid progress in realigning teeth. To find out whether the new braces have to
be worn as long as the old braces, 10 children are randomly chosen to wear the old braces, and another
10 children are chosen to wear the new braces. From the Mann-Whitney U test, you might find that, on
average, children with the new braces did not have to wear the braces as long as children with the old
braces.
Statistics. Mean, standard deviation, minimum, maximum, number of nonmissing cases, and quartiles.
Tests: Mann-Whitney U, Moses extreme reactions, Kolmogorov-Smirnov Z, Wald-Wolfowitz runs.
Two-Independent-Samples Tests Data Considerations
Data. Use numeric variables that can be ordered.
Assumptions. Use independent, random samples. The Mann-Whitney U test tests equality of two
distributions. In order to use it to test for differences in location between two distributions, one must
assume that the distributions have the same shape.
To Obtain Two-Independent-Samples Tests
1. From the menus choose:
Analyze > Nonparametric Tests > Legacy Dialogs > 2 Independent Samples…
2. Select one or more numeric variables.
3. Select a grouping variable and click Define Groups to split the file into two groups or samples.
Two-Independent-Samples Test Types
Test Type. Four tests are available to test whether two independent samples (groups) come from the
same population.
The Mann-Whitney U test is the most popular of the two-independent-samples tests. It is equivalent to
the Wilcoxon rank sum test and the Kruskal-Wallis test for two groups. Mann-Whitney tests that two
sampled populations are equivalent in location. The observations from both groups are combined and
ranked, with the average rank assigned in the case of ties. The number of ties should be small relative to
the total number of observations. If the populations are identical in location, the ranks should be
randomly mixed between the two samples. The test calculates the number of times that a score from
Chapter 1. Core features 145
group 1 precedes a score from group 2 and the number of times that a score from group 2 precedes a
score from group 1. The Mann-Whitney U statistic is the smaller of these two numbers. The Wilcoxon rank
sum W statistic is also displayed. W is the sum of the ranks for the group with the smaller mean rank,
unless the groups have the same mean rank, in which case it is the rank sum from the group that is
named last in the Two-Independent-Samples Define Groups dialog box.
The Kolmogorov-Smirnov Z test and the Wald-Wolfowitz runs test are more general tests that detect
differences in both the locations and shapes of the distributions. The Kolmogorov-Smirnov test is based
on the maximum absolute difference between the observed cumulative distribution functions for both
samples. When this difference is significantly large, the two distributions are considered different. The
Wald-Wolfowitz runs test combines and ranks the observations from both groups. If the two samples are
from the same population, the two groups should be randomly scattered throughout the ranking.
The Moses extreme reactions test assumes that the experimental variable will affect some subjects in
one direction and other subjects in the opposite direction. The test tests for extreme responses compared
to a control group. This test focuses on the span of the control group and is a measure of how much
extreme values in the experimental group influence the span when combined with the control group. The
control group is defined by the group 1 value in the Two-Independent-Samples Define Groups dialog box.
Observations from both groups are combined and ranked. The span of the control group is computed as
the difference between the ranks of the largest and smallest values in the control group plus 1. Because
chance outliers can easily distort the range of the span, 5% of the control cases are trimmed
automatically from each end.
Two-Independent-Samples Tests Define Groups
To split the file into two groups or samples, enter an integer value for Group 1 and another value for
Group 2. Cases with other values are excluded from the analysis.
Two-Independent-Samples Tests Options
Statistics. You can choose one or both summary statistics.
• Descriptive. Displays the mean, standard deviation, minimum, maximum, and the number of
nonmissing cases.
• Quartiles. Displays values corresponding to the 25th, 50th, and 75th percentiles.
Missing Values. Controls the treatment of missing values.
• Exclude cases test-by-test. When several tests are specified, each test is evaluated separately for
missing values.
• Exclude cases listwise. Cases with missing values for any variable are excluded from all analyses.
NPAR TESTS Command Additional Features (Two-Independent-Samples Tests)
The command syntax language also allows you to specify the number of cases to be trimmed for the
Moses test (with the MOSES subcommand).
See the Command Syntax Reference for complete syntax information.
Two-Related-Samples Tests
The Two-Related-Samples Tests procedure compares the distributions of two variables.
Example. In general, do families receive the asking price when they sell their homes? By applying the
Wilcoxon signed-rank test to data for 10 homes, you might learn that seven families receive less than the
asking price, one family receives more than the asking price, and two families receive the asking price.
Statistics. Mean, standard deviation, minimum, maximum, number of nonmissing cases, and quartiles.
Tests: Wilcoxon signed-rank, sign, McNemar. If the Exact Tests option is installed (available only on
Windows operating systems), the marginal homogeneity test is also available.
Two-Related-Samples Tests Data Considerations
Data. Use numeric variables that can be ordered.
146 IBM SPSS Statistics Base V27
Assumptions. Although no particular distributions are assumed for the two variables, the population
distribution of the paired differences is assumed to be symmetric.
To Obtain Two-Related-Samples Tests
1. From the menus choose:
Analyze > Nonparametric Tests > Legacy Dialogs > 2 Related Samples…
2. Select one or more pairs of variables.
Two-Related-Samples Test Types
The tests in this section compare the distributions of two related variables. The appropriate test to use
depends on the type of data.
If your data are continuous, use the sign test or the Wilcoxon signed-rank test. The sign test computes
the differences between the two variables for all cases and classifies the differences as positive, negative,
or tied. If the two variables are similarly distributed, the number of positive and negative differences will
not differ significantly. The Wilcoxon signed-rank test considers information about both the sign of the
differences and the magnitude of the differences between pairs. Because the Wilcoxon signed-rank test
incorporates more information about the data, it is more powerful than the sign test.
If your data are binary, use the McNemar test. This test is typically used in a repeated measures
situation, in which each subject’s response is elicited twice, once before and once after a specified event
occurs. The McNemar test determines whether the initial response rate (before the event) equals the final
response rate (after the event). This test is useful for detecting changes in responses due to experimental
intervention in before-and-after designs.
If your data are categorical, use the marginal homogeneity test. This test is an extension of the McNemar
test from binary response to multinomial response. It tests for changes in response (using the chi-square
distribution) and is useful for detecting response changes due to experimental intervention in before-and-
after designs. The marginal homogeneity test is available only if you have installed Exact Tests.
Two-Related-Samples Tests Options
Statistics. You can choose one or both summary statistics.
• Descriptive. Displays the mean, standard deviation, minimum, maximum, and the number of
nonmissing cases.
• Quartiles. Displays values corresponding to the 25th, 50th, and 75th percentiles.
Missing Values. Controls the treatment of missing values.
• Exclude cases test-by-test. When several tests are specified, each test is evaluated separately for
missing values.
• Exclude cases listwise. Cases with missing values for any variable are excluded from all analyses.
NPAR TESTS Command Additional Features (Two Related Samples)
The command syntax language also allows you to test a variable with each variable on a list.
See the Command Syntax Reference for complete syntax information.
Tests for Several Independent Samples
The Tests for Several Independent Samples procedure compares two or more groups of cases on one
variable.
Example. Do three brands of 100-watt lightbulbs differ in the average time that the bulbs will burn? From
the Kruskal-Wallis one-way analysis of variance, you might learn that the three brands do differ in average
lifetime.
Statistics. Mean, standard deviation, minimum, maximum, number of nonmissing cases, and quartiles.
Tests: Kruskal-Wallis H, median.
Tests for Several Independent Samples Data Considerations
Chapter 1. Core features 147
Data. Use numeric variables that can be ordered.
Assumptions. Use independent, random samples. The Kruskal-Wallis H test requires that the tested
samples be similar in shape.
To Obtain Tests for Several Independent Samples
1. From the menus choose:
Analyze > Nonparametric Tests > Legacy Dialogs > K Independent Samples…
2. Select one or more numeric variables.
3. Select a grouping variable and click Define Range to specify minimum and maximum integer values for
the grouping variable.
Tests for Several Independent Samples Test Types
Three tests are available to determine if several independent samples come from the same population.
The Kruskal-Wallis H test, the median test, and the Jonckheere-Terpstra test all test whether several
independent samples are from the same population.
The Kruskal-Wallis H test, an extension of the Mann-Whitney U test, is the nonparametric analog of one-
way analysis of variance and detects differences in distribution location. The median test, which is a
more general test (but not as powerful), detects distributional differences in location and shape. The
Kruskal-Wallis H test and the median test assume that there is no a priori ordering of the k populations
from which the samples are drawn.
When there is a natural a priori ordering (ascending or descending) of the k populations, the Jonckheere-
Terpstra test is more powerful. For example, the k populations might represent k increasing
temperatures. The hypothesis that different temperatures produce the same response distribution is
tested against the alternative that as the temperature increases, the magnitude of the response
increases. Here, the alternative hypothesis is ordered; therefore, Jonckheere-Terpstra is the most
appropriate test to use. The Jonckheere-Terpstra test is available only if you have installed the Exact
Tests add-on module.
Tests for Several Independent Samples Define Range
To define the range, enter integer values for Minimum and Maximum that correspond to the lowest and
highest categories of the grouping variable. Cases with values outside of the bounds are excluded. For
example, if you specify a minimum value of 1 and a maximum value of 3, only the integer values of 1
through 3 are used. The minimum value must be less than the maximum value, and both values must be
specified.
Tests for Several Independent Samples Options
Statistics. You can choose one or both summary statistics.
• Descriptive. Displays the mean, standard deviation, minimum, maximum, and the number of
nonmissing cases.
• Quartiles. Displays values corresponding to the 25th, 50th, and 75th percentiles.
Missing Values. Controls the treatment of missing values.
• Exclude cases test-by-test. When several tests are specified, each test is evaluated separately for
missing values.
• Exclude cases listwise. Cases with missing values for any variable are excluded from all analyses.
NPAR TESTS Command Additional Features (K Independent Samples)
The command syntax language also allows you to specify a value other than the observed median for the
median test (with the MEDIAN subcommand).
See the Command Syntax Reference for complete syntax information.
148 IBM SPSS Statistics Base V27
Tests for Several Related Samples
The Tests for Several Related Samples procedure compares the distributions of two or more variables.
Example. Does the public associate different amounts of prestige with a doctor, a lawyer, a police officer,
and a teacher? Ten people are asked to rank these four occupations in order of prestige. Friedman’s test
indicates that the public does associate different amounts of prestige with these four professions.
Statistics. Mean, standard deviation, minimum, maximum, number of nonmissing cases, and quartiles.
Tests: Friedman, Kendall’s W, and Cochran’s Q.
Tests for Several Related Samples Data Considerations
Data. Use numeric variables that can be ordered.
Assumptions. Nonparametric tests do not require assumptions about the shape of the underlying
distribution. Use dependent, random samples.
To Obtain Tests for Several Related Samples
1. From the menus choose:
Analyze > Nonparametric Tests > Legacy Dialogs > K Related Samples…
2. Select two or more numeric test variables.
Tests for Several Related Samples Test Types
Three tests are available to compare the distributions of several related variables.
The Friedman test is the nonparametric equivalent of a one-sample repeated measures design or a two-
way analysis of variance with one observation per cell. Friedman tests the null hypothesis that k related
variables come from the same population. For each case, the k variables are ranked from 1 to k. The test
statistic is based on these ranks.
Kendall’s W is a normalization of the Friedman statistic. Kendall’s W is interpretable as the coefficient of
concordance, which is a measure of agreement among raters. Each case is a judge or rater, and each
variable is an item or person being judged. For each variable, the sum of ranks is computed. Kendall’s W
ranges between 0 (no agreement) and 1 (complete agreement).
Cochran’s Q is identical to the Friedman test but is applicable when all responses are binary. This test is
an extension of the McNemar test to the k-sample situation. Cochran’s Q tests the hypothesis that several
related dichotomous variables have the same mean. The variables are measured on the same individual
or on matched individuals.
Tests for Several Related Samples Statistics
You can choose statistics.
• Descriptive. Displays the mean, standard deviation, minimum, maximum, and the number of
nonmissing cases.
• Quartiles. Displays values corresponding to the 25th, 50th, and 75th percentiles.
NPAR TESTS Command Additional Features (K Related Samples)
See the Command Syntax Reference for complete syntax information.
Multiple Response Analysis
Multiple Response Analysis
Two procedures are available for analyzing multiple dichotomy and multiple category sets. The Multiple
Response Frequencies procedure displays frequency tables. The Multiple Response Crosstabs procedure
displays two- and three-dimensional crosstabulations. Before using either procedure, you must define
multiple response sets.
Chapter 1. Core features 149
Example. This example illustrates the use of multiple response items in a market research survey. The
data are fictitious and should not be interpreted as real. An airline might survey passengers flying a
particular route to evaluate competing carriers. In this example, American Airlines wants to know about
its passengers’ use of other airlines on the Chicago-New York route and the relative importance of
schedule and service in selecting an airline. The flight attendant hands each passenger a brief
questionnaire upon boarding. The first question reads: Circle all airlines you have flown at least once in
the last six months on this route–American, United, TWA, USAir, Other. This is a multiple response
question, since the passenger can circle more than one response. However, this question cannot be
coded directly because a variable can have only one value for each case. You must use several variables
to map responses to each question. There are two ways to do this. One is to define a variable
corresponding to each of the choices (for example, American, United, TWA, USAir, and Other). If the
passenger circles United, the variable united is assigned a code of 1, otherwise 0. This is a multiple
dichotomy method of mapping variables. The other way to map responses is the multiple category
method, in which you estimate the maximum number of possible responses to the question and set up
the same number of variables, with codes used to specify the airline flown. By perusing a sample of
questionnaires, you might discover that no user has flown more than three different airlines on this route
in the last six months. Further, you find that due to the deregulation of airlines, 10 other airlines are
named in the Other category. Using the multiple response method, you would define three variables, each
coded as 1 = american, 2 = united, 3 = twa, 4 = usair, 5 = delta, and so on. If a given passenger circles
American and TWA, the first variable has a code of 1, the second has a code of 3, and the third has a
missing-value code. Another passenger might have circled American and entered Delta. Thus, the first
variable has a code of 1, the second has a code of 5, and the third a missing-value code. If you use the
multiple dichotomy method, on the other hand, you end up with 14 separate variables. Although either
method of mapping is feasible for this survey, the method you choose depends on the distribution of
responses.
Multiple Response Define Sets
The Define Multiple Response Sets procedure groups elementary variables into multiple dichotomy and
multiple category sets, for which you can obtain frequency tables and crosstabulations. You can define up
to 20 multiple response sets. Each set must have a unique name. To remove a set, highlight it on the list
of multiple response sets and click Remove. To change a set, highlight it on the list, modify any set
definition characteristics, and click Change.
You can code your elementary variables as dichotomies or categories. To use dichotomous variables,
select Dichotomies to create a multiple dichotomy set. Enter an integer value for Counted value. Each
variable having at least one occurrence of the counted value becomes a category of the multiple
dichotomy set. Select Categories to create a multiple category set having the same range of values as the
component variables. Enter integer values for the minimum and maximum values of the range for
categories of the multiple category set. The procedure totals each distinct integer value in the inclusive
range across all component variables. Empty categories are not tabulated.
Each multiple response set must be assigned a unique name of up to seven characters. The procedure
prefixes a dollar sign ($) to the name you assign. You cannot use the following reserved names: casenum,
sysmis, jdate, date, time, length, and width. The name of the multiple response set exists only for use in
multiple response procedures. You cannot refer to multiple response set names in other procedures.
Optionally, you can enter a descriptive variable label for the multiple response set. The label can be up to
40 characters long.
To Define Multiple Response Sets
1. From the menus choose:
Analyze > Multiple Response > Define Variable Sets…
2. Select two or more variables.
3. If your variables are coded as dichotomies, indicate which value you want to have counted. If your
variables are coded as categories, define the range of the categories.
4. Enter a unique name for each multiple response set.
5. Click Add to add the multiple response set to the list of defined sets.
150 IBM SPSS Statistics Base V27
Multiple Response Frequencies
The Multiple Response Frequencies procedure produces frequency tables for multiple response sets. You
must first define one or more multiple response sets (see “Multiple Response Define Sets”).
For multiple dichotomy sets, category names shown in the output come from variable labels defined for
elementary variables in the group. If the variable labels are not defined, variable names are used as
labels. For multiple category sets, category labels come from the value labels of the first variable in the
group. If categories missing for the first variable are present for other variables in the group, define a
value label for the missing categories.
Missing Values. Cases with missing values are excluded on a table-by-table basis. Alternatively, you can
choose one or both of the following:
• Exclude cases listwise within dichotomies. Excludes cases with missing values for any variable from
the tabulation of the multiple dichotomy set. This applies only to multiple response sets defined as
dichotomy sets. By default, a case is considered missing for a multiple dichotomy set if none of its
component variables contains the counted value. Cases with missing values for some (but not all
variables) are included in the tabulations of the group if at least one variable contains the counted
value.
• Exclude cases listwise within categories. Excludes cases with missing values for any variable from
tabulation of the multiple category set. This applies only to multiple response sets defined as category
sets. By default, a case is considered missing for a multiple category set only if none of its components
has valid values within the defined range.
Example. Each variable created from a survey question is an elementary variable. To analyze a multiple
response item, you must combine the variables into one of two types of multiple response sets: a multiple
dichotomy set or a multiple category set. For example, if an airline survey asked which of three airlines
(American, United, TWA) you have flown in the last six months and you used dichotomous variables and
defined a multiple dichotomy set, each of the three variables in the set would become a category of the
group variable. The counts and percentages for the three airlines are displayed in one frequency table. If
you discover that no respondent mentioned more than two airlines, you could create two variables, each
having three codes, one for each airline. If you define a multiple category set, the values are tabulated by
adding the same codes in the elementary variables together. The resulting set of values is the same as
those for each of the elementary variables. For example, 30 responses for United are the sum of the five
United responses for airline 1 and the 25 United responses for airline 2. The counts and percentages for
the three airlines are displayed in one frequency table.
Statistics. Frequency tables displaying counts, percentages of responses, percentages of cases, number
of valid cases, and number of missing cases.
Multiple Response Frequencies Data Considerations
Data. Use multiple response sets.
Assumptions. The counts and percentages provide a useful description for data from any distribution.
Related procedures. The Multiple Response Define Sets procedure allows you to define multiple
response sets.
To Obtain Multiple Response Frequencies
1. From the menus choose:
Analyze > Multiple Response > Frequencies…
2. Select one or more multiple response sets.
Multiple Response Crosstabs
The Multiple Response Crosstabs procedure crosstabulates defined multiple response sets, elementary
variables, or a combination. You can also obtain cell percentages based on cases or responses, modify
the handling of missing values, or get paired crosstabulations. You must first define one or more multiple
response sets (see “To Define Multiple Response Sets”).
Chapter 1. Core features 151
For multiple dichotomy sets, category names shown in the output come from variable labels defined for
elementary variables in the group. If the variable labels are not defined, variable names are used as
labels. For multiple category sets, category labels come from the value labels of the first variable in the
group. If categories missing for the first variable are present for other variables in the group, define a
value label for the missing categories. The procedure displays category labels for columns on three lines,
with up to eight characters per line. To avoid splitting words, you can reverse row and column items or
redefine labels.
Example. Both multiple dichotomy and multiple category sets can be crosstabulated with other variables
in this procedure. An airline passenger survey asks passengers for the following information: Circle all of
the following airlines you have flown at least once in the last six months (American, United, TWA). Which
is more important in selecting a flight–schedule or service? Select only one. After entering the data as
dichotomies or multiple categories and combining them into a set, you can crosstabulate the airline
choices with the question involving service or schedule.
Statistics. Crosstabulation with cell, row, column, and total counts, and cell, row, column, and total
percentages. The cell percentages can be based on cases or responses.
Multiple Response Crosstabs Data Considerations
Data. Use multiple response sets or numeric categorical variables.
Assumptions. The counts and percentages provide a useful description of data from any distribution.
Related procedures. The Multiple Response Define Sets procedure allows you to define multiple
response sets.
To Obtain Multiple Response Crosstabs
1. From the menus choose:
Analyze > Multiple Response > Crosstabs…
2. Select one or more numeric variables or multiple response sets for each dimension of the
crosstabulation.
3. Define the range of each elementary variable.
Optionally, you can obtain a two-way crosstabulation for each category of a control variable or multiple
response set. Select one or more items for the Layer(s) list.
Multiple Response Crosstabs Define Ranges
Value ranges must be defined for any elementary variable in the crosstabulation. Enter the integer
minimum and maximum category values that you want to tabulate. Categories outside the range are
excluded from analysis. Values within the inclusive range are assumed to be integers (non-integers are
truncated).
Multiple Response Crosstabs Options
Cell Percentages. Cell counts are always displayed. You can choose to display row percentages, column
percentages, and two-way table (total) percentages.
Percentages Based on. You can base cell percentages on cases (or respondents). This is not available if
you select matching of variables across multiple category sets. You can also base cell percentages on
responses. For multiple dichotomy sets, the number of responses is equal to the number of counted
values across cases. For multiple category sets, the number of responses is the number of values in the
defined range.
Missing Values. You can choose one or both of the following:
• Exclude cases listwise within dichotomies. Excludes cases with missing values for any variable from
the tabulation of the multiple dichotomy set. This applies only to multiple response sets defined as
dichotomy sets. By default, a case is considered missing for a multiple dichotomy set if none of its
component variables contains the counted value. Cases with missing values for some, but not all,
variables are included in the tabulations of the group if at least one variable contains the counted value.
152 IBM SPSS Statistics Base V27
• Exclude cases listwise within categories. Excludes cases with missing values for any variable from
tabulation of the multiple category set. This applies only to multiple response sets defined as category
sets. By default, a case is considered missing for a multiple category set only if none of its components
has valid values within the defined range.
By default, when crosstabulating two multiple category sets, the procedure tabulates each variable in the
first group with each variable in the second group and sums the counts for each cell; therefore, some
responses can appear more than once in a table. You can choose the following option:
Match variables across response sets. Pairs the first variable in the first group with the first variable in
the second group, and so on. If you select this option, the procedure bases cell percentages on responses
rather than respondents. Pairing is not available for multiple dichotomy sets or elementary variables.
MULT RESPONSE Command Additional Features
The command syntax language also allows you to:
• Obtain crosstabulation tables with up to five dimensions (with the BY subcommand).
• Change output formatting options, including suppression of value labels (with the FORMAT
subcommand).
See the Command Syntax Reference for complete syntax information.
Reporting Results
Reporting Results
Case listings and descriptive statistics are basic tools for studying and presenting data. You can obtain
case listings with the Data Editor or the Summarize procedure, frequency counts and descriptive statistics
with the Frequencies procedure, and subpopulation statistics with the Means procedure. Each of these
uses a format designed to make information clear. If you want to display the information in a different
format, Report Summaries in Rows and Report Summaries in Columns give you the control you need over
data presentation.
Report Summaries in Rows
Report Summaries in Rows produces reports in which different summary statistics are laid out in rows.
Case listings are also available, with or without summary statistics.
Example. A company with a chain of retail stores keeps records of employee information, including
salary, job tenure, and the store and division in which each employee works. You could generate a report
that provides individual employee information (listing) broken down by store and division (break
variables), with summary statistics (for example, mean salary) for each store, division, and division within
each store.
Data Columns. Lists the report variables for which you want case listings or summary statistics and
controls the display format of data columns.
Break Columns. Lists optional break variables that divide the report into groups and controls the
summary statistics and display formats of break columns. For multiple break variables, there will be a
separate group for each category of each break variable within categories of the preceding break variable
in the list. Break variables should be discrete categorical variables that divide cases into a limited number
of meaningful categories. Individual values of each break variable appear, sorted, in a separate column to
the left of all data columns.
Report. Controls overall report characteristics, including overall summary statistics, display of missing
values, page numbering, and titles.
Display cases. Displays the actual values (or value labels) of the data-column variables for every case.
This produces a listing report, which can be much longer than a summary report.
Preview. Displays only the first page of the report. This option is useful for previewing the format of your
report without processing the whole report.
Chapter 1. Core features 153
Data are already sorted. For reports with break variables, the data file must be sorted by break variable
values before generating the report. If your data file is already sorted by values of the break variables, you
can save processing time by selecting this option. This option is particularly useful after running a preview
report.
To Obtain a Summary Report: Summaries in Rows
1. From the menus choose:
Analyze > Reports > Report Summaries in Rows…
2. Select one or more variables for Data Columns. One column in the report is generated for each variable
selected.
3. For reports sorted and displayed by subgroups, select one or more variables for Break Columns.
4. For reports with summary statistics for subgroups defined by break variables, select the break variable
in the Break Column Variables list and click Summary in the Break Columns group to specify the
summary measure(s).
5. For reports with overall summary statistics, click Summary to specify the summary measure(s).
Report Data Column/Break Format
The Format dialog boxes control column titles, column width, text alignment, and the display of data
values or value labels. Data Column Format controls the format of data columns on the right side of the
report page. Break Format controls the format of break columns on the left side.
Column Title. For the selected variable, controls the column title. Long titles are automatically wrapped
within the column. Use the Enter key to manually insert line breaks where you want titles to wrap.
Value Position within Column. For the selected variable, controls the alignment of data values or value
labels within the column. Alignment of values or labels does not affect alignment of column headings. You
can either indent the column contents by a specified number of characters or center the contents.
Column Content. For the selected variable, controls the display of either data values or defined value
labels. Data values are always displayed for any values that do not have defined value labels. (Not
available for data columns in column summary reports.)
Report Summary Lines for/Final Summary Lines
The two Summary Lines dialog boxes control the display of summary statistics for break groups and for
the entire report. Summary Lines controls subgroup statistics for each category defined by the break
variable(s). Final Summary Lines controls overall statistics, displayed at the end of the report.
Available summary statistics are sum, mean, minimum, maximum, number of cases, percentage of cases
above or below a specified value, percentage of cases within a specified range of values, standard
deviation, kurtosis, variance, and skewness.
Report Break Options
Break Options controls spacing and pagination of break category information.
Page Control. Controls spacing and pagination for categories of the selected break variable. You can
specify a number of blank lines between break categories or start each break category on a new page.
Blank Lines before Summaries. Controls the number of blank lines between break category labels or
data and summary statistics. This is particularly useful for combined reports that include both individual
case listings and summary statistics for break categories; in these reports, you can insert space between
the case listings and the summary statistics.
Report Options
Report Options controls the treatment and display of missing values and report page numbering.
Exclude cases with missing values listwise. Eliminates (from the report) any case with missing values
for any of the report variables.
154 IBM SPSS Statistics Base V27
Missing Values Appear as. Allows you to specify the symbol that represents missing values in the data
file. The symbol can be only one character and is used to represent both system-missing and user-missing
values.
Number Pages from. Allows you to specify a page number for the first page of the report.
Report Layout
Report Layout controls the width and length of each report page, placement of the report on the page, and
the insertion of blank lines and labels.
Page Layout. Controls the page margins expressed in lines (top and bottom) and characters (left and
right) and reports alignment within the margins.
Page Titles and Footers. Controls the number of lines that separate page titles and footers from the body
of the report.
Break Columns. Controls the display of break columns. If multiple break variables are specified, they can
be in separate columns or in the first column. Placing all break variables in the first column produces a
narrower report.
Column Titles. Controls the display of column titles, including title underlining, space between titles and
the body of the report, and vertical alignment of column titles.
Data Column Rows and Break Labels. Controls the placement of data column information (data values
and/or summary statistics) in relation to the break labels at the start of each break category. The first row
of data column information can start either on the same line as the break category label or on a specified
number of lines after the break category label. (Not available for column summary reports.)
Report Titles
Report Titles controls the content and placement of report titles and footers. You can specify up to 10
lines of page titles and up to 10 lines of page footers, with left-justified, centered, and right-justified
components on each line.
If you insert variables into titles or footers, the current value label or value of the variable is displayed in
the title or footer. In titles, the value label corresponding to the value of the variable at the beginning of
the page is displayed. In footers, the value label corresponding to the value of the variable at the end of
the page is displayed. If there is no value label, the actual value is displayed.
Special Variables. The special variables DATE and PAGE allow you to insert the current date or the page
number into any line of a report header or footer. If your data file contains variables named DATE or PAGE,
you cannot use these variables in report titles or footers.
Report Summaries in Columns
Report Summaries in Columns produces summary reports in which different summary statistics appear in
separate columns.
Example. A company with a chain of retail stores keeps records of employee information, including
salary, job tenure, and the division in which each employee works. You could generate a report that
provides summary salary statistics (for example, mean, minimum, and maximum) for each division.
Data Columns. Lists the report variables for which you want summary statistics and controls the display
format and summary statistics displayed for each variable.
Break Columns. Lists optional break variables that divide the report into groups and controls the display
formats of break columns. For multiple break variables, there will be a separate group for each category
of each break variable within categories of the preceding break variable in the list. Break variables should
be discrete categorical variables that divide cases into a limited number of meaningful categories.
Report. Controls overall report characteristics, including display of missing values, page numbering, and
titles.
Preview. Displays only the first page of the report. This option is useful for previewing the format of your
report without processing the whole report.
Chapter 1. Core features 155
Data are already sorted. For reports with break variables, the data file must be sorted by break variable
values before generating the report. If your data file is already sorted by values of the break variables, you
can save processing time by selecting this option. This option is particularly useful after running a preview
report.
To Obtain a Summary Report: Summaries in Columns
1. From the menus choose:
Analyze > Reports > Report Summaries in Columns…
2. Select one or more variables for Data Columns. One column in the report is generated for each variable
selected.
3. To change the summary measure for a variable, select the variable in the Data Column Variables list
and click Summary.
4. To obtain more than one summary measure for a variable, select the variable in the source list and
move it into the Data Column Variables list multiple times, one for each summary measure you want.
5. To display a column containing the sum, mean, ratio, or other function of existing columns, click Insert
Total. This places a variable called total into the Data Columns list.
6. For reports sorted and displayed by subgroups, select one or more variables for Break Columns.
Data Columns Summary Function
Summary Lines controls the summary statistic displayed for the selected data column variable.
Available summary statistics are sum, mean, minimum, maximum, number of cases, percentage of cases
above or below a specified value, percentage of cases within a specified range of values, standard
deviation, variance, kurtosis, and skewness.
Data Columns Summary for Total Column
Summary Column controls the total summary statistics that summarize two or more data columns.
Available total summary statistics are sum of columns, mean of columns, minimum, maximum, difference
between values in two columns, quotient of values in one column divided by values in another column,
and product of columns values multiplied together.
Sum of columns. The total column is the sum of the columns in the Summary Column list.
Mean of columns. The total column is the average of the columns in the Summary Column list.
Minimum of columns. The total column is the minimum of the columns in the Summary Column list.
Maximum of columns. The total column is the maximum of the columns in the Summary Column list.
1st column – 2nd column. The total column is the difference of the columns in the Summary Column list.
The Summary Column list must contain exactly two columns.
1st column / 2nd column. The total column is the quotient of the columns in the Summary Column list.
The Summary Column list must contain exactly two columns.
% 1st column / 2nd column. The total column is the first column’s percentage of the second column in
the Summary Column list. The Summary Column list must contain exactly two columns.
Product of columns. The total column is the product of the columns in the Summary Column list.
Report Column Format
Data and break column formatting options for Report Summaries in Columns are the same as those
described for Report Summaries in Rows.
Report Summaries in Columns Break Options
Break Options controls subtotal display, spacing, and pagination for break categories.
Subtotal. Controls the display subtotals for break categories.
156 IBM SPSS Statistics Base V27
Page Control. Controls spacing and pagination for categories of the selected break variable. You can
specify a number of blank lines between break categories or start each break category on a new page.
Blank Lines before Subtotal. Controls the number of blank lines between break category data and
subtotals.
Report Summaries in Columns Options
Options controls the display of grand totals, the display of missing values, and pagination in column
summary reports.
Grand Total. Displays and labels a grand total for each column; displayed at the bottom of the column.
Missing values. You can exclude missing values from the report or select a single character to indicate
missing values in the report.
Report Layout for Summaries in Columns
Report layout options for Report Summaries in Columns are the same as those described for Report
Summaries in Rows.
REPORT Command Additional Features
The command syntax language also allows you to:
• Display different summary functions in the columns of a single summary line.
• Insert summary lines into data columns for variables other than the data column variable or for various
combinations (composite functions) of summary functions.
• Use Median, Mode, Frequency, and Percent as summary functions.
• Control more precisely the display format of summary statistics.
• Insert blank lines at various points in reports.
• Insert blank lines after every nth case in listing reports.
Because of the complexity of the REPORT syntax, you may find it useful, when building a new report with
syntax, to approximate the report generated from the dialog boxes, copy and paste the corresponding
syntax, and refine that syntax to yield the exact report that you want.
See the Command Syntax Reference for complete syntax information.
Reliability Analysis
Reliability analysis allows you to study the properties of measurement scales and the items that compose
the scales. The Reliability Analysis procedure calculates a number of commonly used measures of scale
reliability and also provides information about the relationships between individual items in the scale.
Intra-class correlation coefficients can be used to compute inter-rater reliability estimates.
Reliability analysis also provides Fleiss’ Multiple Rater Kappa statistics that assess the interrater
agreement to determine the reliability among the various raters. A higher agreement provides more
confidence in the ratings reflecting the true circumstance. The Fleiss’ Multiple Rater Kappa options are
available in the “Reliability Analysis: Statistics” on page 158 dialog.
Example
Does my questionnaire measure customer satisfaction in a useful way? Using reliability analysis, you
can determine the extent to which the items in your questionnaire are related to each other, you can
get an overall index of the repeatability or internal consistency of the scale as a whole, and you can
identify problem items that should be excluded from the scale.
Statistics
Descriptives for each variable and for the scale, summary statistics across items, inter-item
correlations and covariances, reliability estimates, ANOVA table, intraclass correlation coefficients,
Hotelling’s T 2, Tukey’s test of additivity, and Fleiss’ Multiple Rater Kappa.
Chapter 1. Core features 157
Models
The following models of reliability are available:
Alpha (Cronbach)
This model is a measure of internal consistency based on the average inter-item correlation.
Split-half
This model splits the scale into two parts and examines the correlation between the parts.
Guttman
This model computes Guttman’s lower bounds for true reliability.
Parallel
This model assumes that all items have equal variances and equal error variances across
replications.
Strict parallel
This model makes the assumptions of the Parallel model and also assumes equal means across
items.
Reliability Analysis data considerations
Data
Data can be dichotomous, ordinal, or interval, but the data should be coded numerically.
Assumptions
Observations should be independent, and errors should be uncorrelated between items. Each pair of
items should have a bivariate normal distribution. Scales should be additive, so that each item is
linearly related to the total score. The following assumptions apply for Fleiss’ Multiple Rater Kappa
statistics:
• At least two item variables must be selected to run any reliability statistic.
• When at least two ratings variables are selected, the Fleiss’ Multiple Rater Kappa syntax is pasted.
• There is no connection between raters.
• The number of raters is a constant.
• Each subject is rated by the same group containing only a single rater.
• No weights can be assigned to the various disagreements.
Related procedures
If you want to explore the dimensionality of your scale items (to see whether more than one construct
is needed to account for the pattern of item scores), use factor analysis or multidimensional scaling.
To identify homogeneous groups of variables, use hierarchical cluster analysis to cluster variables.
To obtain a Reliability Analysis
1. From the menus choose:
Analyze > Scale > Reliability Analysis…
2. Select two or more variables as potential components of an additive scale.
3. Choose a model from the Model drop-down list.
4. Optionally, click Statistics to select various statistics that describe your scale items or interrater
agreement.
Reliability Analysis: Statistics
You can select various statistics that describe your scale, items and the interrater agreement to
determine the reliability among the various raters. Statistics that are reported by default include the
number of cases, the number of items, and reliability estimates as follows:
Alpha models
Coefficient alpha; for dichotomous data, this is equivalent to the Kuder-Richardson 20 (KR20)
coefficient.
158 IBM SPSS Statistics Base V27
Split-half models
Correlation between forms, Guttman split-half reliability, Spearman-Brown reliability (equal and
unequal length), and coefficient alpha for each half.
Guttman models
Reliability coefficients lambda 1 through lambda 6.
Parallel and Strict parallel models
Test for goodness of fit of model; estimates of error variance, common variance, and true variance;
estimated common inter-item correlation; estimated reliability; and unbiased estimate of reliability.
Descriptives for
Produces descriptive statistics for scales or items across cases.
Item
Produces descriptive statistics for items across cases.
Scale
Produces descriptive statistics for scales.
Scale if item deleted
Displays summary statistics comparing each item to the scale that is composed of the other items.
Statistics include scale mean and variance if the item were to be deleted from the scale,
correlation between the item and the scale that is composed of other items, and Cronbach’s alpha
if the item were to be deleted from the scale.
Summaries
Provides descriptive statistics of item distributions across all items in the scale.
Means
Summary statistics for item means. The smallest, largest, and average item means, the range and
variance of item means, and the ratio of the largest to the smallest item means are displayed.
Variances
Summary statistics for item variances. The smallest, largest, and average item variances, the
range and variance of item variances, and the ratio of the largest to the smallest item variances
are displayed.
Correlations
Summary statistics for inter-item correlations. The smallest, largest, and average inter-item
correlations, the range and variance of inter-item correlations, and the ratio of the largest to the
smallest inter-item correlations are displayed.
Covariances
Summary statistics for inter-item covariances. The smallest, largest, and average inter-item
covariances, the range and variance of inter-item covariances, and the ratio of the largest to the
smallest inter-item covariances are displayed.
Inter-Item
Produces matrices of correlations or covariances between items.
ANOVA Table
Produces tests of equal means.
F test
Displays a repeated measures analysis-of-variance table.
Friedman chi-square
Displays Friedman’s chi-square and Kendall’s coefficient of concordance. This option is
appropriate for data that are in the form of ranks. The chi-square test replaces the usual F test in
the ANOVA table.
Cochran chi-square
Displays Cochran’s Q. This option is appropriate for data that are dichotomous. The Q statistic
replaces the usual F statistic in the ANOVA table.
Chapter 1. Core features 159
Interrater Agreement: Fleiss’ Kappa
Assesses the interrater agreement to determine the reliability among the various raters. A higher
agreement provides more confidence in the ratings reflecting the true circumstance. The generalized
unweighted kappa statistic measures the agreement among any constant number of raters while
assuming:
• At least two item variables must be specified to run any reliability statistic.
• At least two ratings variables must be specified.
• The variables selected as items can also be selected as ratings.
• There is no connection between raters.
• The number of raters is a constant.
• Each subject is rated by the same group containing only a single rater.
• No weights can be assigned to the various disagreements.
Display agreement on individual categories
Specifies whether or not to output the agreement on individual categories. By default, the output
suppresses the estimation on any individual categories. When enabled, multiple tables display in
the output.
Ignore string cases
Controls whether or not the string variables are case sensitive. By default, string rating values are
case sensitive.
String category labels are displayed in uppercase
Controls whether the category labels in the output tables are displayed in uppercase or
lowercase. The setting is enabled by default, which displays the string category labels in
uppercase.
Asymptotic significance level (%)
Specifies the significance level for the asymptotic confidence intervals. 95 is the default setting.
Missing
Exclude both user-missing and system missing values
Controls the exclusion of user-missing and system-missing values. By default, user-missing and
system-missing values are excluded.
User-missing values are treated as valid
When enabled, treats user-missing and system-missing values as valid data. The setting is
disabled by default.
Hotelling’s T-square
Produces a multivariate test of the null hypothesis that all items on the scale have the same mean.
Tukey’s test of additivity
Produces a test of the assumption that there is no multiplicative interaction among the items.
Intraclass correlation coefficient
Produces measures of consistency or agreement of values within cases.
Model
Select the model for calculating the intraclass correlation coefficient. Available models are Two-
Way Mixed, Two-Way Random, and One-Way Random. Select Two-Way Mixed when people
effects are random and the item effects are fixed, select Two-Way Random when people effects
and the item effects are random, or select One-Way Random when people effects are random.
Type
Select the type of index. Available types are Consistency and Absolute Agreement.
Confidence interval (%)
Specify the level for the confidence interval. The default is 95%.
Test value
Specify the hypothesized value of the coefficient for the hypothesis test. This value is the value to
which the observed value is compared. The default value is 0.
160 IBM SPSS Statistics Base V27
RELIABILITY Command Additional Features
The command syntax language also allows you to:
• Read and analyze a correlation matrix.
• Write a correlation matrix for later analysis.
• Specify splits other than equal halves for the split-half method.
See the Command Syntax Reference for complete syntax information.
Weighted Kappa
Cohen’s weighted kappa is broadly used in cross-classification as a measure of agreement between
observed raters. It is an appropriate index of agreement when ratings are nominal scales with no order
structure. The development of Cohen’s weighted kappa was motivated by the factor that some
assignments in a contingency table might be of greater gravity than the others. The statistic relies on the
predefined cell weights reflecting either agreement or disagreement.
The Weighted Kappa procedure provides options for estimating Cohen’s weighted kappa, an important
generalization of the kappa statistic that measures the agreement of two ordinal subjects with identical
categories.
Note: The Weighted Kappa procedure supersedes the functionality previously provided by the STATS
WEIGHTED KAPPA.spe extension.
Example
There are situations where the differences between raters should not be treated as equally important.
An example would be in the healthcare industry where multiple people collect research or clinical
data. In such cases the reliability of the data can come into question given the variability among those
collecting data.
Statistics
Cohen’s weighted kappa, linear scale, quadratic scale, asymptotic confidence interval.
Weighted Kappa data considerations
Data
A two-way table that is based on an active data set is required in order to estimate the Cohen’s
weighted kappa statistic.
Rating variables must be of the same type (all string or all numeric).
The estimation of Cohen’s weighted kappa makes sense only when the categories of the two rating
variables, represented by the row and column in the table, are appropriately ordered (for a pair of
numeric variables, numerical order is applied; for a pair of string variables, alphabetical order is
applied).
Assumptions
When mixed variable pairs are selected, Cohen’s weighted kappa is not estimated.
The rating variables are assumed to share the same set of categories.
To obtain a Weighted Kappa analysis
1. From the menus choose:
Analyze > Scale > Weighted Kappa…
2. Select two or more string or numeric variables to specify as Pairwise raters.
Note: You must select either all string variables or all numeric variables.
3. Optionally, enable the Specify raters for rows and columns setting to control the display of pairwise
raters or rows/column raters.
Chapter 1. Core features 161
• When enabled, pairwise raters are suppressed and row/column raters display. The user interface
updates to provide Row rater(s) and Column rater(s) fields (effectively replacing the Pairwise
raters field.
• When disabled, row/column raters are suppressed and pairwise raters display (the default setting)
When Specify raters for rows and columns is enabled, specify at least one variable for both Row
rater(s) and Column rater(s).
Note: If both Row rater(s) and Column rater(s) contain only one variable, the selected variables
cannot be the same for both.
4. Optionally, click Criteria to specify the weighting scale and missing values settings, or Print to specify
the display format and crosstabulation settings.
Weighted Kappa: Criteria
The Criteria dialog provides options for specifying the estimation of the Cohen’s weighted kappa
statistics.
Weighting Scale
Provides options for specifying either a linear or quadratic weighting for agreement. The use of linear
weighting is the default setting.
Missing Values
Provides options for removing cases with missing values on a pairwise basis and treating user-missing
values as valid.
String rating variables are case sensitive
When selected, string variables are treated as case sensitive.
Asymptotic confidence interval (%)
This optional setting specifies the confidence level for the estimation of the asymptotic confidence
intervals. Must be a single double value between 0 and 100 (95 is the default setting).
Weighted Kappa: Print
The Print dialog provides options for controlling the crosstabulation tables.
Display and Format
Provides options for controlling the crosstabulation table display and format.
Rating categories are displayed in ascending order
When selected, rating categories in the crosstabulation tables display in ascending order. When
the setting is not selected, rating categories in the crosstabulation tables display in descending
order. The setting is enabled by default.
String category labels are displayed in uppercase
When selected, crosstabulation tables display as uppercase. When the setting is not selected,
crosstabulation tables display as lowercase. The setting is enabled by default.
Crosstabulation
Provides options for specifying the rating variables that are used in crosstabulation. By default,
crosstabulation settings are not enabled, which suppresses the crosstabulation of any rating
variables.
Display the crosstabulation of rating variables
When selected, this setting the enables the crosstabulation of all or user-specified rating
variables.
Include all rating variables
When selected, crosstabulation tables are printed for all defined rating variable pairs.
Include user-specified rating variables
When selected, use the Available variables, Row rater(s), and Column rater(s) fields to
select which rating variables are included in the crosstabulation tables.
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Multidimensional Scaling
Multidimensional scaling attempts to find the structure in a set of distance measures between objects or
cases. This task is accomplished by assigning observations to specific locations in a conceptual space
(usually two- or three-dimensional) such that the distances between points in the space match the given
dissimilarities as closely as possible. In many cases, the dimensions of this conceptual space can be
interpreted and used to further understand your data.
If you have objectively measured variables, you can use multidimensional scaling as a data reduction
technique (the Multidimensional Scaling procedure will compute distances from multivariate data for you,
if necessary). Multidimensional scaling can also be applied to subjective ratings of dissimilarity between
objects or concepts. Additionally, the Multidimensional Scaling procedure can handle dissimilarity data
from multiple sources, as you might have with multiple raters or questionnaire respondents.
Example. How do people perceive relationships between different cars? If you have data from
respondents indicating similarity ratings between different makes and models of cars, multidimensional
scaling can be used to identify dimensions that describe consumers’ perceptions. You might find, for
example, that the price and size of a vehicle define a two-dimensional space, which accounts for the
similarities that are reported by your respondents.
Statistics. For each model: data matrix, optimally scaled data matrix, S-stress (Young’s), stress
(Kruskal’s), RSQ, stimulus coordinates, average stress and RSQ for each stimulus (RMDS models). For
individual difference (INDSCAL) models: subject weights and weirdness index for each subject. For each
matrix in replicated multidimensional scaling models: stress and RSQ for each stimulus. Plots: stimulus
coordinates (two- or three-dimensional), scatterplot of disparities versus distances.
Multidimensional Scaling Data Considerations
Data. If your data are dissimilarity data, all dissimilarities should be quantitative and should be measured
in the same metric. If your data are multivariate data, variables can be quantitative, binary, or count data.
Scaling of variables is an important issue–differences in scaling may affect your solution. If your variables
have large differences in scaling (for example, one variable is measured in dollars and the other variable is
measured in years), consider standardizing them (this process can be done automatically by the
Multidimensional Scaling procedure).
Assumptions. The Multidimensional Scaling procedure is relatively free of distributional assumptions. Be
sure to select the appropriate measurement level (ordinal, interval, or ratio) in the Multidimensional
Scaling Options dialog box so that the results are computed correctly.
Related procedures. If your goal is data reduction, an alternative method to consider is factor analysis,
particularly if your variables are quantitative. If you want to identify groups of similar cases, consider
supplementing your multidimensional scaling analysis with a hierarchical or k-means cluster analysis.
To Obtain a Multidimensional Scaling Analysis
1. From the menus choose:
Analyze > Scale > Multidimensional Scaling…
2. Select at least four numeric variables for analysis.
3. In the Distances group, select either Data are distances or Create distances from data.
4. If you select Create distances from data, you can also select a grouping variable for individual
matrices. The grouping variable can be numeric or string.
Optionally, you can also:
• Specify the shape of the distance matrix when data are distances.
• Specify the distance measure to use when creating distances from data.
Multidimensional Scaling Shape of Data
If your active dataset represents distances among a set of objects or represents distances between two
sets of objects, specify the shape of your data matrix in order to get the correct results.
Chapter 1. Core features 163
Note: You cannot select Square symmetric if the Model dialog box specifies row conditionality.
Multidimensional Scaling Create Measure
Multidimensional scaling uses dissimilarity data to create a scaling solution. If your data are multivariate
data (values of measured variables), you must create dissimilarity data in order to compute a
multidimensional scaling solution. You can specify the details of creating dissimilarity measures from
your data.
Measure. Allows you to specify the dissimilarity measure for your analysis. Select one alternative from
the Measure group corresponding to your type of data, and then choose one of the measures from the
drop-down list corresponding to that type of measure. Available alternatives are:
• Interval. Euclidean distance, Squared Euclidean distance, Chebychev, Block, Minkowski, or
Customized.
• Counts. Chi-square measure or Phi-square measure.
• Binary. Euclidean distance, Squared Euclidean distance, Size difference, Pattern difference, Variance,
or Lance and Williams.
Create Distance Matrix. Allows you to choose the unit of analysis. Alternatives are Between variables or
Between cases.
Transform Values. In certain cases, such as when variables are measured on very different scales, you
may want to standardize values before computing proximities (not applicable to binary data). Choose a
standardization method from the Standardize drop-down list. If no standardization is required, choose
None.
Multidimensional Scaling Model
Correct estimation of a multidimensional scaling model depends on aspects of the data and the model
itself.
Level of Measurement. Allows you to specify the level of your data. Alternatives are Ordinal, Interval, or
Ratio. If your variables are ordinal, selecting Untie tied observations requests that the variables be
treated as continuous variables, so that ties (equal values for different cases) are resolved optimally.
Conditionality. Allows you to specify which comparisons are meaningful. Alternatives are Matrix, Row, or
Unconditional.
Dimensions. Allows you to specify the dimensionality of the scaling solution(s). One solution is calculated
for each number in the range. Specify integers between 1 and 6; a minimum of 1 is allowed only if you
select Euclidean distance as the scaling model. For a single solution, specify the same number for
minimum and maximum.
Scaling Model. Allows you to specify the assumptions by which the scaling is performed. Available
alternatives are Euclidean distance or Individual differences Euclidean distance (also known as
INDSCAL). For the Individual differences Euclidean distance model, you can select Allow negative
subject weights, if appropriate for your data.
Multidimensional Scaling Options
You can specify options for your multidimensional scaling analysis.
Display. Allows you to select various types of output. Available options are Group plots, Individual
subject plots, Data matrix, and Model and options summary.
Criteria. Allows you to determine when iteration should stop. To change the defaults, enter values for S-
stress convergence, Minimum s-stress value, and Maximum iterations.
Treat distances less than n as missing. Distances that are less than this value are excluded from the
analysis.
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ALSCAL Command Additional Features
The command syntax language also allows you to:
• Use three additional model types, known as ASCAL, AINDS, and GEMSCAL in the literature about
multidimensional scaling.
• Carry out polynomial transformations on interval and ratio data.
• Analyze similarities (rather than distances) with ordinal data.
• Analyze nominal data.
• Save various coordinate and weight matrices into files and read them back in for analysis.
• Constrain multidimensional unfolding.
See the Command Syntax Reference for complete syntax information.
Ratio Statistics
The Ratio Statistics procedure provides a comprehensive list of summary statistics for describing the ratio
between two scale variables.
You can sort the output by values of a grouping variable in ascending or descending order. The ratio
statistics report can be suppressed in the output, and the results can be saved to an external file.
Example. Is there good uniformity in the ratio between the appraisal price and sale price of homes in
each of five counties? From the output, you might learn that the distribution of ratios varies considerably
from county to county.
Statistics. Median, mean, weighted mean, confidence intervals, coefficient of dispersion (COD), median-
centered coefficient of variation, mean-centered coefficient of variation, price-related differential (PRD),
standard deviation, average absolute deviation (AAD), range, minimum and maximum values, and the
concentration index computed for a user-specified range or percentage within the median ratio.
Ratio Statistics Data Considerations
Data. Use numeric codes or strings to code grouping variables (nominal or ordinal level measurements).
Assumptions. The variables that define the numerator and denominator of the ratio should be scale
variables that take positive values.
To Obtain Ratio Statistics
1. From the menus choose:
Analyze > Descriptive Statistics > Ratio…
2. Select a numerator variable.
3. Select a denominator variable.
Optionally:
• Select a grouping variable and specify the ordering of the groups in the results.
• Choose whether to display the results in the Viewer.
• Choose whether to save the results to an external file for later use, and specify the name of the file to
which the results are saved.
Ratio Statistics
Central Tendency. Measures of central tendency are statistics that describe the distribution of ratios.
• Median. The value such that the number of ratios that are less than this value and the number of ratios
that are greater than this value are the same.
• Mean. The result of summing the ratios and dividing the result by the total number of ratios.
Chapter 1. Core features 165
• Weighted Mean. The result of dividing the mean of the numerator by the mean of the denominator.
Weighted mean is also the mean of the ratios weighted by the denominator.
• Confidence Intervals. Displays confidence intervals for the mean, the median, and the weighted mean
(if requested). Specify a value that is greater than or equal to 0 and less than 100 as the confidence
level.
Dispersion. These statistics measure the amount of variation, or spread, in the observed values.
• AAD. The average absolute deviation is the result of summing the absolute deviations of the ratios
about the median and dividing the result by the total number of ratios.
• COD. The coefficient of dispersion is the result of expressing the average absolute deviation as a
percentage of the median.
• PRD. The price-related differential, also known as the index of regressivity, is the result of dividing the
mean by the weighted mean.
• Median Centered COV. The median-centered coefficient of variation is the result of expressing the root
mean squares of deviation from the median as a percentage of the median.
• Mean Centered COV. The mean-centered coefficient of variation is the result of expressing the
standard deviation as a percentage of the mean.
• Standard deviation. The standard deviation is the result of summing the squared deviations of the
ratios about the mean, dividing the result by the total number of ratios minus one, and taking the
positive square root.
• Range. The range is the result of subtracting the minimum ratio from the maximum ratio.
• Minimum. The minimum is the smallest ratio.
• Maximum. The maximum is the largest ratio.
Concentration Index. The coefficient of concentration measures the percentage of ratios that fall within
an interval. It can be computed in two different ways:
• Ratios Between. Here the interval is defined explicitly by specifying the low and high values of the
interval. Enter values for the low proportion and high proportion, and click Add to obtain an interval.
• Ratios Within. Here the interval is defined implicitly by specifying the percentage of the median. Enter a
value between 0 and 100, and click Add. The lower end of the interval is equal to (1 – 0.01 × value) ×
median, and the upper end is equal to (1 + 0.01 × value) × median.
ROC Analysis
Receiver operating characteristic (ROC) Analysis is a useful way to assess the accuracy of model
predictions by plotting sensitivity versus (1-specificity) of a classification test (as the threshold varies over
an entire range of diagnostic test results). The full area under a given ROC curve, or AUC, formulates an
important statistic that represents the probability that the prediction will be in the correct order when a
test variable is observed (for one subject randomly selected from the case group, and the other randomly
selected from the control group). ROC Analysis supports the inference regarding a single AUC, precision-
recall (PR) curves, and provides options for comparing two ROC curves that are generated from either
independent groups or paired subjects.
PR curves plot precision versus recall, tend to be more informative when the observed data samples are
highly skewed, and provide an alternative to ROC curves for data with a large skew in the class
distribution.
Example
It is in a bank’s interest to correctly classify customers into those customers who will and will not
default on their loans, so special models are developed for making these decisions. ROC Analysis can
be used to evaluate and assess the accuracy of the model predictions.
Statistics
AUC, negative group, missing values, positive classification, cutoff value, strength of conviction, two-
sided asymptotic confidence interval, distribution, standard error, independent-group design, paired-
sample design, nonparametric assumption, bi-negative exponential distribution assumption,
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midpoint, cut point, PR curve, stepwise interpolation, asymptotic significance (2-tail), Sensitivity and
(1-Specicity), Precision and Recall.
Methods
The areas under two ROC curves, that are generated from either independent groups or paired
subjects, are compared. Comparing two ROC curves can provide more information in the accuracy
resulted from two comparative diagnostic approaches.
ROC Analysis data considerations
Data
PR curves plot Precision versus Recall, and tend to be more informative when the observed data
samples are highly skewed. A simple linear interpolation may mistakenly yield an overly-optimistic
estimate of a PR curve.
Assumptions
The prediction will be in the correct order when a test variable is observed for one subject that is
randomly selected from the case group and the other is randomly selected from the control group.
Each defined group will contain at least one valid observation. Only a single grouping variable is used
for a single procedure.
Obtaining an ROC Analysis
1. From the menus choose:
Analyze > Classify > ROC Analysis
2. Select one or more test probability variables.
3. Select one state variable.
4. Identify the positive value for the state variable.
5. Optionally select the Paired-sample design option, or select a single grouping variable (you cannot
select both options).
• Use the Paired-sample design setting to request the paired-sample design for the test variable(s).
The paired-sample design compares two ROC curves in a paired-sample scenario when multiple test
values are measured on the same subjects that are associated with a state variable.
Note: When Paired-sample design is selected, the Grouping Variable and Distribution
Assumption (in the Options dialog) options are disabled.
• When a numeric grouping variable is selected, you can click Define Groups… to request the
independent group design for the test variable(s), and to specify two values, a midpoint, or a cut
point.
6. Optionally, click Options to define the classification, test direction, standard error parameters, and
missing values settings.
7. Optionally, click Display to define the plotting and print settings (which include ROC Curve, Precision-
Recall Curve and model quality settings).
8. Click OK.
ROC Analysis: Options
You can specify the following options for your ROC analysis:
Classification
Allows you to specify whether the cutoff value should be included or excluded when making a positive
classification. This setting currently has no effect on the output.
Test Direction
Provides options for specifying which direction of the test result variable indicates increasing strength
of conviction that the subject is test positive.
Chapter 1. Core features 167
Parameters for Standard Error of Area
Allows you to specify the method of estimating the standard error of the area under the curve.
Available methods are nonparametric and bi-negative exponential. The default Nonparametric
setting provides estimates under the nonparametric assumption. The Bi-negative exponential
setting provides estimates under the bi-negative exponential distribution assumption.
The section also allows you to specify the confidence level for the two-sided asymptotic confidence
interval of the AUC. The available range is 0.0% to 100.0% (the default value is 95%).
Note: The setting only applies to the independent-group design and has no effect in the paired-
sample design.
Missing Values
Allows you to specify how missing values are handled. When the setting is not selected, both user-
missing values and system-missing values are excluded. When the setting is selected, user-missing
values as treated as valid, system-missing values are excluded. Cases with system-missing values, in
either the test variable or the state variable, are always excluded from the analysis.
ROC Analysis: Display
You can specify the following display settings for your ROC analysis:
Plot
Provides options for plotting the ROC and Precision-Recall curves.
ROC Curve
When selected, a ROC Curve chart displays in the output. Select With diagonal reference line to
draw a diagonal reference line on the ROC Curve chart.
Precision-Recall Curve
When selected, a Precision-Recall Curve chart displays in the output. Precision-Recall Curves tend
to be more informative when the observed data samples are highly skewed and provide an
alternative to ROC Curves for data with a large skew in the class distribution. The default
Interpolate along the true positives setting makes the stepwise interpolation along the true
positives. The Interpolate along the false positives setting makes the stepwise interpolation
along the false positives.
Overall model quality
The setting controls whether or not a bar chart is created to display the value of the lower bound
of the confidence interval of the estimated AUC. By default, the setting is not selected, which
suppresses the bar chart.
Print
Provides options for defining the output for the corresponding statistics.
Standard error and confidence interval
The setting controls which statistics display in the “Area Under the Curve” table. When the setting
is not selected, only the estimated AUC displays. When the setting is selected, additional statistics
display, including the standard error of the AUC, the asymptotic significance (2-tail), and the
Asymptotic Confidence Interval bounds under the null hypothesis.
Coordinate points of ROC Curve
The setting controls the coordinate points of the ROC Curve, along with the cutoff values. When
the setting is not selected, the output of coordinate points is suppressed. When the setting is
selected, the pairs of Sensitivity and (1-Specificity) values are given with the cutoff values for each
ROC Curve.
Coordinate points of the Precision-Recall Curve
The setting controls the coordinate points of the Precision-Recall Curve, along with the cutoff
values. When the setting is not selected, the output of coordinate points is suppressed. When the
setting is selected, the pairs of Precision and Recall values are given with the cutoff values for
each Precision-Recall Curve.
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Classifier evaluation metrics
The setting controls the display of the Classifier Evaluation Metrics table in the output. The table
shows how well a classification model fits the data compared to a random assignment and
provides the following information:
• The user-specified test variables
• Group information
• Gini Index (the Gini index is 2*AUC – 1, where AUC is the area under the ROC curve)
• Max K-S and Cutoff values
ROC Analysis: Define Groups (string)
For string grouping variables, enter a string for Group 1 and another value for Group 2, such as yes and no.
Cases with other strings are excluded from the analysis.
Note: The specified values must exist in the variable, otherwise an error message displays to indicate that
at least one of the groups is empty.
ROC Analysis: Define Groups (numeric)
For numeric grouping variables, define the two groups for the t test by specifying two values, a midpoint,
or a cut point.
Note: The specified values must exist in the variable, otherwise an error message displays to indicate that
at least one of the groups is empty.
• Use specified values. Enter a value for Group 1 and another value for Group 2. Cases with any other
values are excluded from the analysis. Numbers need not be integers (for example, 6.25 and 12.5 are
valid).
• Use midpoint value. When selected, the groups are separated into < and ≥ midpoint values.
• Use cut point.
– Cutpoint. Enter a number that splits the values of the grouping variable into two sets. All cases with
values that are less than the cutpoint form one group, and cases with values that are greater than or
equal to the cutpoint form the other group.
ROC Curves
This procedure is a useful way to evaluate the performance of classification schemes in which there is one
variable with two categories by which subjects are classified.
Example. It is in a bank's interest to correctly classify customers into those customers who will and will
not default on their loans, so special methods are developed for making these decisions. ROC curves can
be used to evaluate how well these methods perform.
Statistics. Area under the ROC curve with confidence interval and coordinate points of the ROC curve.
Plots: ROC curve.
Methods. The estimate of the area under the ROC curve can be computed either nonparametrically or
parametrically using a binegative exponential model.
ROC Curve Data Considerations
Data. Test variables are quantitative. Test variables are often composed of probabilities from
discriminant analysis or logistic regression or composed of scores on an arbitrary scale indicating a rater's
"strength of conviction" that a subject falls into one category or another category. The state variable can
be of any type and indicates the true category to which a subject belongs. The value of the state variable
indicates which category should be considered positive.
Assumptions. It is assumed that increasing numbers on the rater scale represent the increasing belief
that the subject belongs to one category, while decreasing numbers on the scale represent the increasing
Chapter 1. Core features 169
belief that the subject belongs to the other category. The user must choose which direction is positive. It
is also assumed that the true category to which each subject belongs is known.
To Obtain an ROC Curve
1. From the menus choose:
Analyze > Classify > ROC Curve…
2. Select one or more test probability variables.
3. Select one state variable.
4. Identify the positive value for the state variable.
ROC Curve Options
You can specify the following options for your ROC analysis:
Classification
Allows you to specify whether the cutoff value should be included or excluded when making a positive
classification. This setting currently has no effect on the output.
Test Direction
Allows you to specify the direction of the scale in relation to the positive category.
Parameters for Standard Error of Area
Allows you to specify the method of estimating the standard error of the area under the curve.
Available methods are nonparametric and binegative exponential. Also allows you to set the level for
the confidence interval. The available range is 50.1% to 99.9%.
Missing Values
Allows you to specify how missing values are handled.
Simulation
Predictive models, such as linear regression, require a set of known inputs to predict an outcome or target
value. In many real world applications, however, values of inputs are uncertain. Simulation allows you to
account for uncertainty in the inputs to predictive models and evaluate the likelihood of various outcomes
of the model in the presence of that uncertainty. For example, you have a profit model that includes the
cost of materials as an input, but there is uncertainty in that cost due to market volatility. You can use
simulation to model that uncertainty and determine the effect it has on profit.
Simulation in IBM SPSS Statistics uses the Monte Carlo method. Uncertain inputs are modeled with
probability distributions (such as the triangular distribution), and simulated values for those inputs are
generated by drawing from those distributions. Inputs whose values are known are held fixed at the
known values. The predictive model is evaluated using a simulated value for each uncertain input and
fixed values for the known inputs to calculate the target (or targets) of the model. The process is repeated
many times (typically tens of thousands or hundreds of thousands of times), resulting in a distribution of
target values that can be used to answer questions of a probabilistic nature. In the context of IBM SPSS
Statistics, each repetition of the process generates a separate case (record) of data that consists of the
set of simulated values for the uncertain inputs, the values of the fixed inputs, and the predicted target (or
targets) of the model.
You can also simulate data in the absence of a predictive model by specifying probability distributions for
variables that are to be simulated. Each generated case of data consists of the set of simulated values for
the specified variables.
To run a simulation, you need to specify details such as the predictive model, the probability distributions
for the uncertain inputs, correlations between those inputs and values for any fixed inputs. Once you’ve
specified all of the details for a simulation, you can run it and optionally save the specifications to a
simulation plan file. You can share the simulation plan with other users, who can then run the simulation
without needing to understand the details of how it was created.
Two interfaces are available for working with simulations. The Simulation Builder is an advanced interface
for users who are designing and running simulations. It provides the full set of capabilities for designing a
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simulation, saving the specifications to a simulation plan file, specifying output and running the
simulation. You can build a simulation based on an IBM SPSS model file, or on a set of custom equations
that you define in the Simulation Builder. You can also load an existing simulation plan into the Simulation
Builder, modify any of the settings and run the simulation, optionally saving the updated plan. For users
who have a simulation plan and primarily want to run the simulation, a simpler interface is available. It
allows you to modify settings that enable you to run the simulation under different conditions, but does
not provide the full capabilities of the Simulation Builder for designing simulations.
To design a simulation based on a model file
1. From the menus choose:
Analyze > Simulation…
2. Click Select SPSS Model File and click Continue.
3. Open the model file.
The model file is an XML file that contains model PMML created from IBM SPSS Statistics or IBM SPSS
Modeler. See the topic “Model tab ” on page 173 for more information.
4. On the Simulation tab (in the Simulation Builder), specify probability distributions for simulated inputs
and values for fixed inputs. If the active dataset contains historical data for simulated inputs, click Fit
All to automatically determine the distribution that most closely fits the data for each such input as
well as determining correlations between them. For each simulated input that is not being fit to
historical data, you must explicitly specify a distribution by selecting a distribution type and entering
the required parameters.
5. Click Run to run the simulation. By default, the simulation plan, specifying the details of the
simulation, is saved to the location specified on the Save settings.
The following options are available:
• Modify the location for the saved simulation plan.
• Specify known correlations between simulated inputs.
• Automatically compute a contingency table of associations between categorical inputs and use those
associations when data are generated for those inputs.
• Specify sensitivity analysis to investigate the effect of varying the value of a fixed input or varying a
distribution parameter for a simulated input.
• Specify advanced options such as setting the maximum number of cases to generate or requesting tail
sampling.
• Customize output.
• Save the simulated data to a data file.
To design a simulation based on custom equations
1. From the menus choose:
Analyze > Simulation…
2. Click Type in the Equations and click Continue.
3. Click New Equation on the Model tab (in the Simulation Builder) to define each equation in your
predictive model.
4. Click the Simulation tab and specify probability distributions for simulated inputs and values for fixed
inputs. If the active dataset contains historical data for simulated inputs, click Fit All to automatically
determine the distribution that most closely fits the data for each such input as well as determining
correlations between them. For each simulated input that is not being fit to historical data, you must
explicitly specify a distribution by selecting a distribution type and entering the required parameters.
5. Click Run to run the simulation. By default, the simulation plan, specifying the details of the
simulation, is saved to the location specified on the Save settings.
Chapter 1. Core features 171
The following options are available:
• Modify the location for the saved simulation plan.
• Specify known correlations between simulated inputs.
• Automatically compute a contingency table of associations between categorical inputs and use those
associations when data are generated for those inputs.
• Specify sensitivity analysis to investigate the effect of varying the value of a fixed input or varying a
distribution parameter for a simulated input.
• Specify advanced options such as setting the maximum number of cases to generate or requesting tail
sampling.
• Customize output.
• Save the simulated data to a data file.
To design a simulation without a predictive model
1. From the menus, choose:
Analyze > Simulation…
2. Click Create Simulated Data and click Continue.
3. On the Model tab (in the Simulation Builder), select the fields that you want to simulate. You can select
fields from the active dataset or you can define new fields by clicking New.
4. Click the Simulation tab and specify probability distributions for the fields that are to be simulated. If
the active dataset contains historical data for any of those fields, click Fit All to automatically
determine the distribution that most closely fits the data and to determine correlations between the
fields. For fields that are not fit to historical data, you must explicitly specify a distribution by selecting
a distribution type and entering the required parameters.
5. Click Run to run the simulation. By default, the simulated data are saved to the new dataset specified
on the Save settings. In addition, the simulation plan, which specifies the details of the simulation, is
saved to the location specified on the Save settings.
The following options are available:
• Modify the location for the simulated data or the saved simulation plan.
• Specify known correlations between simulated fields.
• Automatically compute a contingency table of associations between categorical fields and use those
associations when data are generated for those fields.
• Specify sensitivity analysis to investigate the effect of varying a distribution parameter for a simulated
field.
• Specify advanced options such as setting the number of cases to generate.
To run a simulation from a simulation plan
Two options are available for running a simulation from a simulation plan. You can use the Run Simulation
dialog, which is primarily designed for running from a simulation plan, or you can use the Simulation
Builder.
To use the Run Simulation dialog:
1. From the menus choose:
Analyze > Simulation…
2. Click Open an Existing Simulation Plan.
3. Make sure the Open in Simulation Builder check box is not checked and click Continue.
4. Open the simulation plan.
5. Click Run in the Run Simulation dialog.
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To run the simulation from the Simulation Builder:
1. From the menus choose:
Analyze > Simulation…
2. Click Open an Existing Simulation Plan.
3. Select the Open in Simulation Builder check box and click Continue.
4. Open the simulation plan.
5. Modify any settings you want to modify on the Simulation tab.
6. Click Run to run the simulation.
Optionally, you can do the following:
• Set up or modify sensitivity analysis to investigate the effect of varying the value of a fixed input or
varying a distribution parameter for a simulated input.
• Refit distributions and correlations for simulated inputs to new data.
• Change the distribution for a simulated input.
• Customize output.
• Save the simulated data to a data file.
Simulation Builder
The Simulation Builder provides the full set of capabilities for designing and running simulations. It allows
you to perform the following general tasks:
• Design and run a simulation for an IBM SPSS model defined in a PMML model file.
• Design and run a simulation for a predictive model defined by a set of custom equations that you
specify.
• Design and run a simulation that generates data in the absence of a predictive model.
• Run a simulation based on an existing simulation plan, optionally modifying any plan settings.
Model tab
For simulations based on a predictive model, the Model tab specifies the source of the model. For
simulations that do not include a predictive model, the Model tab specifies the fields that are to be
simulated.
Select an SPSS model file. This option specifies that the predictive model is defined in an IBM SPSS
model file. An IBM SPSS model file is an XML file or a compressed file archive (.zip file) that contains
model PMML created from IBM SPSS Statistics or IBM SPSS Modeler. Predictive models are created by
procedures, such as Linear Regression and Decision Trees within IBM SPSS Statistics, and can be
exported to a model file. You can use a different model file by clicking Browse and navigating to the file
you want.
PMML models supported by Simulation
• Linear Regression
• Automatic Linear Model
• Generalized Linear Model
• Generalized Linear Mixed Model
• General Linear Model
• Binary Logistic Regression
• Multinomial Logistic Regression
• Ordinal Multnomial Regression
• Cox Regression
Chapter 1. Core features 173
• Tree
• Boosted Tree (C5)
• Discriminant
• Two-step Cluster
• K-Means Cluster
• Neural Net
• Ruleset (Decision List)
Note:
• PMML models that have multiple target fields (variables) or splits are not supported for use in
Simulation.
• Values of string inputs to binary logistic regression models are limited to 8 bytes in the model. If you are
fitting such string inputs to the active dataset, make sure that the values in the data do not exceed 8
bytes in length. Data values that exceed 8 bytes are excluded from the associated categorical
distribution for the input, and are displayed as unmatched in the Unmatched Categories output table.
Type in the equations for the model. This option specifies that the predictive model consists of one or
more custom equations to be created by you. Create equations by clicking New Equation. This opens the
Equation Editor. You can modify existing equations, copy them to use as templates for new equations,
reorder them and delete them.
• The Simulation Builder does not support systems of simultaneous equations or equations that are non-
linear in the target variable.
• Custom equations are evaluated in the order in which they are specified. If the equation for a given
target depends on another target, then the other target must be defined by a preceding equation.
For example, given the set of three equations below, the equation for profit depends on the values of
revenue and expenses, so the equations for revenue and expenses must precede the equation for profit.
revenue = price*volume
expenses = fixed + volume*(unit_cost_materials + unit_cost_labor)
profit = revenue – expenses
Create simulated data without a model. Select this option to simulate data without a predictive model.
Specify the fields that are to be simulated by selecting fields from the active dataset or by clicking New to
define new fields.
Equation Editor
The Equation Editor allows you to create or modify a custom equation for your predictive model.
• The expression for the equation can contain fields from the active dataset or new input fields that you
define in the Equation Editor.
• You can specify properties of the target such as its measurement level, value labels and whether output
is generated for the target.
• You can use targets from previously defined equations as inputs to the current equation, allowing you to
create coupled equations.
• You can attach a descriptive comment to the equation. Comments are displayed along with the
equation on the Model tab.
1. Enter the name of the target. Optionally, click Edit under the Target text box to open the Defined
Inputs dialog, allowing you to change the default properties of the target.
2. To build an expression, either paste components into the Numeric Expression field or type directly in
the Numeric Expression field.
• You can build your expression using fields from the active dataset or you can define new inputs by
clicking the New button. This opens the Define Inputs dialog.
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• You can paste functions by selecting a group from the Function group list and double-clicking the
function in the Functions list (or select the function and click the arrow adjacent to the Function group
list). Enter any parameters indicated by question marks. The function group labeled All provides a
listing of all available functions. A brief description of the currently selected function is displayed in a
reserved area in the dialog box.
• String constants must be enclosed in quotation marks.
• If values contain decimals, a period (.) must be used as the decimal indicator.
Note: Simulation does not support custom equations with string targets.
Defined Inputs
The Defined Inputs dialog allows you to define new inputs and set properties for targets.
• If an input to be used in an equation does not exist in the active dataset, you must define it before it can
be used in the equation.
• If you are simulating data without a predictive model, you must define all simulated inputs that do not
exist in the active dataset.
Name. Specify the name for a target or input.
Target. You can specify the measurement level of a target. The default measurement level is continuous.
You can also specify whether output will be created for this target. For example, for a set of coupled
equations you may only be interested in output from the target for the final equation, so you would
suppress output from the other targets.
Input to be simulated. This specifies that the values of the input will be simulated according to a
specified probability distribution (the probability distribution is specified on the Simulation tab). The
measurement level determines the default set of distributions that are considered when finding the
distribution that most closely fits the data for the input (by clicking Fit or Fit All on the Simulation tab).
For example, if the measurement level is continuous, then the normal distribution (appropriate for
continuous data) would be considered but the binomial distribution would not.
Note: Select a measurement level of String for string inputs. String inputs that are to be simulated are
restricted to the Categorical distribution.
Fixed value input. This specifies that the value of the input is known and will be fixed at the known value.
Fixed inputs can be numeric or string. Specify a value for the fixed input. String values should not be
enclosed in quotation marks.
Value labels. You can specify value labels for targets, simulated inputs and fixed inputs. Value labels are
used in output charts and tables.
Simulation tab
The Simulation tab specifies all properties of the simulation other than the predictive model. You can
perform the following general tasks on the Simulation tab:
• Specify probability distributions for simulated inputs and values for fixed inputs.
• Specify correlations between simulated inputs. For categorical inputs, you can specify that associations
that exist between those inputs in the active dataset are used when data are generated for those inputs.
• Specify advanced options such as tail sampling and criteria for fitting distributions to historical data.
• Customize output.
• Specify where to save the simulation plan and optionally save the simulated data.
Simulated Fields
To run a simulation, each input field must be specified as fixed or simulated. Simulated inputs are those
whose values are uncertain and will be generated by drawing from a specified probability distribution.
When historical data are available for the inputs to be simulated, the distributions that most closely fit the
data can be automatically determined, along with any correlations between those inputs. You can also
Chapter 1. Core features 175
manually specify distributions or correlations if historical data are not available or you require specific
distributions or correlations.
Fixed inputs are those whose values are known and remain constant for each case generated in the
simulation. For example, you have a linear regression model for sales as a function of a number of inputs
including price, and you want to hold the price fixed at the current market price. You would then specify
price as a fixed input.
For simulations based on a predictive model, each predictor in the model is an input field for the
simulation. For simulations that do not include a predictive model, the fields that are specified on the
Model tab are the inputs for the simulation.
Automatically fitting distributions and calculating correlations for simulated inputs. If the active
dataset contains historical data for the inputs that you want to simulate, then you can automatically find
the distributions that most closely fit the data for those inputs as well as determine any correlations
between them. The steps are as follows:
1. Verify that each of the inputs that you want to simulate is matched up with the correct field in the
active dataset. Inputs are listed in the Input column and the Fit to column displays the matched field
in the active dataset. You can match an input to a different field in the active dataset by selecting a
different item from the Fit to dropdown list.
A value of -None- in the Fit to column indicates that the input could not be automatically matched to a
field in the active dataset. By default, inputs are matched to dataset fields on name, measurement
level and type (numeric or string). If the active dataset does not contain historical data for the input,
then manually specify the distribution for the input or specify the input as a fixed input, as described
below.
2. Click Fit All.
The closest fitting distribution and its associated parameters are displayed in the Distribution column
along with a plot of the distribution superimposed on a histogram (or bar chart) of the historical data.
Correlations between simulated inputs are displayed on the Correlations settings. You can examine the fit
results and customize automatic distribution fitting for a particular input by selecting the row for the input
and clicking Fit Details. See the topic “Fit Details ” on page 178 for more information.
You can run automatic distribution fitting for a particular input by selecting the row for the input and
clicking Fit. Correlations for all simulated inputs that match fields in the active dataset are also
automatically calculated.
Note:
• Cases with missing values for any simulated input are excluded from distribution fitting, computation of
correlations, and computation of the optional contingency table (for inputs with a Categorical
distribution). You can optionally specify whether user-missing values of inputs with a Categorical
distribution are treated as valid. By default, they are treated as missing. For more information, see the
topic “Advanced Options ” on page 179.
• For continuous and ordinal inputs, if an acceptable fit cannot be found for any of the tested
distributions, then the Empirical distribution is suggested as the closest fit. For continuous inputs, the
Empirical distribution is the cumulative distribution function of the historical data. For ordinal inputs,
the Empirical distribution is the categorical distribution of the historical data.
Manually specifying distributions. You can manually specify the probability distribution for any
simulated input by selecting the distribution from the Type dropdown list and entering the distribution
parameters in the Parameters grid. Once you have entered the parameters for a distribution, a sample
plot of the distribution, based on the specified parameters, will be displayed adjacent to the Parameters
grid. Following are some notes on particular distributions:
• Categorical. The categorical distribution describes an input field that has a fixed number of values,
referred to as categories. Each category has an associated probability such that the sum of the
probabilities over all categories equals one. To enter a category, click the left-hand column in the
Parameters grid and specify the category value. Enter the probability associated with the category in the
right-hand column.
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Note: Categorical inputs from a PMML model have categories that are determined from the model and
cannot be modified.
• Negative Binomial – Failures. Describes the distribution of the number of failures in a sequence of
trials before a specified number of successes are observed. The parameter thresh is the specified
number of successes and the parameter prob is the probability of success in any given trial.
• Negative Binomial – Trials. Describes the distribution of the number of trials required before a
specified number of successes are observed. The parameter thresh is the specified number of
successes and the parameter prob is the probability of success in any given trial.
• Range. This distribution consists of a set of intervals with a probability assigned to each interval such
that the sum of the probabilities over all intervals equals 1. Values within a given interval are drawn
from a uniform distribution defined on that interval. Intervals are specified by entering a minimum
value, a maximum value and an associated probability.
For example, you believe that the cost of a raw material has a 40% chance of falling in the range of $10
– $15 per unit and a 60% chance of falling in the range of $15 – $20 per unit. You would model the cost
with a Range distribution consisting of the two intervals [10 – 15] and [15 – 20], setting the probability
associated with the first interval to 0.4 and the probability associated with the second interval to 0.6.
The intervals do not have to be contiguous and they can even be overlapping. For example, you could
have specified the intervals $10 – $15 and $20 – $25 or $10 – $15 and $13 – $16.
• Weibull. The parameter c is an optional location parameter, which specifies where the origin of the
distribution is located.
Parameters for the following distributions have the same meaning as in the associated random variable
functions available in the Compute Variable dialog box: Bernoulli, beta, binomial, exponential, gamma,
lognormal, negative binomial (trials and failures), normal, Poisson and uniform.
Specifying fixed inputs. Specify a fixed input by selecting Fixed from the Type dropdown list in the
Distribution column and entering the fixed value. The value can be numeric or string depending on
whether the input is numeric or string. String values should not be enclosed in quotation marks.
Specifying bounds on simulated values. Most distributions support specifying upper and lower bounds
on the simulated values. You can specify a lower bound by entering a value into the Min text box and you
can specify an upper bound by entering a value into the Max text box.
Locking inputs. Locking an input, by selecting the check box in the column with the lock icon, excludes
the input from automatic distribution fitting. This is most useful when you manually specify a distribution
or a fixed value and want to ensure that it will not be affected by automatic distribution fitting. Locking is
also useful if you intend to share your simulation plan with users who will be running it in the Run
Simulation dialog and you want to prevent any changes to certain inputs. In that regard, specifications for
locked inputs cannot be modified in the Run Simulation dialog.
Sensitivity Analysis. Sensitivity analysis allows you to investigate the effect of systematic changes in a
fixed input or in a distribution parameter for a simulated input by generating an independent set of
simulated cases—effectively, a separate simulation—for each specified value. To specify sensitivity
analysis, select a fixed or simulated input and click Sensitivity Analysis. Sensitivity analysis is limited to a
single fixed input or a single distribution parameter for a simulated input. See the topic “Sensitivity
Analysis ” on page 179 for more information.
Fit status icons
Icons in the Fit to column indicate the fit status for each input field.
Table 3. Status icons
Icon Description
No distribution has been specified for the input and the input has not been specified
as fixed. In order to run the simulation, you must either specify a distribution for this
input or define it to be fixed and specify the fixed value.
Chapter 1. Core features 177
Table 3. Status icons (continued)
Icon Description
The input was previously fit to a field that does not exist in the active dataset. No
action is necessary unless you want to refit the distribution for the input to the active
dataset.
The closest fitting distribution has been replaced with an alternate distribution from
the Fit Details dialog.
The input is set to the closest fitting distribution.
The distribution has been manually specified or sensitivity analysis iterations have
been specified for this input.
Fit Details
The Fit Details dialog displays the results of automatic distribution fitting for a particular input.
Distributions are ordered by goodness of fit, with the closest fitting distribution listed first. You can
override the closest fitting distribution by selecting the radio button for the distribution you want in the
Use column. Selecting a radio button in the Use column also displays a plot of the distribution
superimposed on a histogram (or bar chart) of the historical data for that input.
Fit statistics. By default and for continuous fields, the Anderson-Darling test is used for determining
goodness of fit. Alternatively, and for continuous fields only, you can specify the Kolmogorov-Smirnoff
test for goodness of fit by selecting that choice on the Advanced Options settings. For continuous inputs,
results of both tests are shown in the Fit Statistics column (A for Anderson-Darling and K for Kolmogorov-
Smirnoff), with the chosen test used to order the distributions. For ordinal and nominal inputs the chi-
square test is used. The p-values associated with the tests are also shown.
Parameters. The distribution parameters associated with each fitted distribution are displayed in the
Parameters column. Parameters for the following distributions have the same meaning as in the
associated random variable functions available in the Compute Variable dialog box: Bernoulli, beta,
binomial, exponential, gamma, lognormal, negative binomial (trials and failures), normal, Poisson and
uniform. See the topic for more information. For the categorical distribution, the parameter names are the
categories and the parameter values are the associated probabilities.
Refitting with a customized distribution set. By default, the measurement level of the input is used to
determine the set of distributions considered for automatic distribution fitting. For example, continuous
distributions such as lognormal and gamma are considered when fitting a continuous input but discrete
distributions such as Poisson and binomial are not. You can choose a subset of the default distributions
by selecting the distributions in the Refit column. You can also override the default set of distributions by
selecting a different measurement level from the Treat as (Measure) dropdown list and selecting the
distributions in the Refit column. Click Run Refit to refit with the custom distribution set.
Note:
• Cases with missing values for any simulated input are excluded from distribution fitting, computation of
correlations, and computation of the optional contingency table (for inputs with a Categorical
distribution). You can optionally specify whether user-missing values of inputs with a Categorical
distribution are treated as valid. By default, they are treated as missing. For more information, see the
topic “Advanced Options ” on page 179.
• For continuous and ordinal inputs, if an acceptable fit cannot be found for any of the tested
distributions, then the Empirical distribution is suggested as the closest fit. For continuous inputs, the
Empirical distribution is the cumulative distribution function of the historical data. For ordinal inputs,
the Empirical distribution is the categorical distribution of the historical data.
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Sensitivity Analysis
Sensitivity analysis allows you to investigate the effect of varying a fixed input or a distribution parameter
for a simulated input over a specified set of values. An independent set of simulated cases–effectively, a
separate simulation–is generated for each specified value, allowing you to investigate the effect of
varying the input. Each set of simulated cases is referred to as an iteration.
Iterate. This choice allows you to specify the set of values over which the input will be varied.
• If you are varying the value of a distribution parameter, then select the parameter from the drop-down
list. Enter the set of values in the Parameter value by iteration grid. Clicking Continue will add the
specified values to the Parameters grid for the associated input, with an index specifying the iteration
number of the value.
• For the Categorical and Range distributions, the probabilities of the categories or intervals respectively
can be varied but the values of the categories and the endpoints of the intervals cannot be varied. Select
a category or interval from the drop-down list and specify the set of probabilities in the Parameter value
by iteration grid. The probabilities for the other categories or intervals will be automatically adjusted
accordingly.
No iterations. Use this option to cancel iterations for an input. Clicking Continue will remove the
iterations.
Correlations
Input fields to be simulated are often known to be correlated–for example, height and weight.
Correlations between inputs that will be simulated must be accounted for in order to ensure that the
simulated values preserve those correlations.
Recalculate correlations when fitting. This choice specifies that correlations between simulated inputs
are automatically calculated when fitting distributions to the active dataset through the Fit All or Fit
actions on the Simulated Fields settings.
Do not recalculate correlations when fitting. Select this option if you want to manually specify
correlations and prevent them from being overwritten when automatically fitting distributions to the
active dataset. Values that are entered in the Correlations grid must be between -1 and 1. A value of 0
specifies that there is no correlation between the associated pair of inputs.
Reset. This resets all correlations to 0.
Use fitted multiway contingency table for inputs with a categorical distribution. For inputs with a
categorical distribution, you can automatically compute a multiway contingency table from the active
dataset that describes the associations between those inputs. The contingency table is then used when
data are generated for those inputs. If you choose to save the simulation plan, the contingency table is
saved in the plan file and is used when you run the plan.
• Compute contingency table from the active dataset. If you are working with an existing simulation
plan that contains a contingency table, you can recompute the contingency table from the active
dataset. This action overrides the contingency table from the loaded plan file.
• Use contingency table from loaded simulation plan. By default, when you load a simulation plan that
contains a contingency table, the table from the plan is used. You can recompute the contingency table
from the active dataset by selecting Compute contingency table from the active dataset.
Advanced Options
Maximum Number of Cases. This specifies the maximum number of cases of simulated data, and
associated target values, to generate. When sensitivity analysis is specified, this is the maximum number
of cases for each iteration.
Target for stopping criteria. If your predictive model contains more than one target, then you can select
the target to which stopping criteria are applied.
Stopping criteria. These choices specify criteria for stopping the simulation, potentially before the
maximum number of allowable cases has been generated.
Chapter 1. Core features 179
• Continue until maximum is reached. This specifies that simulated cases will be generated until the
maximum number of cases is reached.
• Stop when the tails have been sampled. Use this option when you want to ensure that one of the tails
of a specified target distribution has been adequately sampled. Simulated cases will be generated until
the specified tail sampling is complete or the maximum number of cases is reached. If your predictive
model contains multiple targets then select the target, to which this criteria will be applied, from the
Target for stopping criteria dropdown list.
Type. You can define the boundary of the tail region by specifying a value of the target such as
10,000,000 or a percentile such as the 99th percentile. If you choose Value in the Type dropdown list,
then enter the value of the boundary in the Value text box and use the Side dropdown list to specify
whether this is the boundary of the Left tail region or the Right tail region. If you choose Percentile in the
Type dropdown list, then enter a value in the Percentile text box.
Frequency. Specify the number of values of the target that must lie in the tail region in order to ensure
that the tail has been adequately sampled. Generation of cases will stop when this number has been
reached.
• Stop when the confidence interval of the mean is within the specified threshold. Use this option
when you want to ensure that the mean of a given target is known with a specified degree of accuracy.
Simulated cases will be generated until the specified degree of accuracy has been achieved or the
maximum number of cases is reached. To use this option, you specify a confidence level and a
threshold. Simulated cases will be generated until the confidence interval associated the specified level
is within the threshold. For example, you can use this option to specify that cases are generated until
the confidence interval of the mean at the 95% confidence level is within 5% of the mean value. If your
predictive model contains multiple targets then select the target, to which this criteria will be applied,
from the Target for stopping criteria dropdown list.
Threshold Type. You can specify the threshold as a numeric value or as a percent of the mean. If you
choose Value in the Threshold Type dropdown list, then enter the threshold in the Threshold as Value
text box. If you choose Percent in the Threshold Type dropdown list, then enter a value in the
Threshold as Percent text box.
Number of cases to sample. This specifies the number of cases to use when automatically fitting
distributions for simulated inputs to the active dataset. If your dataset is very large you might want to
consider limiting the number of cases used for distribution fitting. If you select Limit to N cases, the first
N cases will be used.
Goodness of fit criteria (Continuous). For continuous inputs, you can use the Anderson-Darling test or
the Kolmogorov-Smirnoff test of goodness of fit to rank distributions when fitting distributions for
simulated inputs to the active dataset. The Anderson-Darling test is selected by default and is especially
recommended when you want to ensure the best possible fit in the tail regions.
Empirical Distribution. For continuous inputs, the Empirical distribution is the cumulative distribution
function of the historical data. You can specify the number of bins used for calculating the Empirical
distribution for continuous inputs. The default is 100 and the maximum is 1000.
Replicate results. Setting a random seed allows you to replicate your simulation. Specify an integer or
click Generate, which will create a pseudo-random integer between 1 and 2147483647, inclusive. The
default is 629111597.
Note: For a particular random seed, results are replicated unless the number of threads is changed. On a
particular computer, the number of threads is constant unless you change it by running SET THREADS
command syntax. The number of threads might change if you run the simulation on a different computer
because an internal algorithm is used to determine the number of threads for each computer.
User-missing values for inputs with a Categorical distribution. These controls specify whether user-
missing values of inputs with a Categorical distribution are treated as valid. System-missing values and
user-missing values for all other types of inputs are always treated as invalid. All inputs must have valid
values for a case to be included in distribution fitting, computation of correlations, and computation of the
optional contingency table.
180 IBM SPSS Statistics Base V27
Density Functions
These settings allow you to customize output for probability density functions and cumulative distribution
functions for continuous targets, as well as bar charts of predicted values for categorical targets.
Probability Density Function (PDF). The probability density function displays the distribution of target
values. For continuous targets, it allows you to determine the probability that the target is within a given
region. For categorical targets (targets with a measurement level of nominal or ordinal), a bar chart is
generated that displays the percentage of cases that fall in each category of the target. Additional options
for categorical targets of PMML models are available with the Category values to report setting described
below.
For Two-Step cluster models and K-Means cluster models, a bar chart of cluster membership is
produced.
Cumulative Distribution Function (CDF). The cumulative distribution function displays the probability
that the value of the target is less than or equal to a specified value. It is only available for continuous
targets.
Slider positions. You can specify the initial positions of the moveable reference lines on PDF and CDF
charts. Values that are specified for the lower and upper lines refer to positions along the horizontal axis,
not percentiles. You can remove the lower line by selecting -Infinity or you can remove the upper line by
selecting Infinity. By default, the lines are positioned at the 5-th and 95-th percentiles. When multiple
distribution functions are displayed on a single chart (because of multiple targets or results from
sensitivity analysis iterations), the default refers to the distribution for the first iteration or first target.
Reference Lines (Continuous). You can request various vertical reference lines to be added to probability
density functions and cumulative distribution functions for continuous targets.
• Sigmas. You can add reference lines at plus and minus a specified number of standard deviations from
the mean of a target.
• Percentiles. You can add reference lines at one or two percentile values of the distribution of a target
by entering values into the Bottom and Top text boxes. For example, a value of 95 in the Top text box
represents the 95th percentile, which is the value below which 95% of the observations fall. Likewise, a
value of 5 in the Bottom text box represents the 5th percentile, which is the value below which 5% of
the observations fall.
• Custom reference lines. You can add reference lines at specified values of the target.
Note: When multiple distribution functions are displayed on a single chart (because of multiple targets or
results from sensitivity analysis iterations), reference lines are only applied to the distribution for the first
iteration or first target. You can add reference lines to the other distributions from the Chart Options
dialog, which is accessed from the PDF or CDF chart.
Overlay results from separate continuous targets. In the case of multiple continuous targets, this
specifies whether distribution functions for all such targets are displayed on a single chart, with one chart
for probability density functions and another for cumulative distribution functions. When this option is not
selected, results for each target will be displayed on a separate chart.
Category values to report. For PMML models with categorical targets, the result of the model is a set of
predicted probabilities, one for each category, that the target value falls in each category. The category
with the highest probability is taken to be the predicted category and used in generating the bar chart
described for the Probability Density Function setting above. Selecting Predicted category will generate
the bar chart. Selecting Predicted probabilities will generate histograms of the distribution of predicted
probabilities for each of the categories of the target.
Grouping for sensitivity analysis. Simulations that include sensitivity analysis generate an independent
set of predicted target values for each iteration defined by the analysis (one iteration for each value of the
input that is being varied). When iterations are present, the bar chart of the predicted category for a
categorical target is displayed as a clustered bar chart that includes the results for all iterations. You can
choose to group categories together or you can group iterations together.
Chapter 1. Core features 181
Output
Tornado charts. Tornado charts are bar charts that display relationships between targets and simulated
inputs using a variety of metrics.
• Correlation of target with input. This option creates a tornado chart of the correlation coefficients
between a given target and each of its simulated inputs. This type of tornado chart does not support
targets with a nominal or ordinal measurement level or simulated inputs with a categorical distribution.
• Contribution to variance. This option creates a tornado chart that displays the contribution to the
variance of a target from each of its simulated inputs, allowing you to assess the degree to which each
input contributes to the overall uncertainty in the target. This type of tornado chart does not support
targets with ordinal or nominal measurement levels, or simulated inputs with any of the following
distributions: categorical, Bernoulli, binomial, Poisson, or negative binomial.
• Sensitivity of target to change. This option creates a tornado chart that displays the effect on the
target of modulating each simulated input by plus or minus a specified number of standard deviations of
the distribution associated with the input. This type of tornado chart does not support targets with
ordinal or nominal measurement levels, or simulated inputs with any of the following distributions:
categorical, Bernoulli, binomial, Poisson, or negative binomial.
Box plots of target distributions. Box plots are available for continuous targets. Select Overlay results
from separate targets if your predictive model has multiple continuous targets and you want to display
the box plots for all targets on a single chart.
Scatterplots of targets versus inputs. Scatterplots of targets versus simulated inputs are available for
both continuous and categorical targets and include scatters of the target with both continuous and
categorical inputs. Scatters involving a categorical target or a categorical input are displayed as a heat
map.
Create a table of percentile values. For continuous targets, you can obtain a table of specified
percentiles of the target distributions. Quartiles (the 25th, 50th, and 75th percentiles) divide the
observations into four groups of equal size. If you want an equal number of groups other than four, select
Intervals and specify the number. Select Custom percentiles to specify individual percentiles–for
example, the 99th percentile.
Descriptive statistics of target distributions. This option creates tables of descriptive statistics for
continuous and categorical targets as well as for continuous inputs. For continuous targets the table
includes the mean, standard deviation, median, minimum and maximum, confidence interval of the mean
at the specified level, and the 5th and 95th percentiles of the target distribution. For categorical targets
the table includes the percentage of cases that fall in each category of the target. For categorical targets
of PMML models, the table also includes the mean probability of each category of the target. For
continuous inputs, the table includes the mean, standard deviation, minimum and maximum.
Correlations and contingency table for inputs. This option displays a table of correlation coefficients
between simulated inputs. When inputs with categorical distributions are generated from a contingency
table, the contingency table of the data that are generated for those inputs is also displayed.
Simulated inputs to include in the output. By default, all simulated inputs are included in the output.
You can exclude selected simulated inputs from output. This will exclude them from tornado charts,
scatterplots and tabular output.
Limit ranges for continuous targets. You can specify the range of valid values for one or more continuous
targets. Values outside of the specified range are excluded from all output and analyses associated with
the targets. To set a lower limit, select Lower in the Limit column and enter a value in the Minimum
column. To set an upper limit, select Upper in the Limit column and enter a value in the Maximum column.
To set both a lower and an upper limit, select Both in the Limit column and enter values in the Minimum
and Maximum columns.
Display Formats. You can set the format used when displaying values of targets and inputs (both fixed
inputs and simulated inputs).
182 IBM SPSS Statistics Base V27
Save
Save the plan for this simulation. You can save the current specifications for your simulation to a
simulation plan file. Simulation plan files have the extension .splan. You can re-open the plan in the
Simulation Builder, optionally make modifications and run the simulation. You can share the simulation
plan with other users, who can then run it in the Run Simulation dialog. Simulation plans include all
specifications except the following: settings for Density Functions; Output settings for charts and tables;
Advanced Options settings for Fitting, Empirical Distribution and Random Seed.
Save the simulated data as a new data file. You can save simulated inputs, fixed inputs and predicted
target values to an SPSS Statistics data file, a new dataset in the current session, or an Excel file. Each
case (or row) of the data file consists of the predicted values of the targets along with the simulated
inputs and fixed inputs that generate the target values. When sensitivity analysis is specified, each
iteration gives rise to a contiguous set of cases that are labeled with the iteration number.
Run Simulation dialog
The Run Simulation dialog is designed for users who have a simulation plan and primarily want to run the
simulation. It also provides the features you need to run the simulation under different conditions. It
allows you to perform the following general tasks:
• Set up or modify sensitivity analysis to investigate the effect of varying the value of a fixed input or
varying a distribution parameter for a simulated input.
• Refit probability distributions for uncertain inputs (and correlations between those inputs) to new data.
• Modify the distribution for a simulated input.
• Customize output.
• Run the simulation.
Simulation tab
The Simulation tab allows you to specify sensitivity analysis, refit probability distributions for simulated
inputs and correlations between simulated inputs to new data, and modify the probability distribution
associated with a simulated input.
The Simulated inputs grid contains an entry for each input field that is defined in the simulation plan. Each
entry displays the name of the input and the probability distribution type associated with the input, along
with a sample plot of the associated distribution curve. Each input also has an associated status icon (a
colored circle with a check mark) that is useful when you are refitting distributions to new data. In
addition, inputs may include a lock icon which indicates that the input is locked and cannot be modified or
refit to new data in the Run Simulation dialog. To modify a locked input you will need to open the
simulation plan in the Simulation Builder.
Each input is either simulated or fixed. Simulated inputs are those whose values are uncertain and will be
generated by drawing from a specified probability distribution. Fixed inputs are those whose values are
known and remain constant for each case generated in the simulation. To work with a particular input,
select the entry for the input in the Simulated inputs grid.
Specifying sensitivity analysis
Sensitivity analysis allows you to investigate the effect of systematic changes in a fixed input or in a
distribution parameter for a simulated input by generating an independent set of simulated cases—
effectively, a separate simulation—for each specified value. To specify sensitivity analysis, select a fixed
or simulated input and click Sensitivity Analysis. Sensitivity analysis is limited to a single fixed input or a
single distribution parameter for a simulated input. See the topic “Sensitivity Analysis ” on page 179 for
more information.
Refitting distributions to new data
To automatically refit probability distributions for simulated inputs (and correlations between simulated
inputs) to data in the active dataset:
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1. Verify that each of the model inputs is matched up with the correct field in the active dataset. Each
simulated input is fit to the field in the active dataset specified in the Field dropdown list associated
with that input. You can easily identify inputs that are unmatched by looking for inputs with a status
icon that includes a check mark with a question mark, as shown below.
2. Modify any necessary field matching by selecting Fit to a field in the dataset and selecting the field
from the list.
3. Click Fit All.
For each input that was fit, the distribution that most closely fits the data is displayed along with a plot of
the distribution superimposed on a histogram (or bar chart) of the historical data. If an acceptable fit
cannot be found then the Empirical distribution is used. For inputs that are fit to the Empirical distribution,
you will only see a histogram of the historical data because the Empirical distribution is in fact
represented by that histogram.
Note: For a complete list of status icons, see the topic “Simulated Fields” on page 175.
Modifying probability distributions
You can modify the probability distribution for a simulated input and optionally change a simulated input
to a fixed input or vice versa.
1. Select the input and select Manually set the distribution.
2. Select the distribution type and specify the distribution parameters. To change a simulated input to a
fixed input, select Fixed in the Type dropdown list.
Once you have entered the parameters for a distribution, the sample plot of the distribution (displayed in
the entry for the input) will be updated to reflect your changes. For more information on manually
specifying probability distributions, see the topic “Simulated Fields” on page 175.
Include user-missing values of categorical inputs when fitting. This specifies whether user-missing
values of inputs with a Categorical distribution are treated as valid when you are refitting to data in the
active dataset. System-missing values and user-missing values for all other types of inputs are always
treated as invalid. All inputs must have valid values for a case to be included in distribution fitting and
computation of correlations.
Output tab
The Output tab allows you to customize the output generated by the simulation.
Density Functions. Density functions are the primary means of probing the set of outcomes from your
simulation.
• Probability Density Function. The probability density function displays the distribution of target values,
allowing you to determine the probability that the target is within a given region. For targets with a fixed
set outcomes–such as “poor service”, “fair service”, “good service” and “excellent service”–a bar chart
is generated that displays the percentage of cases that fall in each category of the target.
• Cumulative Distribution Function. The cumulative distribution function displays the probability that
the value of the target is less than or equal to a specified value.
Tornado Charts. Tornado charts are bar charts that display relationships between targets and simulated
inputs using a variety of metrics.
• Correlation of target with input. This option creates a tornado chart of the correlation coefficients
between a given target and each of its simulated inputs.
• Contribution to variance. This option creates a tornado chart that displays the contribution to the
variance of a target from each of its simulated inputs, allowing you to assess the degree to which each
input contributes to the overall uncertainty in the target.
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• Sensitivity of target to change. This option creates a tornado chart that displays the effect on the
target of modulating each simulated input by plus or minus one standard deviation of the distribution
associated with the input.
Scatterplots of targets versus inputs. This option generates scatterplots of targets versus simulated
inputs.
Box plots of target distributions. This option generates box plots of the target distributions.
Quartiles table. This option generates a table of the quartiles of the target distributions. The quartiles of
a distribution are the 25th, 50th, and 75th percentiles of the distribution, and divide the observations into
four groups of equal size.
Correlations and contingency table for inputs. This option displays a table of correlation coefficients
between simulated inputs. A contingency table of associations between inputs with a categorical
distribution is displayed when the simulation plan specifies generating categorical data from a
contingency table.
Overlay results from separate targets. If the predictive model you are simulating contains multiple
targets, you can specify whether results from separate targets are displayed on a single chart. This setting
applies to charts for probability density functions, cumulative distribution functions and box plots. For
example, if you select this option then the probability density functions for all targets will be displayed on
a single chart.
Save the plan for this simulation. You can save any modifications to your simulation to a simulation plan
file. Simulation plan files have the extension .splan. You can re-open the plan in the Run Simulation dialog
or in the Simulation Builder. Simulation plans include all specifications except output settings.
Save the simulated data as a new data file. You can save simulated inputs, fixed inputs and predicted
target values to an SPSS Statistics data file, a new dataset in the current session, or an Excel file. Each
case (or row) of the data file consists of the predicted values of the targets along with the simulated
inputs and fixed inputs that generate the target values. When sensitivity analysis is specified, each
iteration gives rise to a contiguous set of cases that are labeled with the iteration number.
If you require more customization of output than is available here, then consider running your simulation
from the Simulation Builder. See the topic “To run a simulation from a simulation plan” on page 172 for
more information.
Working with chart output from Simulation
A number of the charts generated from a simulation have interactive features that allow you to customize
the display. Interactive features are available by activating (double-clicking) the chart object in the Output
Viewer. All simulation charts are graphboard visualizations.
Probability density function charts for continuous targets. This chart has two sliding vertical reference
lines that divide the chart into separate regions. The table below the chart displays the probability that
the target is in each of the regions. If multiple density functions are displayed on the same chart, the table
has a separate row for the probabilities associated with each density function. Each of the reference lines
has a slider (inverted triangle) that allows you to easily move the line. A number of additional features are
available by clicking the Chart Options button on the chart. In particular, you can explicitly set the
positions of the sliders, add fixed reference lines and change the chart view from a continuous curve to a
histogram or vice versa. See the topic “Chart Options ” on page 186 for more information.
Cumulative distribution function charts for continuous targets. This chart has the same two moveable
vertical reference lines and associated table described for the probability density function chart above. It
also provides access to the Chart Options dialog, which allows you to explicitly set the positions of the
sliders, add fixed reference lines and specify whether the cumulative distribution function is displayed as
an increasing function (the default) or a decreasing function. See the topic “Chart Options ” on page 186
for more information.
Bar charts for categorical targets with sensitivity analysis iterations. For categorical targets with
sensitivity analysis iterations, results for the predicted target category are displayed as a clustered bar
chart that includes the results for all iterations. The chart includes a dropdown list that allows you to
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cluster on category or on iteration. For Two-Step cluster models and K-Means cluster models, you can
choose to cluster on cluster number or iteration.
Box plots for multiple targets with sensitivity analysis iterations. For predictive models with multiple
continuous targets and sensitivity analysis iterations, choosing to display box plots for all targets on a
single chart produces a clustered box plot. The chart includes a dropdown list that allows you to cluster
on target or on iteration.
Chart Options
The Chart Options dialog allows you to customize the display of activated charts of probability density
functions and cumulative distribution functions generated from a simulation.
View. The View dropdown list only applies to the probability density function chart. It allows you to
toggle the chart view from a continuous curve to a histogram. This feature is not available when multiple
density functions are displayed on the same chart. In that case, the density functions can only be viewed
as continuous curves.
Order. The Order dropdown list only applies to the cumulative distribution function chart. It specifies
whether the cumulative distribution function is displayed as an ascending function (the default) or a
descending function. When displayed as a descending function, the value of the function at a given point
on the horizontal axis is the probability that the target lies to the right of that point.
Slider positions. You can explicitly set the positions of the sliding reference lines by entering values in
the Upper and Lower text boxes. You can remove the left-hand line by selecting -Infinity, effectively
setting the position to negative infinity, and you can remove the right-hand line by selecting Infinity,
effectively setting its position to infinity.
Reference lines. You can add various fixed vertical reference lines to probability density functions and
cumulative distribution functions. When multiple functions are displayed on a single chart (because of
multiple targets or results from sensitivity analysis iterations), you can specify the particular functions to
which the lines are applied.
• Sigmas. You can add reference lines at plus and minus a specified number of standard deviations from
the mean of a target.
• Percentiles. You can add reference lines at one or two percentile values of the distribution of a target
by entering values into the Bottom and Top text boxes. For example, a value of 95 in the Top text box
represents the 95th percentile, which is the value below which 95% of the observations fall. Likewise, a
value of 5 in the Bottom text box represents the 5th percentile, which is the value below which 5% of
the observations fall.
• Custom positions. You can add reference lines at specified values along the horizontal axis.
Label reference lines. This option controls whether labels are applied to the selected reference lines.
Reference lines are removed by clearing the associated choice in the Chart Options dialog and clicking
Continue.
Geospatial Modeling
Geospatial modeling techniques are designed to discover patterns in data that include a geospatial (map)
component. The Geospatial Modeling Wizard provides methods for analyzing geospatial data with and
without a time component.
Find associations based on event and geospatial data (Geospatial Associations Rules)
Using geospatial association rules, you can find patterns in data based on both the spatial and non-
spatial properties. For example, you might identify patterns in crime data by location and
demographic attributes. From these patterns, you can build rules that predict where certain types of
crimes are likely to occur.
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Make predictions using time series and geospatial data (Spatio-Temporal Prediction)
Spatial temporal prediction uses data that contains location data, input fields for prediction
(predictors), one or more time fields, and a target field. Each location has numerous rows in the data
that represent the values of each predictor and the target at each time interval.
Using the Geospatial Modeling Wizard
1. From the menus choose:
Analyze > Spatial and Temporal Modeling > Spatial Modeling
2. Follow the steps in the wizard.
Examples
Detailed examples are available in the help system.
• Geospatial association rules: Help > Topics > Case Studies > Statistics Base > Spatial association
rules
• Spatial temporal prediction: Help > Topics > Case Studies > Statistics Base > Spatial temporal
prediction
Selecting Maps
Geospatial modeling can use one or more map data sources. Map data sources contain information that
defines geographic areas and other geographic features, such as roads or rivers. Many map sources also
contain demographic or other descriptive data and event data such as crime reports or unemployment
rates. You can use a previously defined map specification file or define map specifications here and save
those specifications for subsequent use.
Load a Map Specification
Loads a previously defined map specification (.mplan) file. Map data sources that you define here can
be saved in a map specification file. For spatial temporal prediction, if you select a map specification
file that identifies more than one map, you are prompted to select one map from the file.
Add Map File
Add an ESRI shape (.shp) file or .zip archive that contains an ESRI shape file.
• There must be a corresponding .dbf file in the same location as the .shp file, and that file must have
the same root name as the .shp file.
• If the file is a .zip archive, the .shp and .dbf files must have the same root name as the .zip archive.
• If there is no corresponding projection (.prj) file, you are prompted to select a projection system.
Relationship
For geospatial association rules, this column defines how events relate to the features in the map.
This setting is not available for spatial temporal prediction.
Move up, Move down
The layer order of the map elements is determined by the order in which they appear in the list. The
first map in the list is the bottom layer.
Selecting a Map
For spatial temporal prediction, if you select a map specification file that identifies more than one map,
your are prompted to select one map from the file. Spatial temporal prediction does not support multiple
maps.
Geospatial Relationship
For geospatial association rules, the Geospatial Relationship dialog defines how events relate to the
features in the map.
• This setting applies only to geospatial association rules.
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• This setting only affects data sources associated with maps that are specified as context data on the
step for selecting data sources.
Relationship
Close
The event occurs close to a specified point or area on the map.
Within
The event occurs within a specified area on the map.
Contains
The event area contains a map context object.
Intersects
Locations where lines or regions from the different maps intersect each other.
Cross
For multiple maps, locations where lines (for roads, rivers, railroads) from different lines cross
each other.
North of, Sourth of, East of, West of
The event occurs within an area north, south, east, or west of a specified point on the map.
Set Coordinate System
If there is no projection (.prj) file with the map or you define two fields from a data source as a set of
coordinates, you must set the coordinate system.
Default geographic (longitude and latitude)
The coordinate system is longitude and latitude.
Simple Cartesian (X and Y)
The coordinate system is simple X and Y coordinates.
Use a Well Known ID (WKID)
“Well known ID” for common projections.
Use a Coordinate System Name
The coordinate system is based on the named projection. The name is enclosed in parentheses.
Setting the Projection
If the projection system cannot be determined from the information provided with the map, you need to
specify the projection system. The most common cause of this condition is the absence of a projection
(.prj) file associated with the map or a projection file that cannot be used.
• A city, region or country (Mercator)
• A large country, several countries, or continents (Winkel Tripel)
• An area very close to the equator (Mercator)
• An area close to one of the poles (Stereographic)
The Mercator projection is a common projection used in many maps. This projection treats the globe as
cylinder that is rolled out onto a flat surface. The Mercator projection distorts the size and shape of large
objects. This distortion increases as you move farther from the equator and closer to the poles. The
Winkel Tripel and Stereographic projections make adjustments for the fact that a map represents a
portion of a three-dimensional sphere displayed in two dimensions.
Projection and Coordinate System
If you select more than one map and the maps have different projection and coordinate systems, you
must select the map with the projection system that you want to use. That projection system will be used
for all maps when they are combined together in the output.
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Data Sources
A data source can be a dBase file that is provided with the shape file, an IBM SPSS Statistics data file, or
an open dataset in the current session.
Context Data. A context data identifies features on the map. A context data can also contain fields that
can be used as inputs for the model. To use a context dBase (.dbf) file that is associated with a map shape
(.shp) file, the context dBase file must be in the same location as the shape file and must have the same
root name. For example, if the shape file is geodata.shp, the dBase file must be named geodata.dbf
Event Data. Event data contains information on events that occur, such as crimes or accidents. This
option is available only for geospatial association rules.
Point Density. Time interval and coordinate data for kernel density estimates. This option is available
only for spatial temporal prediction.
Add. Opens a dialog for adding data sources. A data source can be a dBase file that is provided with the
shape file, an IBM SPSS Statistics data file, or an open dataset in the current session.
Associate. Opens a dialog for specifying the identifiers (coordinates or keys) used to associate data with
maps. Each data source must contain one or more identifiers that associate the data with the map. dBase
files that come with a shape file typically contain a field that is automatically used as the default identifier.
For other data sources, you must specify the fields that are used as identifiers.
Validate Key. Opens a dialog to validate key matching between the map and the data source.
Geospatial association rules
• At least one data source must be an event data source.
• All event data sources must use the same form of map association identifiers: coordinates or key
values.
• If the event data sources are associated with the maps with key values, all event sources must use the
same map feature type (for example, polygons, points, lines).
Spatial temporal prediction
• There must be a context data source.
• If there is only one data source (a data file with no associated map), it must include coordinate values.
• If you have two data sources, one data source must be context data, and the other data source must be
point density data.
• You cannot include more than two data sources.
Add a Data Source
A data source can be a dBase file that is provided with the shape file and context file, an IBM SPSS
Statistics data file, or an open dataset in the current session.
You can add the same data source multiple times if you want to use a different spatial association with
each one.
Data and Map Association
Each data source must contain one or more identifiers that associate the data with the map.
Coordinates
The data source contains fields that represent Cartesian coordinates, select the fields that represent
that X and Y coordinates. For geospatial association rules, there can also be a Z coordinate.
Key values
Key values in fields in the data source correspond to selected map keys. For example, a map of
regions might have a name identifier (map key) labeling each region. That identifier corresponds with
a field in the data that also contains the names of the regions (data key). Fields are matched to map
keys based on the order they are displayed in the two lists.
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Validate Keys
The Validate Keys dialog provides a summary of record matching between the map and the data source,
based on the selected identifier keys. If there are unmatched data key values, you can manually match
them to map key values.
Geospatial Association Rules
For geospatial association rules, after defining maps and data sources, the remaining steps in the wizard
are:
• If there are multiple event data sources, define how event data sources are merged.
• Select fields to use as conditions and predictions in the analysis.
Optionally, you can also:
• Select different output options.
• Save a scoring model file.
• Create new fields for predicted values and rules in the data sources used in the model.
• Customize settings for building association rules.
• Customize binning and aggregation settings.
Define Event Data Fields
For geospatial association rules, if there is more than one event data source, the event data sources are
merged.
• By default, only fields that are common to all event data sources are included.
• You can display a list of common fields, fields for a specific data source, or fields from all data sources
and select the fields that you want to include.
• For common fields, the Type and Measurement must be the same for all data sources. If there are
conflicts, you can specify the type and measurement level to use for each common field.
Select Fields
The list of available fields includes fields from the event data sources and fields from the context data
sources.
• You can control the list of displayed fields by selecting a data source from the Data Sources list.
• You must select at least two fields. At least one must be a condition, and at least one must be a
prediction. There are a number of ways to meet this requirement, including selecting two fields for the
Both (Condition and Prediction) list.
• Association rules predict values of the prediction fields that are based on values of the condition fields.
For example, in the rule “If x=1 and y=2, then z=3”, the values of x and y are conditions, and the value of
z is the prediction.
Output
Rules Tables
Each rules table displays the top rules and values for confidence, rule support, lift, condition support,
and deployability. Each table is sorted by values of the selected criterion. You can display all rules or
the top Number of rules, based on the selected criterion.
Sortable Word Cloud
A list of the top rules, based on the values of the selected criterion. The size of the text indicates the
relative importance of the rule. The interactive output object contains the top rules for confidence,
rule support, lift, condition support, and deployability. The selected criterion determines which list of
rules is displayed by default. You can select a different criterion interactively in the output. Max rules
to display determines the number of rules that are displayed in the output.
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Map
Interactive bar chart and map of the top rules, based on the selected criterion. Each interactive output
object contains the top rules for confidence, rule support, lift, condition support, and deployability.
The selected criterion determines which list of rules is displayed by default. You can select a different
criterion interactively in the output. Max rules to display determines the number of rules that are
displayed in the output.
Model Information Tables
Field Transformations.
Describes the transformations that are applied to fields used in the analysis.
Record Summary.
Number and percentage of included and excluded records.
Rule Statistics.
Summary statistics for condition support, confidence, rule support, lift, and deployability. The
statistics include mean, minimum, maximum, and standard deviation.
Most Frequent Items.
Items that occur most frequently. An item is included in a condition or a prediction in a rule. For
example, age < 18 or gender=female.
Most Frequent Fields.
Fields that occur most frequently in the rules.
Excluded Inputs.
Fields that are excluded from the analysis and the reason each field was excluded.
Criterion for Rules Tables, Word Cloud, and Maps
Confidence.
The percentage of correct rule predictions.
Rule Support.
The percentage of cases for which the rule is true. For example, if the rule is "If x=1 and y=2, then
z=3," rule support is the actual percentage of cases in the data for which x=1, y=2, and z=3.
Lift.
Lift is a measure of how much the rule improves prediction compared to random chance. It is the ratio
of correct predictions to the overall occurrence of the predicted value. The value must be greater than
1. For example, if the predicted value occurs 20% of the time and the confidence in the prediction is
80%, then the lift value is 4.
Condition Support.
The percentage of cases for which the rule condition exists. For example, if the rule is "If x=1 and y=2,
then z=3," condition support is the proportion of cases in the data for which x=1 and y=2.
Deployability.
The percentage of incorrect predictions when the conditions are true. Deployability is equal to (1-
confidence) multiplied by condition support or condition support minus rule support.
Save
Save the map and context data as a map specification
Save the map specifications to an external file (.mplan). You can load this map specification file into
the wizard for subsequent analyses. You can also use the map specification file with the SPATIAL
ASSOCIATION RULES command.
Copy any map and data files into the specification
Data from map shape files, external data files, and datasets used in the map specification are
saved in the map specification file.
Scoring
Saves best rule values, confidence values for the rules, and numeric ID values for the rules as new
fields in the specified data source.
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Data Source to Score
The data source or sources where the new fields are created. If the data source is not open in the
current session, it is opened in the current session. You must explicitly save the modified file to
save the new fields.
Target Values
Create new fields for the selected target (prediction) fields.
• Two new fields are created for each target field: predicted value and confidence value.
• For continuous (scale) target fields, the predicted value is a string that describes a value range.
A value of the form "(value1, value2]" means "greater than value1 and less than or equal to
value2."
Number of best rules
Create new fields for the number of best rules specified. Three new fields are created for each
rule: rule value, confidence value, and a numeric ID value for the rule.
Name Prefix
Prefix to use for the new field names.
Rule Building
Rule building parameters set the criteria for the generated association rules.
Items Per Rule
Number of field values that can be included in rule conditions and predictions. The total number of
items cannot exceed 10. For example, in the rule "If x=1 and y=2, then z=3", there are two condition
items and one prediction item.
Maximum predictions.
Maximum number of field values that can occur in the predictions for a rule.
Maximum conditions.
Maximum number of field values that can occur in the conditions for a rule.
Exclude Pair
Excludes the specified pairs of fields from being included in the same rule.
Rule Criteria
Confidence.
Minimum confidence a rule must have to be included in the output. Confidence is the percentage
of correct predictions.
Rule Support.
Minimum rule support a rule must have to be included in the output. The value represents the
percentage of cases for which the rule is true in the observed data. For example, if the rule is "If
x=1 and y=2, then z=3," rule support is the actual percentage of cases in the data for which x=1,
y=2, and z=3.
Condition Support.
Minimum condition support a rule must have to be included in the output. The value represents
the percentage of cases for which the condition exists. For example, if the rule is "If x=1 and y=2,
then z=3," condition support is the percentage of cases in the data for which x=1 and y=2.
Lift.
Minimum lift a rule must have to be included in the output. Lift is a measure of how much the rule
improves prediction over random chance. It is the ratio of correct predictions to the overall
occurrence of the predicted value. For example, if the predicted value occurs 20% of the time and
the confidence in the prediction is 80%, then the lift value is 4.
Treat as same
Identifies pairs of fields that should be treated as the same field.
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Binning and Aggregation
• Aggregation is necessary when there are more records in the data than there are features in the map.
For example, you have data records for individual counties but you have a map of states.
• You can specify the aggregate summary measure method for continuous and ordinal fields. Nominal
fields are aggregated based on the modal value.
Continuous
For continuous (scale) fields, the summary measure can be mean, median, or sum.
Ordinal
For ordinal fields, the summary measure can be median, mode, highest, or lowest.
Number of bins
Sets the maximum number of bins for continuous (scale) fields. Continuous fields are always grouped
or "binned" into ranges of values. For example: less than or equal to 5, greater than 5 and less than or
equal to 10, or greater than 10.
Aggregate the map
Apply aggregation to both data and maps.
Custom settings for specific fields
You can override the default summary measure and number of bins for specific fields.
• Click the icon to open the Field Chooser dialog and select a field to add to the list.
• In the Aggregation column, select a summary measure.
• For continuous fields, click the button in the Bins column to specify a custom number of bins for the
field in the Bins dialog.
Spatial Temporal Prediction
For spatial temporal prediction, after defining maps and data sources, the remaining steps in the wizard
are:
• Specify the target field, time fields, and optional predictors.
• Define time intervals or cyclic periods for time fields.
Optionally, you can also:
• Select different output options.
• Customize model building parameters.
• Customize aggregation settings.
• Save predicted values to a dataset in the current session or to an IBM SPSS Statistics format data file.
Select Fields
The list of available fields includes fields from the selected data sources. You can control the list of
displayed fields by selecting a data source from the Data Sources list.
Target
A target field is required. The target is the field for which values are predicted.
• The target field must be a continuous (scale), numeric field.
• If there are two data sources, the target is kernel density estimates, and "Density" is displayed as
the target name. You cannot change this selection.
Predictors
One or more predictor fields can be specified. This setting is optional.
Time Fields
You must select one or more fields that represent time periods or select Cyclic Periods.
• If there are two data sources, you must select time fields from both data sources. Both time fields
must represent the same interval.
Chapter 1. Core features 193
• For cyclic periods, you must specify the fields that define periodicity cycles in the Time Intervals
panel of the wizard.
Time Intervals
The options in this panel are based on the choice of Time Fields or Cyclic period in the step for selecting
fields.
Time fields
Selected Time Fields. If you select one or more time fields in the step for selecting fields, those fields are
displayed in this list.
Time Interval. Select the appropriate time interval from the list. Depending on the time interval, you can
also specify other settings, such as interval between observations (increment) and starting value. This
time interval is used for all selected time fields.
• The procedure assumes that all cases (records) represent equally spaced intervals.
• Based on the selected time interval, the procedure can detect missing observations or multiple
observations in the same time interval that need to be aggregated together. For example, if the time
interval is days and the date 2014-10-27 is followed by 2014-10-29, then there is a missing
observation for 2014-10-28. If the time interval is month, then multiple dates in the same month are
aggregated together.
• For some time intervals, the additional setting can define breaks in the normal equally spaced intervals.
For example, if the time interval is days, but only weekdays are valid, you can specify that there are five
days in a week, and the week begins on Monday.
• If the selected time field is not a date format or time format field, the time interval is automatically set
to Periods and cannot be changed.
Cycle fields
If you select Cyclic period on the step for selecting fields, you must specify the fields that define the
cyclic periods. A cyclic period identifies repetitive cyclical variation, such as the number of months in a
year or the number of days in a week.
• You can specify up to three fields that define cyclic periods.
• The first cycle field represents the highest level of the cycle. For example, if there is cyclic variation by
year, quarter, and month, the field that represents year is the first cycle field.
• The cycle length for the first and second cycle fields is the periodicity at the subsequent level. For
example, if the cycle fields are year, quarter, and month, the first cycle length is 4 and the second cycle
length is 3.
• The starting value for the second and third cycle fields is the first value in each of those cyclic periods.
• Cycle length and starting values must be positive integers.
Aggregation
• If you select any Predictors in the step for selecting fields, you can select the aggregation summary
method for the predictors.
• Aggregation is necessary when there is more than one record in a defined time interval. For example, if
the time interval is month, then multiple dates in the same month are aggregated together.
• You can specify the aggregation summary measure method for continuous and ordinal fields. Nominal
fields are aggregated based on the modal value.
Continuous
For continuous (scale) fields, the summary measure can be mean, median, or sum.
Ordinal
For ordinal fields, the summary measure can be median, mode, highest, or lowest.
194 IBM SPSS Statistics Base V27
Custom settings for specific fields
You can override the default aggregation summary measure for specific predictors.
• Click the icon to open the Field Chooser dialog and select a field to add to the list.
• In the Aggregation column, select a summary measure.
Output
Maps
Target values.
Map of values for the selected target field.
Correlation
Map of correlations.
Clusters
Map that highlights clusters of locations that are similar to each other. Maps of clusters are
available only for empirical models.
Location similarity threshold.
The similarity that is required to create clusters. The value must be a number greater than
zero and less than 1.
Specify maximum number of clusters.
The maximum number of clusters to display.
Model Evaluation Tables
Model Specifications.
Summary of specifications that are used to run the analysis, including target, input, and location
fields.
Temporal Information Summary.
Identifies the time fields and time intervals that are used in the model.
Test of Effects in Mean Structure.
The output includes test statistics value, degrees of freedom, and significance level for the model
and each effect.
Mean Structure of Model Coefficients.
The output includes the coefficient value, standard error, test statistics value, significance level,
and confidence intervals for each model term.
Autoregressive Coefficients.
The output includes the coefficient value, standard error, test statistics value, significance level,
and confidence intervals for each lag.
Tests of Spatial Covariance.
For variogram-based parametric models, displays the goodness of fit test results for spatial
covariance structure. The test results can determine whether to model the spatial covariance
structure parametrically or to use a nonparametric model.
Parametric Spatial Covariance.
For variogram-based parametric models, displays parameter estimates for parametric spatial
covariance.
Model Options
Model Settings
Automatically include an intercept
Include the intercept in the model.
Maximum autoregression lag
The maximum autoregression lag. The value must be an integer between 1 and 5.
Spatial Covariance
Specifies the estimation method for spatial covariance.
Chapter 1. Core features 195
Parametric
The estimation method is parametric. The method can be Gaussian, Exponential or Power
Exponential. For Power Exponential, you can specify the Power value.
Nonparametric
The estimation method is nonparametric.
Save
Save the map and context data as a map specification
Save the map specifications to an external file (.mplan). You can load this map specification file into
the wizard for subsequent analysis. You can also use the map specification file with the SPATIAL
TEMPORAL PREDICTION command.
Copy any map and data files into the specification
Data from map shape files, external data files, and datasets that are used in the map specification
are saved in the map specification file.
Scoring
Saves predicted values, variance, and upper and lower confidence bounds for the target field in the
selected data file.
• You can save predicted values to an open dataset in the current session or an IBM SPSS Statistics
format data file.
• The data file cannot be a data source that is used in the model.
• The data file must contain all the time fields and predictors that are used in the model.
• The time values must be greater than the time values used in the model.
Advanced
Maximum cases with missing values (%)
The maximum percentage of cases with missing values.
Significance level
The significance level for determining whether a variogram-based parametric model is appropriate.
The value must be greater than 0 and less than 1. The default value is 0.05. The significance level is
used in the goodness of fit test for spatial covariance structure. The goodness of fit statistic is used to
determine whether to use a parametric or non-parametric model.
Uncertainty factor (%)
The uncertainty factor is a percentage value that represents the growth in uncertainty for future
forecasts. The upper and lower limits of forecast uncertainty increase by the specified percentage for
each step into the future.
Finish
In the last step of the Geospatial Modeling Wizard you can either run the model or paste the generated
command syntax to a syntax window. You can modify and save the generated syntax for subsequent use.
196 IBM SPSS Statistics Base V27
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Index
A
adjusted R 2
in Linear Regression 92
adjusted R-square
in linear models 84
Agresti-Caffo
in Independent-Samples Proportions 57
Agresti-Coull
in One-Sample Proportions 52
Agresti-Min
in Paired-Samples Proportions 54
Akaike information criterion
in linear models 84
alpha coefficient
in Reliability Analysis 157, 158
alpha factoring 113
analysis of variance
in Curve Estimation 97
in Linear Regression 92
in Means 47
in One-Way ANOVA 63
Anderson-Rubin factor scores 114
Andrews' wave estimator
in Explore 38
ANOVA
in GLM Univariate 67
in linear models 87
in Means 47
in One-Way ANOVA 63
model 68
Anscombe
in One-Sample Proportions 52
Asymptotic significance level 158
automatic data preparation
in linear models 86
automatic distribution fitting
in simulation 175
auxiliary regression model
in GLM 77
average absolute deviation (AAD)
in Ratio Statistics 165
B
backward elimination
in Linear Regression 89
bagging
in linear models 83
bar charts
in Frequencies 35
Bartlett factor scores 114
Bartlett's test of sphericity
in Factor Analysis 113
best subsets
in linear models 84
beta coefficients
beta coefficients (continued)
in Linear Regression 92
binomial test
One-Sample Nonparametric Tests 127, 128
Binomial Test
command additional features 142
dichotomies 141
missing values 142
options 142
statistics 142
Bivariate Correlations
command additional features 80
confidence interval 78
confidence intervals 79
correlation coefficients 78
missing values 79
options 79
significance level 78
statistics 79
block distance
in Distances 82
Bonett-Price
in Paired-Samples Proportions 54
Bonferroni
in GLM 72
in One-Way ANOVA 64
boosting
in linear models 83
Box's M test
in Discriminant Analysis 109
boxplots
comparing factor levels 38
comparing variables 38
in Explore 38
in simulation 182
Brown-Forsythe statistic
in One-Way ANOVA 66
Brown-Li-Jeffreys
in Independent-Samples Proportions 57
build terms 69, 96
C
case-control study
Paired-Samples T Test 60
casewise diagnostic information
in Linear Regression 92
categorical field information
nonparametric tests 139
charts
case labels 97
in ROC Analysis 166
in ROC Curve 169
Chebychev distance
in Distances 82
chi-square
expected range 140
Index 199
chi-square (continued)
expected values 140
Fisher's exact test 41
for independence 41
in Crosstabs 41
likelihood-ratio 41
linear-by-linear association 41
missing values 141
one-sample test 140
options 141
Pearson 41
statistics 141
Yates' correction for continuity 41
chi-square distance
in Distances 82
chi-square test
One-Sample Nonparametric Tests 127, 129
city-block distance
in Nearest Neighbor Analysis 103
classification
in ROC Analysis 166
in ROC Curve 169
classification table
in Nearest Neighbor Analysis 108
Clopper-Pearson (Exact)
in One-Sample Proportions 52
Clopper-Pearson intervals
One-Sample Nonparametric Tests 128
cluster analysis
efficiency 125
Hierarchical Cluster Analysis 123
K-Means Cluster Analysis 124
cluster frequencies
in TwoStep Cluster Analysis 118
cluster viewer
about cluster models 118
basic view 120
cell content display 120
cell distribution view 121
cluster centers view 119
cluster comparison view 121
cluster display sort 120
cluster predictor importance view 121
cluster sizes view 121
clusters view 119
comparison of clusters 121
distribution of cells 121
feature display sort 120
filtering records 122
flip clusters and features 120
model summary 119
overview 119
predictor importance 121
size of clusters 121
sort cell contents 120
sort clusters 120
sort features 120
summary view 119
transpose clusters and features 120
using 122
clustering
choosing a procedure 115
overall display 119
viewing clusters 119
Cochran's Q
in Tests for Several Related Samples 149
Cochran's Q test
Related-Samples Nonparametric Tests 133, 134
Cochran's statistic
in Crosstabs 41
Codebook
output 31
statistics 33
coefficient of dispersion (COD)
in Ratio Statistics 165
coefficient of variation (COV)
in Ratio Statistics 165
Cohen's kappa
in Crosstabs 41
Cohen's Weighted Kappa 161, 162
collinearity diagnostic information
in Linear Regression 92
column percentages
in Crosstabs 43
column proportions statistics
in Crosstabs 43
column summary reports 155
combining rules
in linear models 85
comparing groups
in OLAP Cubes 50
comparing variables
in OLAP Cubes 50
compound model
in Curve Estimation 98
concentration index
in Ratio Statistics 165
confidence interval
in Bivariate Correlations 78
confidence interval summary
nonparametric tests 136, 137
confidence intervals
in Bivariate Correlations 79
in Explore 38
in GLM 70
in Independent-Samples T Test 60
in Linear Regression 92
in One-Sample T Test 62
in One-Way ANOVA 66
in Paired-Samples T Test 61
in ROC Analysis 167, 168
in ROC Curve 170
saving in Linear Regression 91
contingency coefficient
in Crosstabs 41
contingency tables 40
continuous field information
nonparametric tests 139
contrasts
in GLM 70
in One-Way ANOVA 64
control variables
in Crosstabs 40
convergence
in Factor Analysis 113, 114
in K-Means Cluster Analysis 125
Cook's distance
in GLM 75
200 IBM SPSS Statistics Base V27
Cook's distance (continued)
in Linear Regression 91
correlation matrix
in Discriminant Analysis 109
in Factor Analysis 112, 113
in Ordinal Regression 95
correlations
in Bivariate Correlations 78
in Crosstabs 41
in Partial Correlations 80
in simulation 179
zero-order 81
covariance matrix
in Discriminant Analysis 109, 110
in GLM 75
in Linear Regression 92
in Ordinal Regression 95
covariance ratio
in Linear Regression 91
Cox and Snell R2
in Ordinal Regression 95
Cramér's V
in Crosstabs 41
Cronbach's alpha
in Reliability Analysis 157, 158
Crosstabs
cell display 43
clustered bar charts 41
control variables 40
formats 44
layers 40
statistics 41
suppressing tables 40
crosstabulation
in Crosstabs 40
multiple response 151
cubic model
in Curve Estimation 98
cumulative distribution functions
in simulation 181
cumulative frequencies
in Ordinal Regression 95
Curve Estimation
analysis of variance 97
forecast 98
including constant 97
models 98
saving predicted values 98
saving prediction intervals 98
saving residuals 98
custom models
in GLM 68
D
d
in Crosstabs 41
Define Multiple Response Sets
categories 150
dichotomies 150
set labels 150
set names 150
deleted residuals
in GLM 75
deleted residuals (continued)
in Linear Regression 91
dendrograms
in Hierarchical Cluster Analysis 124
dependent t test
in Paired-Samples T Test 60
descriptive statistics
in Descriptives 36
in Explore 38
in Frequencies 34
in Ratio Statistics 165
in Summarize 45
in TwoStep Cluster Analysis 118
Descriptives
command additional features 37
display order 36
saving z scores 36
statistics 36
designs for heteroskedasticity tests
in GLM 77
detrended normal plots
in Explore 38
deviation contrasts
in GLM 70
DfBeta
in Linear Regression 91
DfFit
in Linear Regression 91
dictionary
Codebook 31
difference contrasts
in GLM 70
differences between groups
in OLAP Cubes 50
differences between variables
in OLAP Cubes 50
direct oblimin rotation
in Factor Analysis 114
Discriminant Analysis
command additional features 111
covariance matrix 110
criteria 110
defining ranges 109
descriptive statistics 109
discriminant methods 110
display options 110
example 108
exporting model information 111
function coefficients 109
grouping variables 108
independent variables 108
Mahalanobis distance 110
matrices 109
missing values 110
plots 110
prior probabilities 110
Rao's V 110
saving classification variables 111
selecting cases 109
statistics 108, 109
stepwise methods 108
Wilks' lambda 110
distance measures
in Distances 82
Index 201
distance measures (continued)
in Hierarchical Cluster Analysis 123
in Nearest Neighbor Analysis 103
Distances
command additional features 83
computing distances between cases 81
computing distances between variables 81
dissimilarity measures 82
example 81
similarity measures 82
statistics 81
transforming measures 82
transforming values 82
distribution fitting
in simulation 175
division
dividing across report columns 156
Duncan's multiple range test
in GLM 72
in One-Way ANOVA 64
Dunnett's C
in GLM 72
in One-Way ANOVA 64
Dunnett's t test
in GLM 72
in One-Way ANOVA 64
Dunnett's T3
in GLM 72
in One-Way ANOVA 64
Durbin-Watson statistic
in Linear Regression 92
E
effect size
in Independent-Samples T Test 59
in Paired-Samples T-Test 60
eigenvalues
in Factor Analysis 113
in Linear Regression 92
ensembles
in linear models 85
equamax rotation
in Factor Analysis 114
error summary
in Nearest Neighbor Analysis 108
eta
in Crosstabs 41
in Means 47
eta-squared
in Means 47
Euclidean distance
in Distances 82
in Nearest Neighbor Analysis 103
Exact Binomial
in Paired-Samples Proportions 55
expected count
in Crosstabs 43
expected frequencies
in Ordinal Regression 95
Explore
command additional features 39
missing values 39
options 39
Explore (continued)
plots 38
power transformations 39
statistics 38
exponential model
in Curve Estimation 98
extreme values
in Explore 38
F
F statistic
in linear models 84
Factor Analysis
coefficient display format 115
command additional features 115
convergence 113, 114
descriptives 113
example 112
extraction methods 113
factor scores 114
loading plots 114
missing values 115
overview 112
rotation methods 114
selecting cases 112
statistics 112, 113
factor scores 114
feature selection
in Nearest Neighbor Analysis 108
feature space chart
in Nearest Neighbor Analysis 106
first
in Means 47
in OLAP Cubes 49
in Summarize 45
Fisher's exact test
in Crosstabs 41
Fisher's LSD
in GLM 72
Fleiss' Multiple Rater Kappa 157, 158
forecast
in Curve Estimation 98
formatting
columns in reports 154
forward selection
in Linear Regression 89
in Nearest Neighbor Analysis 103
forward stepwise
in linear models 84
Frequencies
charts 35
display order 35
formats 35
statistics 34
suppressing tables 35
frequency tables
in Explore 38
in Frequencies 33
Friedman test
in Tests for Several Related Samples 149
Related-Samples Nonparametric Tests 133
full factorial models
in GLM 68
202 IBM SPSS Statistics Base V27
G
Gabriel's pairwise comparisons test
in GLM 72
in One-Way ANOVA 64
Games and Howell's pairwise comparisons test
in GLM 72
in One-Way ANOVA 64
gamma
in Crosstabs 41
generalized least squares
in Factor Analysis 113
geometric mean
in Means 47
in OLAP Cubes 49
in Summarize 45
geospatial modeling 186–196
GLM
model 68
post hoc tests 72
profile plots 70
saving matrices 75
saving variables 75
sum of squares 68
GLM Univariate
contrasts 70
Goodman and Kruskal's gamma
in Crosstabs 41
Goodman and Kruskal's lambda
in Crosstabs 41
Goodman and Kruskal's tau
in Crosstabs 41
goodness of fit
in Ordinal Regression 95
grand totals
in column summary reports 157
group means 46, 48
grouped median
in Means 47
in OLAP Cubes 49
in Summarize 45
growth model
in Curve Estimation 98
Guttman model
in Reliability Analysis 157, 158
H
Hampel's redescending M-estimator
in Explore 38
harmonic mean
in Means 47
in OLAP Cubes 49
in Summarize 45
Hauck-Anderson
in Independent-Samples Proportions 57, 58
Helmert contrasts
in GLM 70
Hierarchical Cluster Analysis
agglomeration schedules 124
cluster membership 124
clustering cases 123
clustering methods 123
clustering variables 123
Hierarchical Cluster Analysis (continued)
command additional features 124
dendrograms 124
distance matrices 124
distance measures 123
example 123
icicle plots 124
plot orientation 124
saving new variables 124
similarity measures 123
statistics 123, 124
transforming measures 123
transforming values 123
hierarchical decomposition 69
histograms
in Explore 38
in Frequencies 35
in Linear Regression 90
Hochberg's GT2
in GLM 72
in One-Way ANOVA 64
Hodges-Lehman estimates
Related-Samples Nonparametric Tests 133
holdout sample
in Nearest Neighbor Analysis 104
homogeneity-of-variance tests
in One-Way ANOVA 66
homogeneous subsets
nonparametric tests 139
Hotelling's T 2
in Reliability Analysis 157, 158
Huber's M-estimator
in Explore 38
hypothesis summary
nonparametric tests 136
I
ICC. See intraclass correlation coefficient 158
icicle plots
in Hierarchical Cluster Analysis 124
image factoring 113
independent samples test
nonparametric tests 138
Independent-Samples Nonparametric Tests
Fields tab 131
Independent-Samples Proportions 56, 57
Independent-Samples T Test
confidence intervals 60
missing values 60
options 60
Independent-Samples T-Test
defining groups 60
grouping variables 60
string variables 60
information criteria
in linear models 84
initial threshold
in TwoStep Cluster Analysis 117
interaction terms 69, 96
Interrater Agreement 158
intraclass correlation coefficient (ICC)
in Reliability Analysis 158
inverse model
Index 203
inverse model (continued)
in Curve Estimation 98
iteration history
in Ordinal Regression 95
iterations
in Factor Analysis 113, 114
in K-Means Cluster Analysis 125
J
Jeffreys
in One-Sample Proportions 52
Jeffreys intervals
One-Sample Nonparametric Tests 128
K
k and feature selection
in Nearest Neighbor Analysis 108
k selection
in Nearest Neighbor Analysis 108
K-Means Cluster Analysis
cluster distances 126
cluster membership 126
command additional features 126
convergence criteria 125
efficiency 125
examples 124
iterations 125
methods 124
missing values 126
overview 124
saving cluster information 126
statistics 124, 126
kappa
in Crosstabs 41
Kendall's coefficient of concordance (W)
Related-Samples Nonparametric Tests 133
Kendall's tau-b
in Bivariate Correlations 78
in Crosstabs 41
Kendall's tau-c
in Crosstabs 41
Kendall's W
in Tests for Several Related Samples 149
Kolmogorov-Smirnov test
One-Sample Nonparametric Tests 127, 129
Kolmogorov-Smirnov Test
Lilliefors Test 129
Kolmogorov-Smirnov Z
in One-Sample Kolmogorov-Smirnov Test 143
in Two-Independent-Samples Tests 145
KR20
in Reliability Analysis 158
Kruskal-Wallis H
in Two-Independent-Samples Tests 147
Kruskal's tau
in Crosstabs 41
Kuder-Richardson 20 (KR20)
in Reliability Analysis 158
kurtosis
in Descriptives 36
in Explore 38
kurtosis (continued)
in Frequencies 34
in Means 47
in OLAP Cubes 49
in Report Summaries in Columns 156
in Report Summaries in Rows 154
in Summarize 45
L
lambda
in Crosstabs 41
Lance and Williams dissimilarity measure
in Distances 82
last
in Means 47
in OLAP Cubes 49
in Summarize 45
layers
in Crosstabs 40
least significant difference
in GLM 72
in One-Way ANOVA 64
Levene test
in Explore 38
in One-Way ANOVA 66
leverage values
in GLM 75
in Linear Regression 91
likelihood ratio intervals
One-Sample Nonparametric Tests 128
likelihood-ratio chi-square
in Crosstabs 41
in Ordinal Regression 95
Lilliefors test
in Explore 38
Lilliefors Test 129, 143, 144
linear model
in Curve Estimation 98
linear models
ANOVA table 87
automatic data preparation 84, 86
coefficients 88
combining rules 85
confidence level 84
ensembles 85
estimated means 88
information criterion 86
model building summary 88
model options 86
model selection 84
model summary 86
objectives 83
outliers 87
predicted by observed 87
predictor importance 86
R-square statistic 86
replicating results 86
residuals 87
Linear Regression
blocks 89
command additional features 93
exporting model information 91
missing values 93
204 IBM SPSS Statistics Base V27
Linear Regression (continued)
plots 90
residuals 91
saving new variables 91
selection variable 90
statistics 92
variable selection methods 89, 93
weights 89
linear-by-linear association
in Crosstabs 41
link
in Ordinal Regression 94
listing cases 44
loading plots
in Factor Analysis 114
location model
in Ordinal Regression 95
logarithmic model
in Curve Estimation 98
logistic model
in Curve Estimation 98
Logit
in One-Sample Proportions 52
M
M-estimators
in Explore 38
Mahalanobis distance
in Discriminant Analysis 110
in Linear Regression 91
Manhattan distance
in Nearest Neighbor Analysis 103
Mann-Whitney U
in Two-Independent-Samples Tests 145
Mantel-Haenszel statistic
in Crosstabs 41
marginal homogeneity test
in Two-Related-Samples Tests 146
Related-Samples Nonparametric Tests 133
matched-pairs study
in Paired-Samples T Test 60
maximum
comparing report columns 156
in Descriptives 36
in Explore 38
in Frequencies 34
in Means 47
in OLAP Cubes 49
in Ratio Statistics 165
in Summarize 45
maximum branches
in TwoStep Cluster Analysis 117
maximum likelihood
in Factor Analysis 113
McFadden R2
in Ordinal Regression 95
McNemar
in Paired-Samples Proportions 55
McNemar (continuity corrected)
in Paired-Samples Proportions 55
McNemar test
in Crosstabs 41
in Two-Related-Samples Tests 146
McNemar test (continued)
Related-Samples Nonparametric Tests 133, 134
mean
in Descriptives 36
in Explore 38
in Frequencies 34
in Means 47
in OLAP Cubes 49
in One-Way ANOVA 66
in Ratio Statistics 165
in Report Summaries in Columns 156
in Report Summaries in Rows 154
in Summarize 45
of multiple report columns 156
subgroup 46, 48
Means
options 47
statistics 47
measures of central tendency
in Explore 38
in Frequencies 34
in Ratio Statistics 165
measures of dispersion
in Descriptives 36
in Explore 38
in Frequencies 34
in Ratio Statistics 165
measures of distribution
in Descriptives 36
in Frequencies 34
median
in Explore 38
in Frequencies 34
in Means 47
in OLAP Cubes 49
in Ratio Statistics 165
in Summarize 45
median test
in Two-Independent-Samples Tests 147
memory allocation
in TwoStep Cluster Analysis 117
Mid-p Adjusted Binomial
in Paired-Samples Proportions 55
minimum
comparing report columns 156
in Descriptives 36
in Explore 38
in Frequencies 34
in Means 47
in OLAP Cubes 49
in Ratio Statistics 165
in Summarize 45
Minkowski distance
in Distances 82
missing values
in Binomial Test 142
in Bivariate Correlations 79
in Chi-Square Test 141
in column summary reports 157
in Explore 39
in Factor Analysis 115
in Independent-Samples Proportions 58
in Independent-Samples T Test 60
in Linear Regression 93
Index 205
missing values (continued)
in Multiple Response Crosstabs 152
in Multiple Response Frequencies 151
in Nearest Neighbor Analysis 105
in One-Sample Kolmogorov-Smirnov Test 144, 145
in One-Sample Proportions 53
in One-Sample T Test 62
in One-Way ANOVA 66
in Paired-Samples Proportions 55
in Paired-Samples T Test 61
in Partial Correlations 81
in Report Summaries in Rows 154
in ROC Analysis 167, 168
in ROC Curve 170
in Runs Test 143
in Tests for Several Independent Samples 148
in Two-Independent-Samples Tests 146
in Two-Related-Samples Tests 147
mode
in Frequencies 34
model view
in Nearest Neighbor Analysis 105
nonparametric tests 135
Monte Carlo simulation 170
Moses extreme reaction test
in Two-Independent-Samples Tests 145
Multidimensional Scaling
command additional features 165
conditionality 164
creating distance matrices 164
criteria 164
defining data shape 163
dimensions 164
display options 164
distance measures 164
example 163
levels of measurement 164
scaling models 164
statistics 163
transforming values 164
multiple comparisons
in One-Way ANOVA 64
multiple R
in Linear Regression 92
multiple regression
in Linear Regression 89
Multiple Response
command additional features 153
multiple response analysis
crosstabulation 151
frequency tables 151
Multiple Response Crosstabs 151
Multiple Response Frequencies 151
Multiple Response Crosstabs
cell percentages 152
defining value ranges 152
matching variables across response sets 152
missing values 152
percentages based on cases 152
percentages based on responses 152
Multiple Response Frequencies
missing values 151
multiple response sets
Codebook 31
multiplication
multiplying across report columns 156
N
Nagelkerke R2
in Ordinal Regression 95
Nearest Neighbor Analysis
feature selection 103
model view 105
neighbors 103
options 105
output 105
partitions 104
saving variables 105
nearest neighbor distances
in Nearest Neighbor Analysis 107
Newcombe
in Independent-Samples Proportions 57
in Paired-Samples Proportions 54
Newcombe (continuity corrected)
in Independent-Samples Proportions 57
Newman-Keuls
in GLM 72
noise handling
in TwoStep Cluster Analysis 117
nonparametric tests
chi-square 140
model view 135
One-Sample Kolmogorov-Smirnov Test 143
Runs Test 142
Tests for Several Independent Samples 147
Tests for Several Related Samples 149
Two-Independent-Samples Tests 145
Two-Related-Samples Tests 146
normal probability plots
in Explore 38
in Linear Regression 90
normality tests
in Explore 38
number of cases
in Means 47
in OLAP Cubes 49
in Summarize 45
O
observed count
in Crosstabs 43
observed frequencies
in Ordinal Regression 95
OLAP Cubes
statistics 49
titles 50
One-Sample Kolmogorov-Smirnov Test
command additional features 145
Lilliefors Test 143, 144
missing values 144, 145
options 144, 145
statistics 144, 145
test distribution 143
One-Sample Nonparametric Tests
binomial test 128
206 IBM SPSS Statistics Base V27
One-Sample Nonparametric Tests (continued)
chi-square test 129
fields 127
Kolmogorov-Smirnov test 129
runs test 129
One-Sample Proportions 51, 52
One-Sample T Test
command additional features 61–63
confidence intervals 62
missing values 62
options 62
One-Samples Proportions 54
One-Way ANOVA
command additional features 67
contrasts 64
factor variables 63
missing values 66
multiple comparisons 64
options 66
polynomial contrasts 64
post hoc tests 64
statistics 66
Ordinal Regression
command additional features 97
link 94
location model 95
options 94
scale model 96
statistics 93
outliers
in Explore 38
in Linear Regression 90
in TwoStep Cluster Analysis 117
overfit prevention criterion
in linear models 84
P
page control
in column summary reports 156
in row summary reports 154
page numbering
in column summary reports 157
in row summary reports 154
Paired-Samples Proportions 53
Paired-Samples T Test
missing values 61
options 61
selecting paired variables 60
Paired-Samples t-Test 60
pairwise comparisons
nonparametric tests 139
parallel model
in Reliability Analysis 157, 158
parameter estimates
in Ordinal Regression 95
Partial Correlations
command additional features 81
in Linear Regression 92
missing values 81
options 81
statistics 81
zero-order correlations 81
Partial Least Squares Regression
Partial Least Squares Regression (continued)
export variables 101
model 100
partial plots
in Linear Regression 90
pattern difference measure
in Distances 82
pattern matrix
in Factor Analysis 112
Pearson chi-square
in Crosstabs 41
in Ordinal Regression 95
Pearson correlation
in Bivariate Correlations 78
in Crosstabs 41
Pearson residuals
in Ordinal Regression 95
peers
in Nearest Neighbor Analysis 107
percentages
in Crosstabs 43
percentiles
in Explore 38
in Frequencies 34
in simulation 182
phi
in Crosstabs 41
phi-square distance measure
in Distances 82
pie charts
in Frequencies 35
PLUM
in Ordinal Regression 93
polynomial contrasts
in GLM 70
in One-Way ANOVA 64
post hoc multiple comparisons 64
Power Analysis
statistics 1
power model
in Curve Estimation 98
predicted values
saving in Curve Estimation 98
saving in Linear Regression 91
prediction intervals
saving in Curve Estimation 98
saving in Linear Regression 91
predictor importance
linear models 86
price-related differential (PRD)
in Ratio Statistics 165
principal axis factoring 113
principal components analysis 112, 113
probability density functions
in simulation 181
profile plots
in GLM 70
Proximities
in Hierarchical Cluster Analysis 123
Q
quadrant map
in Nearest Neighbor Analysis 107
Index 207
quadratic model
in Curve Estimation 98
quartiles
in Frequencies 34
quartimax rotation
in Factor Analysis 114
R
R 2
in Linear Regression 92
in Means 47
R 2 change 92
r correlation coefficient
in Bivariate Correlations 78
in Crosstabs 41
R statistic
in Linear Regression 92
in Means 47
R-E-G-W F
in GLM 72
in One-Way ANOVA 64
R-E-G-W Q
in GLM 72
in One-Way ANOVA 64
R-square
in linear models 86
range
in Descriptives 36
in Frequencies 34
in Means 47
in OLAP Cubes 49
in Ratio Statistics 165
in Summarize 45
rank correlation coefficient
in Bivariate Correlations 78
Rao's V
in Discriminant Analysis 110
Ratio Statistics
statistics 165
reference category
in GLM 70
regression
Linear Regression 89
multiple regression 89
plots 90
regression coefficients
in Linear Regression 92
related samples 146, 149
Related-Samples Nonparametric Tests
Cochran's Q test 134
fields 133
McNemar test 134
relative risk
in Crosstabs 41
Reliability Analysis
ANOVA table 158
command additional features 161
descriptives 158
example 157
Hotelling's T 2 158
inter-item correlations and covariances 158
intraclass correlation coefficient 158
Kuder-Richardson 20 158
Reliability Analysis (continued)
statistics 157, 158
Tukey's test of additivity 158
repeated contrasts
in GLM 70
Report Summaries in Columns
column format 154
command additional features 157
grand total 157
missing values 157
page control 156
page layout 155
page numbering 157
subtotals 156
total columns 156
Report Summaries in Rows
break columns 153
break spacing 154
column format 154
command additional features 157
data columns 153
footers 155
missing values 154
page control 154
page layout 155
page numbering 154
sorting sequences 153
titles 155
variables in titles 155
reports
column summary reports 155
comparing columns 156
composite totals 156
dividing column values 156
multiplying column values 156
row summary reports 153
total columns 156
residuals
in Crosstabs 43
saving in Curve Estimation 98
saving in Linear Regression 91
rho
in Bivariate Correlations 78
in Crosstabs 41
risk
in Crosstabs 41
ROC Analysis
statistics and plots 167, 168
ROC Curve
statistics and plots 170
row percentages
in Crosstabs 43
runs test
One-Sample Nonparametric Tests 127, 129
Runs Test
command additional features 143
cut points 142, 143
missing values 143
options 143
statistics 143
Ryan-Einot-Gabriel-Welsch multiple F
in GLM 72
in One-Way ANOVA 64
Ryan-Einot-Gabriel-Welsch multiple range
208 IBM SPSS Statistics Base V27
Ryan-Einot-Gabriel-Welsch multiple range (continued)
in GLM 72
in One-Way ANOVA 64
S
S model
in Curve Estimation 98
S-stress
in Multidimensional Scaling 163
scale
in Multidimensional Scaling 163
in Reliability Analysis 157
in Weighted Kappa 161
scale model
in Ordinal Regression 96
scatterplot
in simulation 182
scatterplots
in Linear Regression 90
Scheffé test
in GLM 72
in One-Way ANOVA 64
Score 52
Score (Continuity Corrected) 52
selection variable
in Linear Regression 90
sensitivity analysis
in simulation 179
Shapiro-Wilk's test
in Explore 38
Sidak's t test
in GLM 72
in One-Way ANOVA 64
sign test
in Two-Related-Samples Tests 146
Related-Samples Nonparametric Tests 133
similarity measures
in Distances 82
in Hierarchical Cluster Analysis 123
simple contrasts
in GLM 70
simulation
box plots 182
chart options 186
correlations between inputs 179
creating a simulation plan 171, 172
creating new inputs 175
cumulative distribution function 181
customizing distribution fitting 178
display formats for targets and inputs 182
distribution fitting 175
distribution fitting results 178
equation editor 174
interactive charts 185
model specification 173
output 181, 182
percentiles of target distributions 182
probability density function 181
refitting distributions to new data 183
running a simulation plan 172, 183
save simulated data 183
save simulation plan 183
scatter plots 182
simulation (continued)
sensitivity analysis 179
Simulation Builder 173
stopping criteria 179
supported models 173
tail sampling 179
tornado charts 182
what-if analysis 179
Simulation Builder 173
size difference measure
in Distances 82
skewness
in Descriptives 36
in Explore 38
in Frequencies 34
in Means 47
in OLAP Cubes 49
in Report Summaries in Columns 156
in Report Summaries in Rows 154
in Summarize 45
Somers' d
in Crosstabs 41
spatial modeling 186
Spearman correlation coefficient
in Bivariate Correlations 78
in Crosstabs 41
Spearman-Brown reliability
in Reliability Analysis 158
split-half reliability
in Reliability Analysis 157, 158
spread-versus-level plots
in Explore 38
squared Euclidean distance
in Distances 82
standard deviation
in Descriptives 36
in Explore 38
in Frequencies 34
in Means 47
in OLAP Cubes 49
in Ratio Statistics 165
in Report Summaries in Columns 156
in Report Summaries in Rows 154
in Summarize 45
standard error
in Descriptives 36
in Explore 38
in Frequencies 34
in GLM 75
in ROC Analysis 167, 168
in ROC Curve 170
standard error of kurtosis
in Means 47
in OLAP Cubes 49
in Summarize 45
standard error of skewness
in Means 47
in OLAP Cubes 49
in Summarize 45
standard error of the mean
in Means 47
in OLAP Cubes 49
in Summarize 45
standardization
Index 209
standardization (continued)
in TwoStep Cluster Analysis 117
standardized residuals
in GLM 75
in Linear Regression 91
standardized values
in Descriptives 36
stem-and-leaf plots
in Explore 38
stepwise selection
in Linear Regression 89
stress
in Multidimensional Scaling 163
strictly parallel model
in Reliability Analysis 157, 158
Student-Newman-Keuls
in GLM 72
in One-Way ANOVA 64
Student's t test 59
Studentized residuals
in Linear Regression 91
subgroup means 46, 48
subtotals
in column summary reports 156
sum
in Descriptives 36
in Frequencies 34
in Means 47
in OLAP Cubes 49
in Summarize 45
sum of squares
in GLM 68
Summarize
options 44
statistics 45
T
t test
in Independent-Samples T Test 59
in One-Sample T Test 62
in Paired-Samples T Test 60
Tamhane's T2
in GLM 72
in One-Way ANOVA 64
tau-b
in Crosstabs 41
tau-c
in Crosstabs 41
test of parallel lines
in Ordinal Regression 95
tests for independence
chi-square 41
tests for linearity
in Means 47
Tests for Several Independent Samples
command additional features 148
defining range 148
grouping variables 148
missing values 148
options 148
statistics 148
test types 148
Tests for Several Related Samples
Tests for Several Related Samples (continued)
command additional features 149
statistics 149
test types 149
time series analysis
forecast 98
predicting cases 98
titles
in OLAP Cubes 50
tolerance
in Linear Regression 92
tornado charts
in simulation 182
total column
in reports 156
total percentages
in Crosstabs 43
training sample
in Nearest Neighbor Analysis 104
transformation matrix
in Factor Analysis 112
tree depth
in TwoStep Cluster Analysis 117
trimmed mean
in Explore 38
Tukey's b test
in GLM 72
in One-Way ANOVA 64
Tukey's biweight estimator
in Explore 38
Tukey's honestly significant difference
in GLM 72
in One-Way ANOVA 64
Tukey's test of additivity
in Reliability Analysis 157, 158
Two-Independent-Samples Tests
command additional features 146
defining groups 146
grouping variables 146
missing values 146
options 146
statistics 146
test types 145
Two-Related-Samples Tests
command additional features 147
missing values 147
options 147
statistics 147
test types 147
two-sample t test
in Independent-Samples T Test 59
TwoStep Cluster Analysis
options 117
save to external file 118
save to working file 118
statistics 118
U
uncertainty coefficient
in Crosstabs 41
unstandardized residuals
in GLM 75
unweighted least squares
210 IBM SPSS Statistics Base V27
unweighted least squares (continued)
in Factor Analysis 113
V
V
in Crosstabs 41
variable importance
in Nearest Neighbor Analysis 107
variance
in Descriptives 36
in Explore 38
in Frequencies 34
in Means 47
in OLAP Cubes 49
in Report Summaries in Columns 156
in Report Summaries in Rows 154
in Summarize 45
variance inflation factor
in Linear Regression 92
varimax rotation
in Factor Analysis 114
visualization
clustering models 119
W
Wald
in Independent-Samples Proportions 57, 58
in One-Sample Proportions 52
in Paired-Samples Proportions 54, 55
Wald (continuity corrected)
in Independent-Samples Proportions 57
in One-Sample Proportions 52
in Paired-Samples Proportions 54
Wald (Continuity Corrected)
in Independent-Samples Proportions 58
in Paired-Samples Proportions 55
Wald H0
in Independent-Samples Proportions 58
Wald H0 (Continuity Corrected)
in Independent-Samples Proportions 58
Wald-Wolfowitz runs
in Two-Independent-Samples Tests 145
Waller-Duncan t test
in GLM 72
in One-Way ANOVA 64
Weighted Kappa
criteria 162
crosstabulation 162
example 161
print 162
statistics 161, 162
weighted least squares
in Linear Regression 89
weighted mean
in Ratio Statistics 165
weighted predicted values
in GLM 75
Welch statistic
in One-Way ANOVA 66
what-if analysis
in simulation 179
Wilcoxon signed-rank test
in Two-Related-Samples Tests 146
One-Sample Nonparametric Tests 127
Related-Samples Nonparametric Tests 133
Wilks' lambda
in Discriminant Analysis 110
Wilson Score
in One-Sample Proportions 52
Wilson Score (continuity corrected)
in One-Sample Proportions 52
Y
Yates' correction for continuity
in Crosstabs 41
Z
z scores
in Descriptives 36
saving as variables 36
zero-order correlations
in Partial Correlations 81
Index 211
212 IBM SPSS Statistics Base V27
IBM®
Contents
Chapter 1. Core features
Power Analysis
Means
Power Analysis of One-Sample T Test
Power Analysis of One-Sample T Test: Plot
Power Analysis of Paired-Samples T Test
Power Analysis of Paired-Samples T Test: Plot
Power Analysis of Independent-Samples T Test
Power Analysis of Independent-Samples T Test: Plot
Power Analysis of One-Way ANOVA
Power Analysis of One-way ANOVA: Contrast
Power Analysis of One-way ANOVA: Plot
Proportions
Power Analysis of Related-Sample Binomial Test
Power Analysis of Related-Sample Binomial: Plot
Power Analysis of Independent-Sample Binomial Test
Power Analysis of Independent-Samples Binomial Test: Plot
Power Analysis of One-Sample Binomial Test
Power Analysis of One-Sample Binomial: Plot
Correlations
Power Analysis of One-Sample Pearson Correlation Test
Power Analysis of One-Sample Pearson Correlation: Plot
Power Analysis of One-Sample Spearman Correlation Test
Power Analysis of One-Sample Spearman Correlation: Plot
Power Analysis of Partial Pearson Correlation Test
Power Analysis of Partial Pearson Correlation: Plot
Regression
Power Analysis of Univariate Linear Regression Test
Power Analysis of Univariate Linear Regression: Plot
Codebook
Codebook Output Tab
Codebook Statistics Tab
Frequencies
Frequencies Statistics
Frequencies Charts
Frequencies Format
Descriptives
Descriptives Options
DESCRIPTIVES Command Additional Features
Explore
Explore Statistics
Explore Plots
Explore Power Transformations
Explore Options
EXAMINE Command Additional Features
Crosstabs
Crosstabs layers
Crosstabs clustered bar charts
Crosstabs displaying layer variables in table layers
Crosstabs statistics
Crosstabs cell display
Crosstabs table format
Summarize
Summarize Options
Summarize Statistics
Means
Means Options
OLAP Cubes
OLAP Cubes Statistics
OLAP Cubes Differences
OLAP Cubes Title
Proportions
Proportions introduction
One-Sample Proportions
One-Sample Proportions: Confidence Intervals
One-Sample Proportions: Tests
One-Sample Proportions: Missing Values
Paired-Samples Proportions
Paired-Samples Proportions: Confidence Intervals
Paired-Samples Proportions: Tests
Paired-Samples Proportions: Missing Values
Independent-Samples Proportions
Independent-Samples Proportions: Confidence Intervals
Independent-Samples Proportions: Tests
Independent-Samples Proportions: Missing Values
T Tests
T Tests
Independent-Samples T Test
Independent-Samples T-Test Define Groups
Independent-Samples T Test Options
Paired-Samples T Test
Paired-Samples T Test Options
T TEST Command Additional Features
One-Sample T Test
One-Sample T Test Options
T TEST Command Additional Features
T TEST Command Additional Features
One-Way ANOVA
One-Way ANOVA Contrasts
One-Way ANOVA Post Hoc Tests
One-Way ANOVA Options
ONEWAY Command Additional Features
GLM Univariate Analysis
GLM Model
Build Terms and Custom Terms
Sum of Squares
GLM Contrasts
Contrast Types
GLM Profile Plots
GLM Options
UNIANOVA Command Additional Features
GLM Post Hoc Comparisons
GLM Options
UNIANOVA Command Additional Features
GLM Save
GLM Estimated Marginal Means
GLM Options
GLM Auxiliary Regression Model
UNIANOVA Command Additional Features
Bivariate Correlations
Bivariate Correlations Options
Bivariate Correlations Confidence Interval
CORRELATIONS and NONPAR CORR Command Additional Features
Partial Correlations
Partial Correlations Options
PARTIAL CORR Command Additional Features
Distances
Distances Dissimilarity Measures
Distances Similarity Measures
PROXIMITIES Command Additional Features
Linear models
To obtain a linear model
Objectives
Basics
Model Selection
Ensembles
Advanced
Model Options
Model Summary
Automatic Data Preparation
Predictor Importance
Predicted By Observed
Residuals
Outliers
Effects
Coefficients
Estimated Means
Model Building Summary
Linear Regression
Linear Regression Variable Selection Methods
Linear Regression Set Rule
Linear Regression Plots
Linear Regression: Saving New Variables
Linear Regression Statistics
Linear Regression Options
REGRESSION Command Additional Features
Ordinal Regression
Ordinal Regression Options
Ordinal Regression Output
Ordinal Regression Location Model
Build Terms and Custom Terms
Ordinal Regression Scale Model
Build Terms and Custom Terms
PLUM Command Additional Features
Curve Estimation
Curve Estimation Models
Curve Estimation Save
Partial Least Squares Regression
Model
Options
Nearest Neighbor Analysis
Neighbors
Features
Partitions
Save
Output
Options
Model View
Feature Space
Adding and removing fields/variables
Variable Importance
Peers
Nearest Neighbor Distances
Quadrant map
Feature selection error log
k selection error log
k and Feature Selection Error Log
Classification Table
Error Summary
Discriminant Analysis
Discriminant Analysis Define Range
Discriminant Analysis Select Cases
Discriminant Analysis Statistics
Discriminant Analysis Stepwise Method
Discriminant Analysis Classification
Discriminant Analysis Save
DISCRIMINANT Command Additional Features
Factor Analysis
Factor Analysis Select Cases
Factor Analysis Descriptives
Factor Analysis Extraction
Factor Analysis Rotation
Factor Analysis Scores
Factor Analysis Options
FACTOR Command Additional Features
Choosing a Procedure for Clustering
TwoStep Cluster Analysis
TwoStep Cluster Analysis Options
TwoStep Cluster Analysis Output
The Cluster Viewer
Cluster Viewer
Model Summary View
Clusters View
Transpose Clusters and Features
Sort Features
Sort Clusters
Cell Contents
Cluster Predictor Importance View
Cluster Sizes View
Cell Distribution View
Cluster Comparison View
Navigating the Cluster Viewer
Filtering Records
Hierarchical Cluster Analysis
Hierarchical Cluster Analysis Method
Hierarchical Cluster Analysis Statistics
Hierarchical Cluster Analysis Plots
Hierarchical Cluster Analysis Save New Variables
CLUSTER Command Syntax Additional Features
K-Means Cluster Analysis
K-Means Cluster Analysis Efficiency
K-Means Cluster Analysis Iterate
K-Means Cluster Analysis Save
K-Means Cluster Analysis Options
QUICK CLUSTER Command Additional Features
Nonparametric Tests
One-Sample Nonparametric Tests
Obtaining One-Sample Nonparametric Tests
Fields Tab
Settings Tab
Choose Tests
Binomial Test Options
Chi-Square Test Options
Kolmogorov-Smirnov Options
Runs Test Options
Test Options
User-Missing Values
NPTESTS command additional features
Independent-Samples Nonparametric Tests
To Obtain Independent-Samples Nonparametric Tests
Fields Tab
Settings Tab
Choose Tests
Test Options
User-Missing Values
NPTESTS command additional features
Related-Samples Nonparametric Tests
To Obtain Related-Samples Nonparametric Tests
Fields Tab
Settings Tab
Choose Tests
McNemar's Test: Define Success
Cochran's Q: Define Success
Test Options
User-Missing Values
NPTESTS command additional features
Model View
Model View
Hypothesis Summary
Confidence Interval Summary
One Sample Test
Related Samples Test
Independent Samples Test
Categorical Field Information
Continuous Field Information
Pairwise Comparisons
Homogeneous Subsets
NPTESTS command additional features
Legacy Dialogs
Chi-Square Test
Chi-Square Test Expected Range and Expected Values
Chi-Square Test Options
NPAR TESTS Command Additional Features (Chi-Square Test)
Binomial Test
Binomial Test Options
NPAR TESTS Command Additional Features (Binomial Test)
Runs Test
Runs Test Cut Point
Runs Test Options
NPAR TESTS Command Additional Features (Runs Test)
One-Sample Kolmogorov-Smirnov Test
One-Sample Kolmogorov-Smirnov Test: Simulation
One-Sample Kolmogorov-Smirnov Test: Options
NPAR TESTS Command Additional Features (One-Sample Kolmogorov-Smirnov Test)
Two-Independent-Samples Tests
Two-Independent-Samples Test Types
Two-Independent-Samples Tests Define Groups
Two-Independent-Samples Tests Options
NPAR TESTS Command Additional Features (Two-Independent-Samples Tests)
Two-Related-Samples Tests
Two-Related-Samples Test Types
Two-Related-Samples Tests Options
NPAR TESTS Command Additional Features (Two Related Samples)
Tests for Several Independent Samples
Tests for Several Independent Samples Test Types
Tests for Several Independent Samples Define Range
Tests for Several Independent Samples Options
NPAR TESTS Command Additional Features (K Independent Samples)
Tests for Several Related Samples
Tests for Several Related Samples Test Types
Tests for Several Related Samples Statistics
NPAR TESTS Command Additional Features (K Related Samples)
Multiple Response Analysis
Multiple Response Analysis
Multiple Response Define Sets
Multiple Response Frequencies
Multiple Response Crosstabs
Multiple Response Crosstabs Define Ranges
Multiple Response Crosstabs Options
MULT RESPONSE Command Additional Features
Reporting Results
Reporting Results
Report Summaries in Rows
To Obtain a Summary Report: Summaries in Rows
Report Data Column/Break Format
Report Summary Lines for/Final Summary Lines
Report Break Options
Report Options
Report Layout
Report Titles
Report Summaries in Columns
To Obtain a Summary Report: Summaries in Columns
Data Columns Summary Function
Data Columns Summary for Total Column
Report Column Format
Report Summaries in Columns Break Options
Report Summaries in Columns Options
Report Layout for Summaries in Columns
REPORT Command Additional Features
Reliability Analysis
Reliability Analysis: Statistics
RELIABILITY Command Additional Features
Weighted Kappa
Weighted Kappa: Criteria
Weighted Kappa: Print
Multidimensional Scaling
Multidimensional Scaling Shape of Data
Multidimensional Scaling Create Measure
Multidimensional Scaling Model
Multidimensional Scaling Options
ALSCAL Command Additional Features
Ratio Statistics
Ratio Statistics
ROC Analysis
ROC Analysis: Options
ROC Analysis: Display
ROC Analysis: Define Groups (string)
ROC Analysis: Define Groups (numeric)
ROC Curves
ROC Curve Options
Simulation
To design a simulation based on a model file
To design a simulation based on custom equations
To design a simulation without a predictive model
To run a simulation from a simulation plan
Simulation Builder
Model tab
Equation Editor
Defined Inputs
Simulation tab
Simulated Fields
Fit Details
Sensitivity Analysis
Correlations
Advanced Options
Density Functions
Output
Save
Run Simulation dialog
Simulation tab
Output tab
Working with chart output from Simulation
Chart Options
Geospatial Modeling
Selecting Maps
Selecting a Map
Geospatial Relationship
Set Coordinate System
Setting the Projection
Projection and Coordinate System
Data Sources
Add a Data Source
Data and Map Association
Validate Keys
Geospatial Association Rules
Define Event Data Fields
Select Fields
Output
Save
Rule Building
Binning and Aggregation
Spatial Temporal Prediction
Select Fields
Time Intervals
Aggregation
Output
Model Options
Save
Advanced
Finish
Notices
Trademarks
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Y
Z
1
SPSS Basics
Ø Tutorial 1: SPSS Windows
There are six different windows that can be opened when using SPSS. The following will give
a description of each of them.
The Data Editor
The Data Editor is a spreadsheet in which you define your variables and enter data. Each row
corresponds to a case while each column represents a variable. The title bar displays the
name of the open data file or “Untitled” if the file has not yet been saved. This window opens
automatically when SPSS is started.
The Output Navigator
The Output Navigator window displays the statistical results, tables, and charts from the
analysis you performed. An Output Navigator window opens automatically when you run a
procedure that generates output. In the Output Navigator windows, you can edit, move,
delete and copy your results in a Microsoft Explorer-like environment.
2
The Pivot Table Editor
Output displayed in pivot tables can be modified in many ways with the Pivot Table Editor.
You can edit text, swap data in rows and columns, add color, create multidimensional tables,
and selectively hide and show results.
The Chart Editor
You can modify and save high-resolution charts and plots by invoking the Chart Editor for a
certain chart (by double-clicking the chart) in an Output Navigator window. You can change
the colors, select different type fonts or sizes, switch the horizontal and vertical axes, rotate
3-D scatterplots, and change the chart type.
The Text Output Editor
Text output not displayed in pivot tables can be modified with the Text Output Editor. You can
edit the output and change font characteristics (type, style, color, size).
The Syntax Editor
You can paste your dialog box selections into a Syntax Editor window, where your selections
appear in the form of command syntax.
Ø Tutorial 2: Starting A SPSS Session
1. Logon to your Polaris account.
2. Select Programs from the Start menu.
3. Select Scientific from the Programs drop down menu.
4. Select SPSS 7.5 from the Scientific drop down menu.
Ø Tutorial 3: Getting Help on SPSS
q Locating Topics in the Help Menu
1. Select Topics from the Help Menu on the Data Editor.
2. Select the Contents tab. This will give a set of books to look under for the required
information.
q Searching for Information in the Help Menu
1. Select Topics from the Help menu.
2. Select the Index tab.
3. Type a word in the text box describing the information to search for. This will give a list of
headings on the desired information.
Ø Tutorial 4: Ending A SPSS Session
1. Select Exit SPSS from the File menu on the Data Editor.
3
Creating and Manipulating Data in SPSS
When creating or accessing data in SPSS, the Data Editor window is used.
Ø Tutorial 1: Creating a New Data Set
There are three steps that must be followed to create a new data set in SPSS. The following
tutorial will list the steps needed and will give an example of creating a new data set.
STEP 1: Defining Variables in a New Data Set
Variables are defined one at a time using the Define Variable dialog box. This box assigns
data definition information to variables. To access the Define Variable dialog box, double-
click on the top of a column where the word var appears or select Define Variable from the
Data menu.
Variable Name: This field describes the name of the variable being defined. To change the
name, place the cursor in this field and type the name. The variable name
must begin with a letter of the alphabet and cannot exceed 8 characters.
Spaces are not allowed within the variable name. Each variable name must
be unique.
Type: This field describes the type of variable that is being defined.
To change this field, click on the Type… button. This will open the Define Variable
Type: dialog box. Select the appropriate type of data. When done, click on the Continue
button.
Variable Label: There are two types of variable labels:
1. Variable Label: A name for the variable that can be up to 120 characters
long and can include spaces (which variable names cannot). If a variable
label is entered, the label will be printed on charts and reports instead of
the name, making them easier to understand.
4
2. Value Label: Provides a key for translating numeric data.
To change the variable label, click on the Labels… button. This will open the
Define Labels: dialog box. Enter the appropriate information into the fields.
When done, click on the Continue button.
Missing Values: This field indicates which subset of the data will not be included in the data
set. To change this field, click on the Missing Values… button. This will
open the Define Missing Values: dialog box. Enter the appropriate
information into the fields. When done, click on the Continue button.
Alignment: This field indicates column alignment and width. To change this field, click on the
Column Format… button. This will open the Define Column Format: dialog box.
Enter the appropriate information into the fields. When done, click on the
Continue button.
STEP 2: Entering Data in a New Data Set
Once all of the variables are defined, enter the data manually (assuming that the data is not
already in an external file). The data is typed into the spreadsheet one cell at a time. Each
cell represents an observation.
When information is typed into a cell, it appears in the edit area at the top of the window. The
information is entered into the cell when the active cell is changed. The mouse and the tab,
enter, and cursor keys can be used to enter data.
To indicate a cell that does not have a data value, a period is entered. A period represents
the system-missing value.
5
STEP 3: Saving a New Data Set
Work performed on a data set only lasts during the current session. To retain the current data
set, it must be saved to a file.
1. Select Save from the File menu. The Save Data As dialog box opens.
2. From the Save as Type drop-down list, select SPSS (*.sav).
3. From the Save in drop-down list, select the path where the file will be saved.
4. In the File name box, enter a name for the file. SPSS automatically adds the extension
.sav.
5. Click Save.
Problem
The following data regarding a person’s name, age and weight must be entered into a data
set using SPSS.
Name Age Weight
Mark 39 250
Allison 43 1
25
Tom 27 180
Cindy 24 130
Solution
1. Double click on the top of the first column in the Data Editor window. This will open the
Define Variable dialog box. Type Name in the Variable Name box.
2. Select Type… in the Change Settings area. This will open the Define Variable Type
dialog box. Left click on String.
3. Select Continue. This will close the Define Variable Type dialog box and will re-open the
Define Variable dialog box.
4. Click OK. This will define the first column as a string variable called Name.
5. Double click on the top of the second column. This will open the Define Variable dialog
box. Type Age in the Variable Name box.
6. Select Type… in the Change Settings area. This will open the Define Variable Type
dialog box. Left click on Numeric. In the Width box, set it to 3. In the Decimal Places box,
set it to 0.
7. Select Continue. This will close the Define Variable Type dialog box and will re-open the
Define Variable dialog box.
8. Click OK. This will define the second column as a numeric variable called Age.
9. Double click on the top of the third column. This will open the Define Variable dialog box.
Type Weight in the Variable Name box.
6
10. Select Type… in the Change Settings area. This will open the Define Variable Type
dialog box. Left click on Numeric. In the Width box, set it to 3. In the Decimal Places box,
set it to 0.
11. Select Continue. This will close the Define Variable Type dialog box and will re-open the
Define Variable dialog box.
12. Click OK. This will define the third column as a numeric variable called Weight.
13. Enter the above information into the cells of the spreadsheet. The Data Editor should look
like the following.
14. Select Save from the File menu.
15. Choose the path where the file will be saved.
16. Type temp in the File name box and click Save. SPSS will save this file as temp.sav in
the specified directory.
Ø Tutorial 2: Creating a New Data Set From Other File Formats
SPSS is designed to handle a wide variety of formats including:
• Spreadsheet files created with Lotus 1-2-3 and Excel
• Database files created with dBASE
• Tab-deliminated and other types of ASCII text files
• SPSS data files create on other operating systems
• SYSTAT data files
The following tutorial will indicate how to read in a spreadsheet or text file into a data set in
SPSS. Examples will be given of each method.
6
q Reading Spreadsheet Files (Lotus 1-2-3 and Excel)
Problem
Read the following file, ~/SPSS/nba.xls, into a SPSS data set.
Solution
1. From the File menu, select Open. This will open the Open File dialog box.
2. Change the path name to your home directory and open the SPSS folder. This is
where the file to be opened should be.
3. Select Excel(*.xls) (or Lotus(*.w*) for Lotus files) from the Files of type box.
4. Select nba.xls.
5. Click Open. This will open the Opening File Options dialog box. Click on the Read
variable names dialog box. Click OK. This will close the Opening File Options dialog
box and will open nba.xls in the Data Editor. The Output Navigator will also be
opened.
NOTE:
If only a partial file is to be read into SPSS, the following steps are taken.
• For Lotus files, in the Range box, specify the beginning column letter and row
number followed by two periods followed by the ending column letter and row
number. Ie. A1..C
12
• For Excel files, in the Range box, specify the beginning column letter and row
number followed by a colon followed by the ending column letter and row
number. Ie. A1:C12
7
Window Output
8
q Reading Text Files
Two ways to read a text file are by using freefield or fixed columns.
Freefield
This method is used if the variables are recorded in the same order for each case but not
necessarily in the same column locations.
Problem
Read the following file, ~/SPSS/citydata.txt, into an SPSS data set.
Solution
1. Select Read ASCII Data from the File Menu. From the Read ASCII Data drop down
menu, choose Freefield. This will open the Define Freefield Variables dialog box.
2. Specify the variable name and data type. The following gives a description of each of
these fields.
Name: Variable names must begin with a letter and cannot exceed eight characters.
Each variable name must be unique.
Data Type: Select a data type.
3. Click Add for each separate variable. This will enter the variable name and data type
onto the Defined Variables list.
4. Once all variables are defined, click Browse to specify the name of the file to be read.
This will open the Define Freefield Variables: Browse dialog box. Change the path
name to your home directory and open the SPSS folder. This is where the file to be
opened should be.
5. Select citydata.txt and click Open. The Define Freefield Variables dialog box will be
returned.
6. Click OK. This will close the Define Freefield Variables dialog box and will open
citydata.txt in the Data Editor.
9
Window Output
Fixed Columns
This method is used if each variable is recorded in the same column location for each
case in the data file.
Problem
Read the following file, ~/SPSS/nba.txt, into an SPSS data set.
Solution
1. Select Read ASCII Data from the File Menu. From the Read ASCII Data drop down
menu, choose Fixed Columns. This will open the Define Fixed Variables dialog box
which will be used to define each variable.
2. Specify the variable name, record, column locations, and data type. The following
gives a description of each of these fields.
Name: Variable names must begin with a letter and cannot exceed eight characters.
Each variable name must be unique.
10
Record: A case can have data on more than one line. The record number indicates
the line within the case where the variable is located.
Start Column/End Column: These specifications indicate the location of the variable
within the record. The value for the variable can appear
anywhere within the range of columns.
Data Type: Select a data type.
For this problem, the following is a list of the required information.
Name Record Column Locations Data Type
Player 1 1-3 Numeric as is
Height 1 4-7 Numeric as is
Weight 1 8-12 Numeric as is
3. When all information is added for a variable, click Add. This will enter the record
number, start and end columns, variable name, and data type onto the Defined
Variables list.
4. Once all variables are defined, click Browse to specify the name of the file to be read.
This will open the Define Fixed Variables: Browse dialog box. Change the path name
to your home directory and open the SPSS folder. This is where the file to be opened
should be.
5. Select nba.txt and click Open. The Define Fixed Variables dialog box will be returned.
6. Click OK. This will close the Define Fixed Variables dialog box and will open nba.txt
in the Data Editor.
Window Output
11
Ø Tutorial 3: Opening an Existing SPSS Data Set
1. Select Open from the File menu. This will open the Open File dialog box.
2. From the Files of type drop-down list, select .sav.
3. From the Look in drop-down list, select the appropriate drive where the file is located.
4. In the File name box, type in the name of the file to be opened.
5. Click Open.
Ø Tutorial 4: Printing a Data Set
1. Highlight the data that will be printed. To print all of the data, ignore this step and
continue to step 2.
2. Select Print from the File menu. The Print dialog box opens. Change the options where
appropriate.
3. Click OK.
12
Generating Descriptive Statistics in SPSS
The following tutorials will demonstrate how to generate descriptive statistics in SPSS.
Ø Tutorial 1: Mean, Sum, Standard Deviation, Variance, Minimum Value,
Maximum Value, and Range
When generating these statistics, the Data Editor must be open with the appropriate data set
before continuing.
Problem
Using the data in the file nba.txt that is located in ~/SPSS/, determine the mean, sum,
standard deviation, variance, minimum value, maximum value, and range for height only.
Solution
1. From the Statistics menu, select Summarize. From the Summarize drop down menu,
select Descriptives. This will open the Descriptives dialog box.
2. In the variable list, select the variable height. Left click on the right arrow button between
the boxes to move this variable over to the Variable(s) box. To calculate statistics for
many variables, simultaneously add variables to the Variable(s) box.
3. Click on the Options button. This will open the Descriptives: Options dialog box.
Click on mean, sum, standard deviation, variance, minimum value, maximum value, and
range.
Click on the Continue button when done.
13
4. Click OK. The Descriptives dialog box closes and SPSS activates the Output Navigator to
illustrate the statistics.
Window Output
Ø Tutorial 2: Correlation
Two or more variables may be included in a correlation matrix. When generating the
correlation matrix, the Data Editor must be open with the appropriate data set before
continuing.
Problem
Using the data in the file nba.txt that is located in ~/SPSS/, determine the correlation between
a player’s height and weight.
Solution
1. From the Statistics menu, select Correlate. From the Correlate drop down menu, select
Bivariate. This will open the Bivariate Correlations dialog box.
2. In the variable list, select height and weight. Left click on the right arrow button between
the boxes to move a variable over to the Variable(s) box.
3. Select the type of correlation coefficients that will be generated. In this case, use
Pearson.
14
4. Select the test of significance to be used. In this case, use two-tailed.
5. Check mark the Flag significant correlations box.
6. Click on the Options…button. This will open the Bivariate Correlations: Options dialog
box.
To display the mean and standard deviation for each variable, select Means and
standard deviations. In this case, this option is not used.
To display cross product deviations and covariances for each pair of variables, select
Cross-product devations and covariances. In this case, this option will not be used.
When done, click the Continue button.
7. Click OK. The Bivariate Correlations dialog box closes and SPSS activates the Output
Navigator. The correlation coefficient for each pair of variables is displayed. The number
of cases appears at the bottom.
Window Output
15
Generating Graphical Statistics in SPSS
The following tutorials introduce how to create scatter plots, histograms, stem and leaf plots, and
box plots using the SPSS Graphs menu located on the Data Editor menu bar.
Ø Tutorial 1: How to Generate Scatter Plots
Problem
Using the data in ~/SPSS/nba.txt, create an x-y plot of a player’s weight versus height.
Solution
1. From the Graphs menu, select Scatter… This will open the Scatterplot dialog box.
2. Select the Simple icon and click Define. This will open the Simple Scatterplot dialog box.
3. From the variable list, select weight. Left click on the right arrow button between the
variable list and the Y Axis box to move the variable, weight, to this box.
4. From the variable list, select height. Left click on the right arrow button between the
variable list and the X Axis box to move the variable, height, to this box.
5. Click on the Options… button. This will open the Options dialog box.
16
To display a report of missing values, select Display groups defined by missing values. In
this case, this option will not be used.
When done, click the Continue button.
6. To display titles, subtitles, or footnotes on the histogram, click on the Titles… button. This
will open the Titles dialog box.
In the Line 1 box, type “Scatter Plot Height vs. Weight”.
When done, click the Continue button.
7. Click OK. The Simple Scatterplot dialog box closes and SPSS activates the Output
Navigator.
Window Output
17
Ø Tutorial 2: How to Generate a Histogram
Problem
Using the data in ~ /SPSS/statdata.txt, create histogram of per capita income.
Solution
1. From the Graphs menu, select Histogram… This will open the Histogram dialog box.
2. From the variable list, select income. Left click on the right arrow button between the
variable list and the Variable box to move the variable, income, to this box.
3. Select Display normal curve box to show a normal curve on the histogram.
4. To display titles, subtitles, or footnotes on the histogram, click on the Titles… button. This
will open the Titles dialog box.
In the Line 1 box, type “Histogram of Per Capita Income”.
Click on the Continue button when done.
5. Click OK. The Histogram dialog box will close and SPSS activates the Output Navigator
to display the histogram.
18
Window Output
Ø Tutorial 3: How to Generate a Stem and Leaf Plot
Problem
Using the data in ~ /SPSS/statdata.txt, create a stem and leaf plot of per capita income.
Solution
1. From the Statistics menu, select Summarize. From the Summarize drop-down menu,
select Explore… This will open the Explore dialog box.
2. From the variable list, select income. Left click on the right arrow button between the
variable list and the Dependent List box to move the variable, income, to this box.
3. Click on the Statistics… button. This will open the Explore: Statistics dialog box.
19
To display descriptive statistics, select Descriptives.
To display maximum likelihood estimators, select M-estimators.
To display cases with the five largest and smallest values, select Outliers.
To display percentiles, select Percentiles.
In this case, none of these options are used.
When done, click on the Continue button.
4. In the Display area, select Plots. This will display the specified plot only (i.e. no statistics
are given).
5. Click on the Plots… button. This opens the Explore: Plots dialog box.
Ensure that the Stem-and-leaf box is selected.
Click on the Continue button.
6. Click on the Options button. This will open the Explore: Options button.
To exclude cases that have missing values for any of the variables used in any of the
analyses, select Exclude cases listwise. In this case, this option is used.
To exclude cases that have missing values for either or both of the pair of variables in a
specific correlation coefficient, select Exclude cases pairwise.
20
However, to treat missing values as a separate category, select Report values.
Click the Continue button when done.
7. Click OK. This will close the Explore dialog box and SPSS activates the Output Navigator
to display the stem and leaf plot.
Window Output
21
Ø Tutorial 4: How to Generate a Box Plot
Problem
Using the data in the file, ~ /SPLUS/statdata.dat, produce a boxplot of per capita income
Solution
1. From the Graphs menu, select Boxplot… This will open the Boxplot dialog box.
2. Select the Simple button.
3. Select Summaries of separate variables in the Data in Chart Are area.
4. Click on the Define button. This will open the Define Simple Boxplot: Summaries of
Separate Variables dialog box.
5. From the variable list, select income. Left click on the right arrow button between the
variable list and the Boxes Represent box to move the variable, income, to this box.
6. Click on the Options… button. This will open the Options dialog box.
To display a report of missing values, select Display groups defined by missing values. In
this case, this option will not be used.
When done, click the Continue button.
22
7. Click OK. This will close the Define Simple Boxplot: Summaries of Separate Variables
dialog box and SPSS activates the Output Navigator to display the box plot.
Window Output
23
Statistical Models in SPSS
Ø Tutorial 1: Linear Regression
The Regression submenu on the Statistics menu of the Data Editor provides regression
techniques. The following tutorial will introduce how to perform linear regression using SPSS.
The output contains goodness of fit statistics and the coefficients for the variables.
Problem
Using the data in ~/SPSS/nba.txt, compute a least squares regression line to investigate if a
player’s height can predict his weight.
Solution
1. From the Statistics menu, select Regression. From the Regression drop down menu,
select Linear… This will open the Linear Regression dialog box.
2. From the variable list, select weight. Left click on the right arrow button between the
variable list and the Dependent box to move the variable, weight, to this box.
3. From the variable list, select height. Left click on the right arrow button between the
variable list and the Independent(s) box to move the variable, height, to this box.
4. Select the method the independent variables are entered into the analysis. From the
Method drop-down menu, there is a choice of enter, stepwise, remove, backward, and
forward. In this case, we will use the enter method.
5. To limit the analysis to a subset of cases having a particular value for a variable, enter
this variable into the Selection Variable box. In this case, this option is not used.
6. Determine the variable that will identify the points on plots. Select the variable and left
click on the right arrow between the variable list and the Case Labels box. In this case,
this option is not used.
24
7. To display statistics, click on the Statistics… button. This will open the Linear Regression:
Statistics dialog box.
Select the appropriate statistics to be displayed and click on the Continue button when
done. In this case, this option is not used.
8. To display specific plots, click on the Plots… button. This will open the Linear
Regression: Plots dialog box.
From the variable list, select the variable that will be displayed on the Y axis. Left click on
the right arrow button between the variable list and the Y box. Do this also for the X axis.
When done, click on the Next button. If more plots are needed, follow the same
procedure. In this case, this option is not used.
When done defining the plots, click on the Continue button.
9. To indicate which statistics should be displayed, click on the Save button. This will open
the Linear Regression: Save dialog box.
25
Select the appropriate statistics. To save the coefficient statistics, click on the box and
indicate the file to which you want them saved. In this case, this option is not used.
10. To indicate the stepping method criteria, click the Options… button. This will open the
Linear Regression: Options dialog box.
Select the method to be used. When the selection is made, click on the Continue button.
11. Click OK. This will close the Linear Regression dialog box. SPSS activates the Output
Navigator to display the results of the analysis.
Window Output
26
Ø Tutorial 2: Analysis of Variance
Problem
Using the data in ~/SPSS/teller1.txt, test if the mean number of customers served per hour by
each of the four tellers is the same.
Solution
1. From the Statistics menu, select Compare Means. From the Compare Means drop down
menu, select One-Way ANOVA… This will open the One-Way ANOVA dialog box.
2. From the variable list, select num_cus. Left click on the right arrow button between the
variable list and the Dependent List box to move the variable, num_cus, to this box.
3. From the variable list, select teller. Left click on the right arrow button between the
variable list and the Factor box to move the variable, teller, to this box.
4. Click on the Contrasts… button. This will open the One-Way ANOVA: Contrasts dialog
box.
To partition between-groups sum of squares into polynomial trend components, select
the Polynomial box and select the highest degree of the polynomial to be modelled. In
this case, this option will not be used.
To enter a numeric coefficient value for each level, click Add. However, the number of
coefficients must equal the number of groups or the analysis is not performed. Because
the levels in this problem are already numeric, this option does not need to be used.
27
5. Click on the Post Hoc… button. This will open the One-Way ANOVA: Post Hoc Multiple
Comparisons dialog box.
If equal variances are assumed between the different factor levels, select the type of
comparison method to be used.
If equal variance are not assumed between the different factor levels, select the type of
comparison method to be used.
To get a description on each of the methods listed, right click on the word. A description
window will appear.
Click the Continue button when done.
6. Click on the Options… button. This will open the One-Way ANOVA: Options dialog box.
To display descriptive statistics, select Descriptive in the Statistics area. In this case,
select this option.
To exclude cases that have missing values for the variable involved in that test, select
Exclude cases analysis by analysis. In this case, select this option.
However, to exclude cases that have missing values for any of the variables used in any
of the analyses, select Exclude cases listwise.
Click the Continue button when done.
7. Click OK. The One-Way ANOVA dialog box closes and SPSS activates the Output
Navigator. The means of the dependent variable for each category of the independent
variable can be found under “Descriptives”.
28
Window Output
Measures of Variability
& Dispersion
The Concept of Dispersion
Dispersion refers to the variety, diversity, or amount of variation among scores
The greater the dispersion of a variable, the greater the range of scores and the greater the differences between scores
Introduction
Mueller’s & Schuessler’s Index of Qualitative Variation
Range
Variance
Standard deviation
Measures of variability or dispersion– looking at the central tendency is not enough to get a full understanding of the data.
Nominal data: Mueller’s and Schuessler’s index of qualitative variation.
Range– distance between over which particular proportions of scores are spread. (like our interval range that we already talked about).
Deviation Score– distances of scores from the means of their distribution.
Standard Deviation– the square root of the variance—important for decision making.
3
Index of qualitative variation
IQV= X 100
Number of Products=
Mueller’s and Schuessler’s index of qualitative variation– the percentage of actual heterogeneity for a particular attribute according to the expected distribution or maximum heterogeneity of that attribute.
The X100 turns the proportion to a percentage.
Heterogeneity– amount of diversity
Sum of products = the observed amount of heterogeneity
Sum of the products of the expected frequencies would be the sum of products on the expected frequency.
4
Distribution of 1,000 rape victims according to relationship with rapist
Relationship of rapist to victim
Observed rapes
Expected Rapes
Date
200
200
Close friend
100
200
Family acquaintance
200
200
Stranger
350
200
Relative
150
200
Totals
1000
1000
IQV= 95.6
100% all are the same
200 in each category would have meant that there was an equal distribution.
5
Range (R)
Range indicates the distance between the highest and lowest scores in a distribution
Range (R) = High Score – Low Score
Quick and easy indication of variability
Can be used with ordinal or interval-ratio variables
Why can’t the range be used with variables measured at the nominal level?
The range
20, 23, 25, 27, 28, 30, 35, 35, 35, 36, 39, 40, 42, 43, 44, 45, 45, 45, 46, 49
Range– distance over which 100 percent of the scores in a distribution are spread.
49-20=29
Locate Q3 and Q1
Q1: 0.25 x 20 =5
Q3: 0.75 x 20=15
Interquartile Range: 44-28 =16
7
Interquartile Range (Q)
A type of range measure
Considers only the middle 50% of the cases in a distribution
Avoids some of the problems of the range by focusing on just the middle 50% of scores
Limitation: Because the Interquartile Range is based on only two scores, it fails to yield any information from all of the other scores
Satisfaction Score
Interval
f
cf
175-179
4
111
170-174
6
107
165-169
3
101
160164
13
98
155-159
8
85
150-154
7
77
145-149
10
70
140-144
9
60
135-139
10
51
130-134
15
41
125-129
11
26
120-124
10
15
115-119
5
5
N=111
Mdn=+(fn/ff) (i)
111 x .5 =55.5
51 is a close are we can get to 55.5
Mdn=139.5+ 4.5/9 X 5
=139.5+22.5/9
=139.5 + 2.5
=142
175.5- 114.5= 61 Very unstable measure because it is very sensitive to deviant scores– poor choice if you have outliers.
Interquartile Range (Q) for grouped
111 X .25= 27.5
111
9
Range (R): Limitations
Range is based on only two scores:
Distorted by atypically high or low scores
No information about variation between high and low scores
The average deviation
AD=
x
x-x̅
23
-6
30
1
31
2
15
-14
46
17
The AD is the average variation of scores from the mean of their distribution.
= deviation score
= the sum of the absolute deviation scores
N= sample size.
Take each score and subtract it from the mean to get .
Taking the absolute of each deviation turns the deviations into positive numbers.
Way to check yourself– if the mean was calculated correctly, the sum of all the deviation scores will always equal 0.
11
Standard Deviation: Calculations
To solve:
Subtract mean from each score
Square the deviations
Sum the squared deviations
Divide the sum of the squared deviations by N
Find the square root of the result
Ungrouped Data:
Variance & Standard deviation
X
1
20
-5
25
2
21
-4
16
3
22
-3
9
4
23
-2
4
5
24
1
1
6
25
0
0
7
26
1
1
8
27
2
4
9
28
3
9
10
29
4
16
11
30
5
25
N=11
= 110
S=
S=
Variance– the sum of the squared deviations scores divided by N
= the sum of the squared deviation scores
N= sample size.
Standard deviation is the square root of the variance
13
Grouped Data:
variance & standard deviation
=
14
Distribution of Scores
Interval
f
652-653
4
650-651
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IBM
SPSS Statistics V27 Brief Guide
IBM
Note
Before using this information and the product it supports, read the information in “
” on page
81.
Product Information
This edition applies to version 27, release 0, modification 0 of
IBM®
SPSS® Statistics and to all subsequent releases and
modifications until otherwise indicated in new editions.
© Copyright International Business Machines Corporation .
US Government Users Restricted Rights – Use, duplication or disclosure restricted by GSA ADP Schedule Contract with
IBM Corp.
Chapter 1. Introduction…………………………………………………………………………….. 1
Sample Files………………………………………………………………………………………………………………………………. 1
Opening a Data File…………………………………………………………………………………………………………………….. 1
Running an Analysis …………………………………………………………………………………………………………………… 2
Creating Charts……………………………………………………………………………………………………………………………4
Chapter 2. Reading Data……………………………………………………………………………. 7
Basic Structure of IBM SPSS Statistics Data Files………………………………………………………………………….. 7
Reading IBM SPSS Statistics Data Files………………………………………………………………………………………… 7
Reading Excel Data…………………………………………………………………………………………………………………….. 8
Reading Data from a Database……………………………………………………………………………………………………11
Reading Data from a Text File……………………………………………………………………………………………………. 13
Chapter 3. Using the Data Editor……………………………………………………………….. 17
Entering Numeric Data……………………………………………………………………………………………………………….17
Entering String Data…………………………………………………………………………………………………………………..18
Defining Data…………………………………………………………………………………………………………………………….19
Adding Variable Labels………………………………………………………………………………………………………….19
Changing Variable Type and Format………………………………………………………………………………………. 20
Adding Value Labels…………………………………………………………………………………………………………….. 20
Handling Missing Data…………………………………………………………………………………………………………..21
Missing Values for a Numeric Variable…………………………………………………………………………………… 21
Missing Values for a String Variable………………………………………………………………………………………..22
Chapter 4. Examining Summary Statistics for Individual Variables……………………23
Level of Measurement………………………………………………………………………………………………………………. 23
Summary Measures for Categorical Data……………………………………………………………………………………..23
Charts for Categorical Data…………………………………………………………………………………………………… 24
Summary Measures for Scale Variables……………………………………………………………………………………….25
Histograms for Scale Variables……………………………………………………………………………………………… 26
Chapter 5. Creating and editing charts……………………………………………………….. 27
Chart creation basics………………………………………………………………………………………………………………… 27
Using the Chart Builder gallery……………………………………………………………………………………………… 27
Defining variables and statistics……………………………………………………………………………………………. 28
Adding text…………………………………………………………………………………………………………………………. 29
Creating the chart…………………………………………………………………………………………………………………30
Chapter 6. Working with Output…………………………………………………………………33
Using the Viewer………………………………………………………………………………………………………………………. 33
Using the Pivot Table Editor………………………………………………………………………………………………………. 34
Accessing Output Definitions…………………………………………………………………………………………………34
Pivoting Tables……………………………………………………………………………………………………………………. 35
Creating and Displaying Layers………………………………………………………………………………………………36
Editing Tables……………………………………………………………………………………………………………………… 36
Hiding Rows and Columns……………………………………………………………………………………………………. 37
Changing Data Display Formats…………………………………………………………………………………………….. 37
TableLooks……………………………………………………………………………………………………………………………….39
Using Predefined Formats……………………………………………………………………………………………………..39
Customizing TableLook Styles………………………………………………………………………………………………. 39
iii
Changing the Default Table Formats……………………………………………………………………………………… 41
Customizing the Initial Display Settings………………………………………………………………………………….42
Displaying Variable and Value Labels…………………………………………………………………………………….. 43
Using Results in Other Applications……………………………………………………………………………………………. 44
Pasting Results as Word Tables……………………………………………………………………………………………..45
Pasting Results as Text………………………………………………………………………………………………………… 45
Exporting Results to Microsoft Word, PowerPoint, and Excel Files…………………………………………….46
Exporting Results to PDF……………………………………………………………………………………………………….51
Exporting Results to HTML…………………………………………………………………………………………………….53
Chapter 7. Working with Syntax…………………………………………………………………55
Pasting Syntax…………………………………………………………………………………………………………………………..55
Editing Syntax………………………………………………………………………………………………………………………….. 56
Opening and Running a Syntax File……………………………………………………………………………………………..57
Using Breakpoints……………………………………………………………………………………………………………………..57
Chapter 8. Modifying Data Values……………………………………………………………….59
Creating a Categorical Variable from a Scale Variable……………………………………………………………………59
Computing New Variables…………………………………………………………………………………………………………. 61
Using Functions in Expressions…………………………………………………………………………………………….. 62
Using Conditional Expressions……………………………………………………………………………………………….63
Working with Dates and Times……………………………………………………………………………………………………63
Calculating the Length of Time between Two Dates…………………………………………………………………64
Adding a Duration to a Date………………………………………………………………………………………………….. 65
Chapter 9. Sorting and Selecting Data………………………………………………………… 67
Sorting Data………………………………………………………………………………………………………………………………67
Split-File Processing…………………………………………………………………………………………………………………. 67
Sorting Cases for Split-File Processing……………………………………………………………………………………69
Turning Split-File Processing On and Off…………………………………………………………………………………69
Selecting Subsets of Cases…………………………………………………………………………………………………………69
Selecting Cases Based on Conditional Expressions………………………………………………………………….70
Selecting a Random Sample…………………………………………………………………………………………………. 71
Selecting a Time Range or Case Range………………………………………………………………………………….. 71
Treatment of Unselected Cases……………………………………………………………………………………………..72
Case Selection Status……………………………………………………………………………………………………………….. 72
Chapter 10. Sample Files…………………………………………………………………………. 73
Notices………………………………………………………………………………………………….81
Trademarks……………………………………………………………………………………………………………………………… 82
…………………………………………………………………………………………………… 83
iv
Chapter 1. Introduction
This guide will show you how to use many of the available features. It is designed to provide a step-by-
step, hands-on guide. All of the files shown in the examples are installed with the application so that you
can follow along, performing the same analyses and obtaining the same results shown here.
If you want detailed examples of various statistical analysis techniques, try the step-by-step Case
Studies, available from the Help menu.
Sample Files
Most of the examples that are presented here use the data file demo.sav. This data file is a fictitious
survey of several thousand people, containing basic demographic and consumer
information.
If you are using the Student version, your version of demo.sav is a representative sample of the original
data file, reduced to meet the 1,500-case limit. Results that you obtain using that data file will differ from
the results shown here.
The sample files installed with the product can be found in the Samples subdirectory of the installation
directory. There is a separate folder within the Samples subdirectory for each of the following languages:
English, French, German, Italian, Japanese, Korean, Polish, Russian, Simplified Chinese, Spanish, and
Traditional Chinese.
Not all sample files are available in all languages. If a sample file is not available in a language, that
language folder contains an English version of the sample file.
Opening a Data File
To open a data file:
1. From the menus choose:
File > Open > Data…
A dialog box for opening files is displayed.
By default, IBM SPSS Statistics data files (.sav extension) are displayed.
This example uses the file demo.sav.
Figure 1. demo.sav file in Data Editor
The data file is displayed in the Data Editor. In Data View, if you put the mouse cursor on a variable
name (the column headings), a more descriptive variable label is displayed (if a label has been defined
for that variable).
By default, the actual data values are displayed. To display labels:
2. From the menus choose:
View > Value Labels
Figure 2. Value Labels button
Alternatively, you can use the Value Labels button on the toolbar.
Figure 3. Value labels displayed in the Data Edit
or
Descriptive value labels are now displayed to make it easier to interpret the responses.
Running an Analysis
If you have any add-on options, the Analyze menu contains a list of reporting and statistical analysis
categories.
We will start by creating a simple frequency table (table of counts). This example requires the Statistics
Base option.
1. From the menus choose:
Analyze > Descriptive Statistics > Frequencies…
The Frequencies dialog box is displayed.
2 IBM SPSS Statistics V27 Brief Guide
Figure 4. Frequencies dialog box
An icon next to each variable provides information about data type and level of measurement.
Numeric String Date Time
Scale (Continuous) n/a
Ordinal
Nominal
If the variable label and/or name appears truncated in the list, the complete label/name is displayed
when the cursor is positioned over it. The variable name inccat is displayed in square brackets after
the descriptive variable label. Income category in thousands is the variable label. If there were no
variable label, only the variable name would appear in the list box.
You can resize dialog boxes just like windows, by clicking and dragging the outside borders or corners.
For example, if you make the dialog box wider, the variable lists will also be wider.
In the dialog box, you choose the variables that you want to analyze from the source list on the left and
drag and drop them into the Variable(s) list on the right. The OK button, which runs the analysis, is
disabled until at least one variable is placed in the Variable(s) list.
In many dialogs, you can obtain additional information by right-clicking any variable name in the list
and selecting Variable Information from the pop-up menu.
2. Click Gender [gender] in the source variable list and drag the variable into the target Variable(s) list.
3. Click Income category in thousands [inccat] in the source list and drag it to the target list.
Chapter 1. Introduction 3
Figure 5. Variables selected for analysis
4. Click OK to run the procedure.
Results are displayed in the Viewer window.
Figure 6. Frequency table of income categories
Creating Charts
Although some statistical procedures can create charts, you can also use the Graphs menu to create
charts.
For example, you can create a chart that shows the relationship between wireless telephone service and
PDA (personal digital assistant) ownership.
1. From the menus choose:
Graphs > Chart Builder…
4 IBM SPSS Statistics V27 Brief Guide
Figure 7. Chart Builder dialog box with completed drop zones
2. Click the Gallery tab (if it is not selected).
3. Click Bar (if it is not selected).
4. Drag the Clustered Bar icon onto the canvas, which is the large area above the Gallery.
5. Scroll down the Variables list, right-click Wireless service [wireless], and then choose Nominal as its
measurement level.
6. Drag the Wireless service [wireless] variable to the x axis.
7. Right-click Owns PDA [ownpda] and choose Nominal as its measurement level.
8. Drag the Owns PDA [ownpda] variable to the cluster drop zone in the upper right corner of the canvas.
9. Click OK to create the chart.
Chapter 1. Introduction 5
Figure 8. Bar chart displayed in Viewer window
The bar chart is displayed in the Viewer. The chart shows that people with wireless phone service are far
more likely to have PDAs than people without wireless service.
You can edit charts and tables by double-clicking them in the contents pane of the Viewer window, and
you can copy and paste your results into other applications. Those topics will be covered later.
6 IBM SPSS Statistics V27 Brief Guide
Chapter 2. Reading Data
Data can be entered directly, or it can be imported from a number of different sources. The processes for
reading data stored in IBM SPSS Statistics data files; spreadsheet applications, such as Microsoft Excel;
database applications, such as Microsoft Access; and text files are all discussed in this chapter.
Basic Structure of IBM SPSS Statistics Data Files
Figure 9. Data Editor
IBM SPSS Statistics data files are organized by cases (rows) and variables (columns). In this data file,
cases represent individual respondents to a survey. Variables represent responses to each question
asked in the survey.
Reading IBM SPSS Statistics Data Files
IBM SPSS Statistics data files, which have a .sav file extension, contain your saved data.
1. From the menus choose:
File > Open > Data…
2. Browse to and open demo.sav. See the topic Chapter 10, “Sample Files,” on page 73 for more
information.
The data are now displayed in the Data Editor.
Figure 10. Opened data file
Reading Excel Data
Rather than typing all of your data directly into the Data Editor, you can read data from applications such
as Microsoft Excel. You can also read column headings as variable names.
1. From the menus choose:
File > Import Data > Excel
2. Go to the Samples\English folder and select demo.xlsx.
The Read Excel File dialog displays a preview of the data file. The contents of the first sheet in the file
are displayed. If the file has multiple sheets, you can select the sheet from the list.
You can see that some of the string values for Gender have leading spaces. Some of the values for
MaritalStatus are displayed as periods (.).
8 IBM SPSS Statistics V27 Brief Guide
Figure 11. Read Excel File dialog
3. Make sure Read variable names from the first row of data is selected. If the column headings do not
conform to variable name rules, they are converted to valid variable names. The original column
headings are saved as variable labels.
4. Select Remove leading spaces from string values.
5. Deselect Percentage of values that determine data type.
Chapter 2. Reading Data 9
The string value “no answer” is now displayed in the cells that were system-missing. If there is no
percentage of values parameter and the column contains a mix of data type, the variable is read as a
string data type. All values are preserved, but numeric values are treated as string values.
6. Select (check) Percentage of values that determine data type to treat MaritalStatus as a numeric
variable.
7. Click OK to read the Excel file.
The data now appear in the Data Editor, with the column headings used as variable names. Since variable
names can’t contain spaces, the spaces from the original column headings are removed. For example, the
column heading”Marital Status” is converted to the variable MaritalStatus. The original column heading is
retained as a variable label.
Figure 12. Imported Excel data
10 IBM SPSS Statistics V27 Brief Guide
Related information
“Sample Files” on page 73
Reading Data from a Database
Data from database sources are easily imported using the Database Wizard. Any database that uses
ODBC (Open Database Connectivity) drivers can be read directly after the drivers are installed. ODBC
drivers for many database formats are supplied on the installation CD. Additional drivers can be obtained
from third-party vendors. One of the most common database applications, Microsoft Access, is discussed
in this example.
Note: This example is specific to Microsoft Windows and requires an ODBC driver for Access. The
Microsoft Access ODBC driver only works with the 32-bit version of IBM SPSS Statistics. The steps are
similar on other platforms but may require a third-party ODBC driver for Access.
1. From the menus choose:
File > Import Data > Database > New Query…
Figure 13. Database Wizard Welcome dialog box
2. Select MS Access Database from the list of data sources and click Next.
Note: Depending on your installation, you may also see a list of OLEDB data sources on the left side of
the wizard (Windows operating systems only), but this example uses the list of ODBC data sources
displayed on the right side.
Chapter 2. Reading Data 11
3. Click Browse to navigate to the Access database file that you want to open.
4. Open demo.mdb. See the topic Chapter 10, “Sample Files,” on page 73 for more information.
5. Click OK in the login dialog box.
In the next step, you can specify the tables and variables that you want to import.
Figure 14. Select Data step
6. Drag the entire demo table to the Retrieve Fields In This Order list.
7. Click Next.
In the next step, you can select which records (cases) to import.
If you do not want to import all cases, you can import a subset of cases (for example, males older
than 30), or you can import a random sample of cases from the data source. For large data sources,
you may want to limit the number of cases to a small, representative sample to reduce the
processing time.
8. Click Next to continue.
Field names are used to create variable names. If necessary, the names are converted to valid
variable names. The original field names are preserved as variable labels. You can also change the
variable names before importing the database.
12 IBM SPSS Statistics V27 Brief Guide
Figure 15. Define Variables step
9. Click the Recode to Numeric cell in the Gender field. This option converts string variables to integer
variables and retains the original value as the value label for the new variable.
10. Click Next to continue.
The SQL statement created from your selections in the Database Wizard appears in the Results step.
This statement can be executed now or saved to a file for later use.
11. Click Finish to import the data.
All of the data in the Access database that you selected to import are now available in the Data Editor.
Reading Data from a Text File
Text files represent another common source of data. Many spreadsheet programs and databases can
save their contents in one of many text file formats. Comma- or tab-delimited files refer to rows of data
that use commas or tabs to indicate each variable. In this example, the data is tab-delimited.
1. From the menus choose:
File > Import Data > Text Data
2. Go to the Samples\English folder and select demo.txt.
The Text Import Wizard guides you through the process of defining how the specified text file is
interpreted.
Chapter 2. Reading Data 13
Figure 16. Text Import Wizard: Step 1 of 6
3. In Step 1, you can choose a predefined format or create a new format in the wizard. Select No.
4. Click Next to continue.
As stated earlier, this file uses tab-delimited formatting. Also, the variable names are defined on the
top line of this file.
5. In step 2 of the wizard, select Delimited to indicate that the file has a delimited formatting structure.
6. Select Yes to indicate that the file includes variable names at the top of the file.
7. Click Next to continue.
8. In step 3, enter 2 for the line number where the first case of data begins (because variable names are
on the first line).
9. Keep the default values for the remainder of this step, and click Next to continue.
The Data preview in Step 4 provides you with a quick way to ensure that the file is read correctly
10. Select Tab and deselect the other options for delimiters. Space is selected by default because the
file contains spaces. For this file, spaces are part of the data values, not delimiters. You need to
deselect Space to read the file correctly.
11. Select Remove leading spaces for string values. Spaces at the start of string values affect how
string values are evaluated in expressions. In this file, some values for Gender have leading spaces
that are not part of the value. If you do not remove those spaces, a value of ” f” is treated as a
different value than “f”.
14 IBM SPSS Statistics V27 Brief Guide
Figure 17. Text Import Wizard: Step 4 of 6
12. Click Next to continue.
Because the variable names are modified to conform to naming rules, step 5 gives you the
opportunity to edit any undesirable names.
Data types can be defined here as well. For example, you can change Income to dollar currency
format.
To change a data type:
13. In the Data preview, select Income.
14. Select Dollar from the Data format drop-down list.
Figure 18. Change the data type
Chapter 2. Reading Data 15
The variable MaritalStatus contains both string and numeric values. Less than five percent of the
values are strings. With the default setting of 95% for Percentage of values that determine the
Automatic data format, the variable is treated as numeric and the string values are set to system-
missing. If no data format meets the percentage value, the variable is treated as a string variable. If
you change the setting to 100, all values are preserved, but all numeric values are treated as strings.
15. Click Next to continue.
16. Leave the default selections in the last step, and click Finish to import the data.
16 IBM SPSS Statistics V27 Brief Guide
Chapter 3. Using the Data Editor
The Data Editor displays the contents of the active data file. The information in the Data Editor consists of
variables and cases.
• In Data View, columns represent variables, and rows represent cases (observations).
• In Variable View, each row is a variable, and each column is an attribute that is associated with that
variable.
Variables are used to represent the different types of data that you have compiled. A common analogy is
that of a survey. The response to each question on a survey is equivalent to a variable. Variables come in
many different types, including numbers, strings, currency, and dates.
Entering Numeric Data
Data can be entered into the Data Editor, which may be useful for small data files or for making minor
edits to larger data files.
1. Click the Variable View tab at the bottom of the Data Editor window.
You need to define the variables that will be used. In this case, only three variables are needed: age,
marital status, and income.
Figure 19. Variable names in Variable View
2. In the first row of the first column, type age.
3. In the second row, type marital.
4. In the third row, type income.
New variables are automatically given a Numeric data type.
If you don’t enter variable names, unique names are automatically created. However, these names
are not descriptive and are not recommended for large data files.
5. Click the Data View tab to continue entering the data.
The names that you entered in Variable View are now the headings for the first three columns in Data
View.
Begin entering data in the first row, starting at the first column.
Figure 20. Values entered in Data View
6. In the age column, type 55.
7. In the marital column, type 1.
8. In the income column, type 72000.
9. Move the cursor to the second row of the first column to add the next subject’s data.
10. In the age column, type 53.
11. In the marital column, type 0.
12. In the income column, type 153000.
Currently, the age and marital columns display decimal points, even though their values are intended
to be integers. To hide the decimal points in these variables:
13. Click the Variable View tab at the bottom of the Data Editor window.
14. In the Decimals column of the age row, type 0 to hide the decimal.
15. In the Decimals column of the marital row, type 0 to hide the decimal.
Entering String Data
Non-numeric data, such as strings of text, can also be entered into the Data Editor.
1. Click the Variable View tab at the bottom of the Data Editor window.
2. In the first cell of the first empty row, type sex for the variable name.
3. Click the Type cell next to your entry.
4. Click the button on the right side of the Type cell to open the Variable Type dialog box.
5. Select String to specify the variable type.
6. Click OK to save your selection and return to the Data Editor.
18 IBM SPSS Statistics V27 Brief Guide
Figure 21. Variable Type dialog box
Defining Data
In addition to defining data types, you can also define descriptive variable labels and value labels for
variable names and data values. These descriptive labels are used in statistical reports and charts.
Adding Variable Labels
Labels are meant to provide descriptions of variables. These descriptions are often longer versions of
variable names. Labels can be up to 255 bytes. These labels are used in your output to identify the
different
variables.
1. Click the Variable View tab at the bottom of the Data Editor window.
2. In the Label column of the age row, type Respondent’s Age.
3. In the Label column of the marital row, type Marital Status.
4. In the Label column of the income row, type Household Income.
5. In the Label column of the sex row, type Gender.
Figure 22. Variable labels entered in Variable View
Chapter 3. Using the Data Editor 19
Changing Variable Type and Format
The Type column displays the current data type for each variable. The most common data types are
numeric and string, but many other formats are supported. In the current data file, the income variable is
defined as a numeric type.
1. Click the Type cell for the income row, and then click the button on the right side of the cell to open the
Variable Type dialog box.
2. Select Dollar.
Figure 23. Variable Type dialog box
The formatting options for the currently selected data type are displayed.
3. For the format of the currency in this example, select $###,###,###.
4. Click OK to save your changes.
Adding Value Labels
Value labels provide a method for mapping your variable values to a string label. In this example, there
are two acceptable values for the marital variable. A value of 0 means that the subject is single, and a
value of 1 means that he or she is married.
1. Click the Values cell for the marital row, and then click the button on the right side of the cell to open
the Value Labels dialog box.
The value is the actual numeric value.
The value label is the string label that is applied to the specified numeric value.
2. Type 0 in the Value field.
3. Type Single in the Label field.
4. Click Add to add this label to the list.
20 IBM SPSS Statistics V27 Brief Guide
Figure 24. Value Labels dialog box
5. Type 1 in the Value field, and type Married in the Label field.
6. Click Add, and then click OK to save your changes and return to the Data Editor.
These labels can also be displayed in Data View, which can make your data more readable.
7. Click the Data View tab at the bottom of the Data Editor window.
8. From the menus choose:
View > Value Labels
The labels are now displayed in a list when you enter values in the Data Editor. This setup has the benefit
of suggesting a valid response and providing a more descriptive answer.
If the Value Labels menu item is already active (with a check mark next to it), choosing Value Labels
again will turn off the display of value labels.
Handling Missing Data
Missing or invalid data are generally too common to ignore. Survey respondents may refuse to answer
certain questions, may not know the answer, or may answer in an unexpected format. If you don’t filter or
identify these data, your analysis may not provide accurate results.
For numeric data, empty data fields or fields containing invalid entries are converted to system-missing,
which is identifiable by a single period.
The reason a value is missing may be important to your analysis. For example, you may find it useful to
distinguish between those respondents who refused to answer a question and those respondents who
didn’t answer a question because it was not applicable.
Missing Values for a Numeric Variable
1. Click the Variable View tab at the bottom of the Data Editor window.
2. Click the Missing cell in the age row, and then click the button on the right side of the cell to open the
Missing Values dialog box.
In this dialog box, you can specify up to three distinct missing values, or you can specify a range of
values plus one additional discrete value.
Chapter 3. Using the Data Editor 21
Figure 25. Missing Values dialog box
3. Select Discrete missing values.
4. Type 999 in the first text box and leave the other two text boxes empty.
5. Click OK to save your changes and return to the Data Editor.
Now that the missing data value has been added, a label can be applied to that value.
6. Click the Values cell in the age row, and then click the button on the right side of the cell to open the
Value Labels dialog box.
7. Type 999 in the Value field.
8. Type No Response in the Label field.
9. Click Add to add this label to your data file.
10. Click OK to save your changes and return to the Data Editor.
Missing Values for a String Variable
Missing values for string variables are handled similarly to the missing values for numeric variables.
However, unlike numeric variables, empty fields in string variables are not designated as system-missing.
Rather, they are interpreted as an empty string.
1. Click the Variable View tab at the bottom of the Data Editor window.
2. Click the Missing cell in the sex row, and then click the button on the right side of the cell to open the
Missing Values dialog box.
3. Select Discrete missing values.
4. Type NR in the first text box.
Missing values for string variables are case sensitive. So, a value of nr is not treated as a missing
value.
5. Click OK to save your changes and return to the Data Editor.
Now you can add a label for the missing value.
6. Click the Values cell in the sex row, and then click the button on the right side of the cell to open the
Value Labels dialog box.
7. Type NR in the Value field.
8. Type No Response in the Label field.
9. Click Add to add this label to your project.
10. Click OK to save your changes and return to the Data Editor.
22 IBM SPSS Statistics V27 Brief Guide
Chapter 4. Examining Summary Statistics for
Individual Variables
This section discusses simple summary measures and how the level of measurement of a variable
influences the types of statistics that should be used. We will use the data file demo.sav. See the topic
Chapter 10, “Sample Files,” on page 73 for more information.
Level of Measurement
Different summary measures are appropriate for different types of data, depending on the level of
measurement:
Categorical. Data with a limited number of distinct values or categories (for example, gender or marital
status). Also referred to as qualitative data. Categorical variables can be string (alphanumeric) data or
numeric variables that use numeric codes to represent categories (for example, 0 = Unmarried and 1 =
Married). There are two basic types of categorical data:
• Nominal. Categorical data where there is no inherent order to the categories. For example, a job
category of sales is not higher or lower than a job category of marketing or research.
• Ordinal. Categorical data where there is a meaningful order of categories, but there is not a measurable
distance between categories. For example, there is an order to the values high, medium, and low, but
the “distance” between the values cannot be calculated.
Scale. Data measured on an interval or ratio scale, where the data values indicate both the order of
values and the distance between values. For example, a salary of $72,195 is higher than a salary of
$52,398, and the distance between the two values is $19,797. Also referred to as quantitative or
continuous data.
Summary Measures for Categorical Data
For categorical data, the most typical summary measure is the number or percentage of cases in each
category. The mode is the category with the greatest number of cases. For ordinal data, the median (the
value at which half of the cases fall above and below) may also be a useful summary measure if there is a
large number of categories.
The Frequencies procedure produces frequency tables that display both the number and percentage of
cases for each observed value of a variable.
1. From the menus choose:
Analyze > Descriptive Statistics > Frequencies…
Note: This feature requires the Statistics Base option.
2. Select Owns PDA [ownpda] and Owns TV [owntv] and move them into the Variable(s) list.
Figure 26. Categorical variables selected for analysis
3. Click OK to run the procedure.
Figure 27. Frequency tables
The frequency tables are displayed in the Viewer window. The frequency tables reveal that only 20.4% of
the people own PDAs, but almost everybody owns a TV (99.0%). These might not be interesting
revelations, although it might be interesting to find out more about the small group of people who do not
own televisions.
Charts for Categorical Data
You can graphically display the information in a frequency table with a bar chart or pie chart.
1. Open the Frequencies dialog box again. (The two variables should still be selected.)
You can use the Dialog Recall button on the toolbar to quickly return to recently used procedures.
Figure 28. Dialog Recall button
2. Click Charts.
24 IBM SPSS Statistics V27 Brief Guide
3. Select Bar charts and then click Continue.
4. Click OK in the main dialog box to run the procedure.
Figure 29. Bar chart
In addition to the frequency tables, the same information is now displayed in the form of bar charts,
making it easy to see that most people do not own PDAs but almost everyone owns a TV.
Summary Measures for Scale Variables
There are many summary measures available for scale variables, including:
• Measures of central tendency. The most common measures of central tendency are the mean
(arithmetic average) and median (value at which half the cases fall above and below).
• Measures of dispersion. Statistics that measure the amount of variation or spread in the data include
the standard deviation, minimum, and maximum.
1. Open the Frequencies dialog box again.
2. Click Reset to clear any previous settings.
3. Select Household income in thousands [income] and move it into the Variable(s) list.
4. Click Statistics.
5. Select Mean, Median, Std. deviation, Minimum, and Maximum.
6. Click Continue.
7. Deselect Display frequency tables in the main dialog box. (Frequency tables are usually not useful for
scale variables since there may be almost as many distinct values as there are cases in the data file.)
8. Click OK to run the procedure.
The Frequencies Statistics table is displayed in the Viewer window.
Chapter 4. Examining Summary Statistics for Individual Variables 25
Figure 30. Frequencies Statistics table
In this example, there is a large difference between the mean and the median. The mean is almost
25,000 greater than the median, indicating that the values are not normally distributed. You can visually
check the distribution with a histogram.
Histograms for Scale Variables
1. Open the Frequencies dialog box again.
2. Click Charts.
3. Select Histograms and With normal curve.
4. Click Continue, and then click OK in the main dialog box to run the procedure.
Figure 31. Histogram
The majority of cases are clustered at the lower end of the scale, with most falling below 100,000. There
are, however, a few cases in the 500,000 range and beyond (too few to even be visible without modifying
the histogram). These high values for only a few cases have a significant effect on the mean but little or no
effect on the median, making the median a better indicator of central tendency in this example.
26 IBM SPSS Statistics V27 Brief Guide
Chapter 5. Creating and editing charts
You can create and edit a wide variety of chart types. In this chapter, we will create and edit bar charts.
You can apply the principles to any chart type.
Chart creation basics
To demonstrate the basics of chart creation, we will create a bar chart of mean income for different levels
of job satisfaction. This example uses the data file demo.sav. See the topic Chapter 10, “Sample Files,” on
page 73 for more information.
1. From the menus choose:
Graphs > Chart Builder…
The Chart Builder dialog box is an interactive window that allows you to preview how a chart will look
while you build it.
Figure 32. Chart Builder dialog box
Using the Chart Builder gallery
1. Click the Gallery tab if it is not selected.
The Gallery includes many different predefined charts, which are organized by chart type. The Basic
Elements tab also provides basic elements (such as axes and graphic elements) for creating charts
from scratch, but it’s easier to use the Gallery.
2. Click Bar if it is not selected.
Icons representing the available bar charts in the Gallery appear in the dialog box. The pictures should
provide enough information to identify the specific chart type. If you need more information, you can
also display a ToolTip description of the chart by pausing your cursor over an icon.
3. Drag the icon for the simple bar chart onto the “canvas,” which is the large area above the Gallery. The
Chart Builder displays a preview of the chart on the canvas. Note that the data used to draw the chart
are not your actual data. They are example data.
Figure 33. Bar chart on Chart Builder canvas
Defining variables and statistics
Although there is a chart on the canvas, it is not complete because there are no variables or statistics to
control how tall the bars are and to specify which variable category corresponds to each bar. You can’t
have a chart without variables and statistics. You add variables by dragging them from the Variables list,
which is located to the left of the canvas.
A variable’s measurement level is important in the Chart Builder. You are going to use the Job satisfaction
variable on the x axis. However, the icon (which looks like a ruler) next to the variable indicates that its
measurement level is defined as scale. To create the correct chart, you must use a categorical
measurement level. Instead of going back and changing the measurement level in the Variable View, you
can change the measurement level temporarily in the Chart Builder.
1. Right-click Job satisfaction in the Variables list and choose Ordinal. Ordinal is an appropriate
measurement level because the categories in Job satisfaction can be ranked by level of satisfaction.
Note that the icon changes after you change the measurement level.
2. Now drag Job satisfaction from the Variables list to the x axis drop zone.
28 IBM SPSS Statistics V27 Brief Guide
The y axis drop zone defaults to the Count statistic. If you want to use another statistic (such as
percentage or mean), you can easily change it. You will not use either of these statistics in this
example, but we will review the process in case you need to change this statistic at another time.
3. Click the Element Properties tab in the side bar of the Chart Builder. (If the side bar is not displayed,
click the button in the upper right corner of the Chart Builder to display the side bar.)
Figure 34. Element Properties
Element Properties allows you to change the properties of the various chart elements. These elements
include the graphic elements (such as the bars in the bar chart) and the axes on the chart. Select one
of the elements in the Edit Properties of list to change the properties associated with that element.
Also note the red X located to the right of the list. This button deletes a graphic element from the
canvas. Because Bar1 is selected, the properties shown apply to graphic elements, specifically the bar
graphic element.
The Statistic drop-down list shows the specific statistics that are available. The same statistics are
usually available for every chart type. Be aware that some statistics require that the y axis drop zone
contains a variable.
4. Drag Household income in thousands from the Variables list to the y axis drop zone. Because the
variable on the y axis is scalar and the x axis variable is categorical (ordinal is a type of categorical
measurement level), the y axis drop zone defaults to the Mean statistic. These are the variables and
statistics you want, so there is no need to change the element properties.
Adding text
You can also add titles and footnotes to the chart.
1. Click the Titles/Footnotes tab.
2. Select Title 1.
Chapter 5. Creating and editing charts 29
Figure 35. Title 1 displayed on canvas
The title appears on the canvas with the label T1.
3. In the Element Properties tab, select Title 1 in the Edit Properties of list.
4. In the Content text box, type Income by Job Satisfaction. This is the text that the title will
display.
Creating the chart
1. Click OK to create the bar chart.
30 IBM SPSS Statistics V27 Brief Guide
Figure 36. Bar chart
The bar chart reveals that respondents who are more satisfied with their jobs tend to have higher
household incomes.
Chapter 5. Creating and editing charts 31
32 IBM SPSS Statistics V27 Brief Guide
Chapter 6. Working with Output
The results from running a statistical procedure are displayed in the Viewer. The output produced can be
statistical tables, charts, graphs, or text, depending on the choices you make when you run the procedure.
This section uses the files viewertut.spv and demo.sav. See the topic Chapter 10, “Sample Files,” on page
73 for more information.
Using the Viewer
Figure 37. Viewer
The Viewer window is divided into two panes. The outline pane contains an outline of all of the
information stored in the Viewer. The contents pane contains statistical tables, charts, and text output.
Use the scroll bars to navigate through the window’s contents, both vertically and horizontally. For easier
navigation, click an item in the outline pane to display it in the contents pane.
1. Click and drag the right border of the outline pane to change its width.
An open book icon in the outline pane indicates that it is currently visible in the Viewer, although it may
not currently be in the visible portion of the contents pane.
2. To hide a table or chart, double-click its book icon in the outline pane.
The open book icon changes to a closed book icon, signifying that the information associated with it is
now hidden.
3. To redisplay the hidden output, double-click the closed book icon.
You can also hide all of the output from a particular statistical procedure or all of the output in the
Viewer.
4. Click the box with the minus sign (−) to the left of the procedure whose results you want to hide, or
click the box next to the topmost item in the outline pane to hide all of the output.
The outline collapses, visually indicating that these results are hidden.
You can also change the order in which the output is displayed.
5. In the outline pane, click the items that you want to move.
6. Drag the selected items to a new location in the outline.
Figure 38. Reordered output in the Viewer
You can also move output items by clicking and dragging them in the contents pane.
Using the Pivot Table Editor
The results from most statistical procedures are displayed in pivot tables.
Accessing Output Definitions
Many statistical terms are displayed in the output. Definitions of these terms can be accessed directly in
the Viewer.
1. Double-click the Owns PDA * Gender * Internet Crosstabulation table.
2. Right-click Expected Count and choose What’s This? from the pop-up menu.
The definition is displayed in a pop-up window.
Figure 39. Pop-up definition
34 IBM SPSS Statistics V27 Brief Guide
Pivoting Tables
The default tables produced may not display information as neatly or as clearly as you would like. With
pivot tables, you can transpose rows and columns (“flip” the table), adjust the order of data in a table, and
modify the table in many other ways. For example, you can change a short, wide table into a long, thin one
by transposing rows and columns. Changing the layout of the table does not affect the results. Instead,
it’s a way to display your information in a different or more desirable manner.
1. If it’s not already activated, double-click the Owns PDA * Gender * Internet Crosstabulation table to
activate it.
2. If the Pivoting Trays window is not visible, from the menus choose:
Pivot > Pivoting Trays
Pivoting trays provide a way to move data between columns, rows, and layers.
Figure 40. Pivoting trays
3. Drag the Statistics element from the Row dimension to the Column dimension, below Gender. The
table is immediately reconfigured to reflect your changes.
The order of the elements in the pivoting tray reflects the order of the elements in the table.
4. Drag and drop the Owns PDA element before the Internet element in the row dimension to reverse the
order of these two rows.
Chapter 6. Working with Output 35
Figure 41. Swap rows
Creating and Displaying Layers
Layers can be useful for large tables with nested categories of information. By creating layers, you
simplify the look of the table, making it easier to read.
1. Drag the Gender element from the Column dimension to the Layer dimension.
Figure 42. Gender pivot icon in the Layer dimension
To display a different layer, select a category from the drop-down list in the table.
Editing Tables
Unless you’ve taken the time to create a custom TableLook, pivot tables are created with standard
formatting. You can change the formatting of any text within a table. Formats that you can change include
font name, font size, font style (bold or italic), and color.
1. Double-click the Level of education table.
2. If the Formatting toolbar is not visible, from the menus choose:
View > Toolbar
3. Click the title text, Level of education.
36 IBM SPSS Statistics V27 Brief Guide
4. From the drop-down list of font sizes on the toolbar, choose 12.
5. To change the color of the title text, click the text color tool and choose a new color.
Figure 43. Reformatted title text in the pivot table
You can also edit the contents of tables and labels. For example, you can change the title of this table.
6. Double-click the title.
7. Type Education Level for the new label.
Note: If you change the values in a table, totals and other statistics are not recalculated.
Hiding Rows and Columns
Some of the data displayed in a table may not be useful or it may unnecessarily complicate the table.
Fortunately, you can hide entire rows and columns without losing any data.
1. If it’s not already activated, double-click the Education Level table to activate it.
2. Click Valid Percent column label to select it.
3. From the Edit menu or the right-click pop-up menu choose:
Select > Data and Label Cells
4. From the View menu choose Hide or from the right-click pop-up menu choose Hide Category.
The column is now hidden but not deleted.
Figure 44. Valid Percent column hidden in table
To redisplay the column:
5. From the menus choose:
View > Show All
Rows can be hidden and displayed in the same way as columns.
Changing Data Display Formats
You can easily change the display format of data in pivot tables.
1. If it’s not already activated, double-click the Education Level table to activate it.
Chapter 6. Working with Output 37
2. Click the Percent column label to select it.
3. From the Edit menu or the right-click pop-up menu choose:
Select > Data Cells
4. From the Format menu or the right-click pop-up menu choose Cell Properties.
5. Click the Format Value tab.
6. Type 0 in the Decimals field to hide all decimal points in this column.
Figure 45. Cell Properties, Format Value tab
You can also change the data type and format in this dialog box.
7. Select the type that you want from the Category list, and then select the format for that type in the
Format list.
8. Click OK or Apply to apply your changes.
Figure 46. Decimals hidden in Percent column
The decimals are now hidden in the Percent column.
38 IBM SPSS Statistics V27 Brief Guide
TableLooks
The format of your tables is a critical part of providing clear, concise, and meaningful results. If your table
is difficult to read, the information contained within that table may not be easily understood.
Using Predefined Formats
1. Double-click the Marital status table.
2. From the menus choose:
Format > TableLooks…
The TableLooks dialog box lists a variety of predefined styles. Select a style from the list to preview it
in the Sample window on the right.
Figure 47. TableLooks dialog box
You can use a style as is, or you can edit an existing style to better suit your needs.
3. To use an existing style, select one and click OK.
Customizing TableLook Styles
You can customize a format to fit your specific needs. Almost all aspects of a table can be customized,
from the background color to the border styles.
1. Double-click the Marital status table.
2. From the menus choose:
Format > TableLooks…
3. Select the style that is closest to the format you want and click Edit Look.
4. Click the Cell Formats tab to view the formatting options.
Chapter 6. Working with Output 39
Figure 48. Table Properties dialog box
The formatting options include font name, font size, style, and color. Additional options include
alignment, text and background colors, and margin sizes.
The Sample window on the right provides a preview of how the formatting changes affect your table.
Each area of the table can have different formatting styles. For example, you probably wouldn’t want
the title to have the same style as the data. To select a table area to edit, you can either choose the
area by name in the Area drop-down list, or you can click the area that you want to change in the
Sample window.
5. Select Data from the Area drop-down list.
6. Select a new color from the Background drop-down palette.
7. Then select a new text color.
The Sample window shows the new style.
40 IBM SPSS Statistics V27 Brief Guide
Figure 49. Changing table cell formats
8. Click OK to return to the TableLooks dialog box.
You can save your new style, which allows you to apply it to future tables easily.
9. Click Save As.
10. Navigate to the target directory and enter a name for your new style in the File Name text box.
11. Click Save.
12. Click OK to apply your changes and return to the Viewer.
The table now contains the custom formatting that you specified.
Figure 50. Custom TableLook
Changing the Default Table Formats
Although you can change the format of a table after it has been created, it may be more efficient to
change the default TableLook so that you do not have to change the format every time you create a table.
Chapter 6. Working with Output 41
To change the default TableLook style for your pivot tables, from the menus choose:
Edit > Options…
1. Click the Pivot Tables tab in the Options dialog box.
Figure 51. Options dialog box
2. Select the TableLook style that you want to use for all new tables.
The Sample window on the right shows a preview of each TableLook.
3. Click OK to save your settings and close the dialog box.
All tables that you create after changing the default TableLook automatically conform to the new
formatting rules.
Customizing the Initial Display Settings
The initial display settings include the alignment of objects in the Viewer, whether objects are shown or
hidden by default, and the width of the Viewer window. To change these settings:
1. From the menus choose:
Edit > Options…
2. Click the Viewer tab.
42 IBM SPSS Statistics V27 Brief Guide
Figure 52. Viewer options
The settings are applied on an object-by-object basis. For example, you can customize the way charts
are displayed without making any changes to the way tables are displayed. Simply select the object
that you want to customize, and make the changes.
3. Click the Title icon to display its settings.
4. Click Center to display all titles in the (horizontal) center of the Viewer.
You can also hide elements, such as the log and warning messages, that tend to clutter your output.
Double-clicking on an icon automatically changes that object’s display property.
5. Double-click the Warnings icon to hide warning messages in the output.
6. Click OK to save your changes and close the dialog box.
Displaying Variable and Value Labels
In most cases, displaying the labels for variables and values is more effective than displaying the variable
name or the actual data value. There may be cases, however, when you want to display both the names
and the labels.
1. From the menus choose:
Edit > Options…
2. Click the Output Labels tab.
Chapter 6. Working with Output 43
Figure 53. Pivot Table Labeling settings
You can specify different settings for the outline and contents panes. For example, to show labels in
the outline and variable names and data values in the contents:
3. In the Pivot Table Labeling group, select Names from the Variables in Labels drop-down list to show
variable names instead of labels.
4. Then, select Values from the Variable Values in Labels drop-down list to show data values instead of
labels.
Subsequent tables produced in the session will reflect these changes.
Figure 54. Variable names and values displayed
Using Results in Other Applications
Your results can be used in many applications. For example, you may want to include a table or chart in a
presentation or report.
The following examples are specific to Microsoft Word, but they may work similarly in other word
processing applications.
44 IBM SPSS Statistics V27 Brief Guide
Pasting Results as Word Tables
You can paste pivot tables into Word as native Word tables. All table attributes, such as font sizes and
colors, are retained. Because the table is pasted in the Word table format, you can edit it in Word just like
any other table.
1. Click a table in the Viewer to select it.
2. From the menus choose:
Edit > Copy
3. Open your word processing application.
4. From the word processor’s menus choose:
Edit > Paste Special…
5. Select Formatted Text (RTF) in the Paste Special dialog box.
6. Click OK to paste your results into the current document.
The table is now displayed in your document. You can apply custom formatting, edit the data, and resize
the table to fit your needs.
Pasting Results as Text
Pivot tables can be copied to other applications as plain text. Formatting styles are not retained in this
method, but you can edit the table data after you paste it into the target application.
1. Click a table in the Viewer to select it.
2. From the menus choose:
Edit > Copy
3. Open your word processing application.
4. From the word processor’s menus choose:
Edit > Paste Special…
5. Select Unformatted Text in the Paste Special dialog box.
6. Click OK to paste your results into the current document.
Figure 55. Pivot table displayed in Word
Each column of the table is separated by tabs. You can change the column widths by adjusting the tab
stops in your word processing application.
Chapter 6. Working with Output 45
Exporting Results to Microsoft Word, PowerPoint, and Excel Files
You can export results to a Microsoft Word , PowerPoint, or Excel file. You can export selected items or all
items in the Viewer. This section uses the files msouttut.spv and demo.sav. See the topic Chapter 10,
“Sample Files,” on page 73 for more information.
Note: Export to PowerPoint is available only on Windows operating systems and is not available with the
Student Version.
In the Viewer’s outline pane, you can select specific items that you want to export or export all items or
all visible items.
Figure 56. Viewer
1. From the Viewer menus choose:
File > Export…
Instead of exporting all objects in the Viewer, you can choose to export only visible objects (open
books in the outline pane) or those that you selected in the outline pane. If you did not select any
items in the outline pane, you do not have the option to export selected objects.
46 IBM SPSS Statistics V27 Brief Guide
Figure 57. Export Output dialog box
2. In the Objects to Export group, select All.
3. From the Type drop-down list select Word/RTF file (* ).
4. Click OK to generate the Word file.
When you open the resulting file in Word, you can see how the results are exported. Notes, which are not
visible objects, appear in Word because you chose to export all objects.
Pivot tables become Word tables, with all of the formatting of the original pivot table retained, including
fonts, colors, borders, and so on.
Chapter 6. Working with Output 47
Figure 58. Pivot tables in Word
Charts are included in the Word document as graphic images.
Figure 59. Charts in Word
Text output is displayed in the same font used for the text object in the Viewer. For proper alignment, text
output should use a fixed-pitch (monospaced) font.
48 IBM SPSS Statistics V27 Brief Guide
Figure 60. Text output in Word
If you export to a PowerPoint file, each exported item is placed on a separate slide. Pivot tables exported
to PowerPoint become Word tables, with all of the formatting of the original pivot table, including fonts,
colors, borders, and so on.
Figure 61. Pivot tables in PowerPoint
Charts selected for export to PowerPoint are embedded in the PowerPoint file.
Chapter 6. Working with Output 49
Figure 62. Charts in PowerPoint
Note: Export to PowerPoint is available only on Windows operating systems and is not available with the
Student Version.
If you export to an Excel file, results are exported differently.
Figure 63. Output.xls in Excel
Pivot table rows, columns, and cells become Excel rows, columns, and cells.
Each line in the text output is a row in the Excel file, with the entire contents of the line contained in a
single cell.
50 IBM SPSS Statistics V27 Brief Guide
Figure 64. Text output in Excel
Exporting Results to PDF
You can export all or selected items in the Viewer to a PDF (portable document format) file.
1. From the menus in the Viewer window that contains the result you want to export to PDF choose:
File > Export…
2. In the Export Output dialog box, from the Export Format File Type drop-down list choose Portable
Document Format.
Chapter 6. Working with Output 51
Figure 65. Export Output dialog box
• The outline pane of the Viewer document is converted to bookmarks in the PDF file for easy navigation.
• Page size, orientation, margins, content and display of page headers and footers, and printed chart size
in PDF documents are controlled by page setup options (File menu, Page Setup in the Viewer window).
• The resolution (DPI) of the PDF document is the current resolution setting for the default or currently
selected printer (which can be changed using Page Setup). The maximum resolution is 1200 DPI. If the
printer setting is higher, the PDF document resolution will be 1200 DPI. Note: High-resolution
documents may yield poor results when printed on lower-resolution printers.
52 IBM SPSS Statistics V27 Brief Guide
Figure 66. PDF file with bookmarks
Exporting Results to HTML
You can also export results to HTML (hypertext markup language). When saving as HTML, all non-graphic
output is exported into a single HTML file.
Figure 67. Output.htm in Web browser
When you export to HTML, charts can be exported as well, but not to a single file.
Chapter 6. Working with Output 53
Figure 68. Chart in HTML
Each chart will be saved as a file in a format that you specify, and references to these graphics files will be
placed in the HTML. There is also an option to export all charts (or selected charts) to separate graphics
files.
54 IBM SPSS Statistics V27 Brief Guide
Chapter 7. Working with Syntax
You can save and automate many common tasks by using the powerful command language. It also
provides some functionality not found in the menus and dialog boxes. Most commands are accessible
from the menus and dialog boxes. However, some commands and options are available only by using the
command language. The command language also allows you to save your jobs in a syntax file so that you
can repeat your analysis at a later date.
A command syntax file is simply a text file that contains IBM SPSS Statistics syntax commands. You can
open a syntax window and type commands directly, but it is often easier to let the dialog boxes do some
or all of the work for you.
The examples in this chapter use the data file demo.sav. See the topic Chapter 10, “Sample Files,” on
page 73 for more information.
Note: Command syntax is not available with the Student Version.
Pasting Syntax
The easiest way to create syntax is to use the Paste button located on most dialog boxes.
1. Open the data file demo.sav. See the topic Chapter 10, “Sample Files,” on page 73 for more
information.
2. From the menus choose:
Analyze > Descriptive Statistics > Frequencies…
3. Select Marital status [marital] and move it into the Variable(s) list.
4. Click Charts.
5. In the Charts dialog box, select Bar charts.
6. In the Chart Values group, select Percentages.
7. Click Continue.Click Paste to copy the syntax created as a result of the dialog box selections to the
Syntax Editor.
Figure 69. Frequencies dialog box
Figure 70. Frequencies syntax
8. To run the syntax currently displayed, from the menus choose:
Run > Selection
Editing Syntax
In the syntax window, you can edit the syntax. For example, you could change the subcommand /
BARCHART to display frequencies instead of percentages. (A subcommand is indicated by a slash.) If you
know the keyword for displaying frequencies you can enter it directly. If you don’t know the keyword, you
can obtain a list of the available keywords for the subcommand by positioning the cursor anywhere
following the subcommand name and pressing Ctrl+Spacebar. This displays the auto-completion control
for the subcommand.
Delete the keyword PERCENT from the BARCHART subcommand.
Press Ctrl-Spacebar.
1. click the item labelled FREQ for frequencies. Clicking on an item in the auto-completion control will
insert it at the current cursor position.
By default, the auto-completion control will prompt you with a list of available terms as you type. For
example, you’d like to include a pie chart along with the bar chart. The pie chart is specified with a
separate subcommand.
2. Press Enter after the FREQ keyword and type a forward slash to indicate the start of a subcommand.
The Syntax Editor prompts you with the list of subcommands for the current command.
Figure 71. Auto-completion control displaying subcommands
56 IBM SPSS Statistics V27 Brief Guide
To obtain more detailed help for the current command, press the F1 key. This takes you directly to the
command syntax reference information for the current command.
You may have noticed that text displayed in the syntax window is colored. Color coding allows you to
quickly identify unrecognized terms, since only recognized terms are colored. For example, you misspell
the FORMAT subcommand as FRMAT. Subcommands are colored green by default, but the text FRMAT will
appear uncolored since it is not recognized.
Opening and Running a Syntax File
1. To open a saved syntax file, from the menus choose:
File > Open > Syntax…
A standard dialog box for opening files is displayed.
2. Select a syntax file. If no syntax files are displayed, make sure Syntax (*.sps) is selected as the file
type you want to view.
3. Click Open.
4. Use the Run menu in the syntax window to run the commands.
If the commands apply to a specific data file, the data file must be opened before running the commands,
or you must include a command that opens the data file. You can paste this type of command from the
dialog boxes that open data files.
Using Breakpoints
Breakpoints allow you to stop execution of command syntax at specified points within the syntax and
continue execution when ready. This allows you to view output or data at an intermediate point in a
syntax job, or to run command syntax that displays information about the current state of the data, such
as FREQUENCIES. Breakpoints can only be set at the level of a command, not on specific lines within a
command.
To insert a breakpoint on a command:
1. Click anywhere in the region to the left of the text associated with the command.
The breakpoint is represented as a red circle in the region to the left of the command text and on the
same line as the command name regardless of where you clicked.
Figure 72. Execution stopped at a breakpoint
Chapter 7. Working with Syntax 57
When you run command syntax containing breakpoints, execution stops prior to each command
containing a breakpoint.
The downward pointing arrow to the left of the command text shows the progress of the syntax run. It
spans the region from the first command run through the last command run and is particularly useful
when running command syntax containing breakpoints.
To resume execution following a breakpoint:
2. From the menus in the Syntax Editor choose:
Run > Continue
58 IBM SPSS Statistics V27 Brief Guide
Chapter 8. Modifying Data Values
The data you start with may not always be organized in the most useful manner for your analysis or
reporting needs. For example, you may want to:
• Create a categorical variable from a scale variable.
• Combine several response categories into a single category.
• Create a new variable that is the computed difference between two existing variables.
• Calculate the length of time between two dates.
This chapter uses the data file demo.sav. See the topic Chapter 10, “Sample Files,” on page 73 for more
information.
Creating a Categorical Variable from a Scale Variable
Several categorical variables in the data file demo.sav are, in fact, derived from scale variables in that data
file. For example, the variable inccat is simply income grouped into four categories. This categorical
variable uses the integer values 1–4 to represent the following income categories (in thousands): less
than $25, $25–$49, $50–$74, and $75 or higher.
To create the categorical variable inccat:
1. From the menus in the Data Editor window choose:
Transform > Visual Binning…
In the initial Visual Binning dialog box, you select the scale and/or ordinal variables for which you
want to create new, binned variables. Binning means taking two or more contiguous values and
grouping them into the same category.
Since Visual Binning relies on actual values in the data file to help you make good binning choices, it
needs to read the data file first. Since this can take some time if your data file contains a large
number of cases, this initial dialog box also allows you to limit the number of cases to read (“scan”).
This is not necessary for our sample data file. Even though it contains more than 6,000 cases, it does
not take long to scan that number of cases.
2. Drag and drop Household income in thousands [income] from the Variables list into the Variables to
Bin list, and then click Continue.
Figure 73. Main Visual Binning dialog box
3. In the main Visual Binning dialog box, select Household income in thousands [income] in the Scanned
Variable List.
A histogram displays the distribution of the selected variable (which in this case is highly skewed).
4. Enter inccat2 for the new binned variable name and Income category [in thousands] for the
variable label.
5. Click Make Cutpoints.
6. Select Equal Width Intervals.
7. Enter 25 for the first cutpoint location, 3 for the number of cutpoints, and 25 for the width.
The number of binned categories is one greater than the number of cutpoints. So in this example, the
new binned variable will have four categories, with the first three categories each containing ranges
of 25 (thousand) and the last one containing all values above the highest cutpoint value of 75
(thousand).
8. Click Apply.
The values now displayed in the grid represent the defined cutpoints, which are the upper endpoints
of each category. Vertical lines in the histogram also indicate the locations of the cutpoints.
By default, these cutpoint values are included in the corresponding categories. For example, the first
value of 25 would include all values less than or equal to 25. But in this example, we want categories
that correspond to less than 25, 25–49, 50–74, and 75 or higher.
9. In the Upper Endpoints group, select Excluded (<). 10. Then click Make Labels.
60 IBM SPSS Statistics V27 Brief Guide
Figure 74. Automatically generated value labels
This automatically generates descriptive value labels for each category. Since the actual values
assigned to the new binned variable are simply sequential integers starting with 1, the value labels
can be very useful.
You can also manually enter or change cutpoints and labels in the grid, change cutpoint locations by
dragging and dropping the cutpoint lines in the histogram, and delete cutpoints by dragging cutpoint
lines off of the histogram.
11. Click OK to create the new, binned variable.
The new variable is displayed in the Data Editor. Since the variable is added to the end of the file, it is
displayed in the far right column in Data View and in the last row in Variable View.
Computing New Variables
Using a wide variety of mathematical functions, you can compute new variables based on highly complex
equations. In this example, however, we will simply compute a new variable that is the difference
between the values of two existing variables.
The data file demo.sav contains a variable for the respondent’s current age and a variable for the number
of years at current job. It does not, however, contain a variable for the respondent’s age at the time he or
she started that job. We can create a new variable that is the computed difference between current age
and number of years at current job, which should be the approximate age at which the respondent started
that job.
1. From the menus in the Data Editor window choose:
Transform > Compute Variable…
2. For Target Variable, enter jobstart.
3. Select Age in years [age] in the source variable list and click the arrow button to copy it to the Numeric
Expression text box.
4. Click the minus (–) button on the calculator pad in the dialog box (or press the minus key on the
keyboard).
5. Select Years with current employer [employ] and click the arrow button to copy it to the expression.
Chapter 8. Modifying Data Values 61
Figure 75. Compute Variable dialog box
Note: Be careful to select the correct employment variable. There is also a recoded categorical version
of the variable, which is not what you want. The numeric expression should be age–employ, not age–
empcat.
6. Click OK to compute the new variable.
The new variable is displayed in the Data Editor. Since the variable is added to the end of the file, it is
displayed in the far right column in Data View and in the last row in Variable View.
Using Functions in Expressions
You can also use predefined functions in expressions. More than 70 built-in functions are available,
including:
• Arithmetic functions
• Statistical functions
• Distribution functions
• Logical functions
• Date and time aggregation and extraction functions
• Missing-value functions
• Cross-case functions
• String functions
Functions are organized into logically distinct groups, such as a group for arithmetic operations and
another for computing statistical metrics. For convenience, a number of commonly used system variables,
such as $TIME (current date and time), are also included in appropriate function groups.
Pasting a Function into an Expression
To paste a function into an expression:
62 IBM SPSS Statistics V27 Brief Guide
1. Position the cursor in the expression at the point where you want the function to appear.
2. Select the appropriate group from the Function group list. The group labeled All provides a listing of all
available functions and system variables.
3. Double-click the function in the Functions and Special Variables list (or select the function and click
the arrow adjacent to the Function group list).
The function is inserted into the expression. If you highlight part of the expression and then insert the
function, the highlighted portion of the expression is used as the first argument in the function.
Editing a Function in an Expression
The function is not complete until you enter the arguments, represented by question marks in the pasted
function. The number of question marks indicates the minimum number of arguments required to
complete the function.
1. Highlight the question mark(s) in the pasted function.
2. Enter the arguments. If the arguments are variable names, you can paste them from the variable list.
Using Conditional Expressions
You can use conditional expressions (also called logical expressions) to apply transformations to selected
subsets of cases. A conditional expression returns a value of true, false, or missing for each case. If the
result of a conditional expression is true, the transformation is applied to that case. If the result is false or
missing, the transformation is not applied to the case.
To specify a conditional expression:
1. Click If in the Compute Variable dialog box. This opens the If Cases dialog box.
2. Select Include if case satisfies condition.
3. Enter the conditional expression.
Most conditional expressions contain at least one relational operator, as in:
age>=21
or
income*3<100
In the first example, only cases with a value of 21 or greater for Age [age] are selected. In the second
example, Household income in thousands [income] multiplied by 3 must be less than 100 for a case to be
selected.
You can also link two or more conditional expressions using logical operators, as in:
age>=21 | ed>=4
or
income*3<100 & ed=5
In the first example, cases that meet either the Age [age] condition or the Level of education [ed] condition
are selected. In the second example, both the Household income in thousands [income] and Level of
education [ed] conditions must be met for a case to be selected.
Working with Dates and Times
A number of tasks commonly performed with dates and times can be easily accomplished using the Date
and Time Wizard. Using this wizard, you can:
• Create a date/time variable from a string variable containing a date or time.
• Construct a date/time variable by merging variables containing different parts of the date or time.
• Add or subtract values from date/time variables, including adding or subtracting two date/time
variables.
Chapter 8. Modifying Data Values 63
• Extract a part of a date or time variable; for example, the day of month from a date/time variable which
has the form mm/dd/yyyy.
The examples in this section use the data file upgrade.sav. See the topic Chapter 10, “Sample Files,” on
page 73 for more information.
To use the Date and Time Wizard:
1. From the menus choose:
Transform > Date and Time Wizard…
Figure 76. Date and Time Wizard introduction screen
The introduction screen of the Date and Time Wizard presents you with a set of general tasks. Tasks that
do not apply to the current data are disabled. For example, the data file upgrade.sav doesn’t contain any
string variables, so the task to create a date variable from a string is disabled.
If you’re new to dates and times in IBM SPSS Statistics, you can select Learn how dates and times are
represented and click Next. This leads to a screen that provides a brief overview of date/time variables
and a link, through the Help button, to more detailed information.
Calculating the Length of Time between Two Dates
One of the most common tasks involving dates is calculating the length of time between two dates. As an
example, consider a software company interested in analyzing purchases of upgrade licenses by
determining the number of years since each customer last purchased an upgrade. The data file
upgrade.sav contains a variable for the date on which each customer last purchased an upgrade but not
the number of years since that purchase. A new variable that is the length of time in years between the
date of the last upgrade and the date of the next product release will provide a measure of this quantity.
To calculate the length of time between two dates:
1. Select Calculate with dates and times on the introduction screen of the Date and Time Wizard and
click Next.
2. Select Calculate the number of time units between two dates and click Next.
64 IBM SPSS Statistics V27 Brief Guide
Figure 77. Calculating the length of time between two dates: Step 2
3. In step 2, select Date of next release for Date1.
4. Select Date of last upgrade for Date2.
5. Select Years for the Unit and Truncate to Integer for the Result Treatment. (These are the default
selections.)
6. Click Next.
7. In step 3, enter YearsLastUp for the name of the result variable. Result variables cannot have the same
name as an existing variable.
8. Enter Years since last upgrade as the label for the result variable. Variable labels for result variables
are optional.
9. Leave the default selection of Create the variable now, and click Finish to create the new variable.
The new variable, YearsLastUp, displayed in the Data Editor is the integer number of years between the
two dates. Fractional parts of a year have been truncated.
Adding a Duration to a Date
You can add or subtract durations, such as 10 days or 12 months, to a date. Continuing with the example
of the software company from the previous section, consider determining the date on which each
customer’s initial tech support contract ends. The data file upgrade.sav contains a variable for the number
of years of contracted support and a variable for the initial purchase date. You can then determine the end
date of the initial support by adding years of support to the purchase date.
To add a duration to a date:
1. Select Calculate with dates and times on the introduction screen of the Date and Time Wizard and
click Next.
2. In step 1, select Add or subtract a duration from a date and click Next.
Chapter 8. Modifying Data Values 65
Figure 78. Adding a duration to a date: Step 2
3. Select Date of initial product license for Date.
4. In step 2, select Years of tech support for the Duration Variable.
Since Years of tech support is simply a numeric variable, you need to indicate the units to use when
adding this variable as a duration.
5. Select Years from the Units drop-down list.
6. Click Next.
7. In step 3, enter SupEndDate for the name of the result variable. Result variables cannot have the same
name as an existing variable.
8. Enter End date for support as the label for the result variable. Variable labels for result variables are
optional.
9. Click Finish to create the new variable.
The new variable is displayed in the Data Editor.
66 IBM SPSS Statistics V27 Brief Guide
Chapter 9. Sorting and Selecting Data
Data files are not always organized in the ideal form for your specific needs. To prepare data for analysis,
you can select from a wide range of file transformations, including the ability to:
• Sort data. You can sort cases based on the value of one or more variables.
• Select subsets of cases. You can restrict your analysis to a subset of cases or perform simultaneous
analyses on different subsets.
The examples in this chapter use the data file demo.sav. See the topic Chapter 10, “Sample Files,” on
page 73 for more information.
Sorting Data
Sorting cases (sorting rows of the data file) is often useful and sometimes necessary for certain types of
analysis.
To reorder the sequence of cases in the data file based on the value of one or more sorting variables:
1. From the menus choose:
Data > Sort Cases…
The Sort Cases dialog box is displayed.
Figure 79. Sort Cases dialog box
2. Add the Age in years [age] and Household income in thousands [income] variables to the Sort by list.
If you select multiple sort variables, the order in which they appear on the Sort by list determines the
order in which cases are sorted. In this example, based on the entries in the Sort by list, cases will be
sorted by the value of Household income in thousands [income] within categories of Age in years [age]. For
string variables, uppercase letters precede their lowercase counterparts in sort order (for example, the
string value Yes comes before yes in the sort order).
Split-File Processing
To split your data file into separate groups for analysis:
1. From the menus choose:
Data > Split File…
The Split File dialog box is displayed.
Figure 80. Split File dialog box
2. Select Compare groups or Organize output by groups. (The examples following these steps show the
differences between these two options.)
3. Select Gender [gender] to split the file into separate groups for these variables.
You can use numeric, short string, and long string variables as grouping variables. A separate analysis is
performed for each subgroup that is defined by the grouping variables. If you select multiple grouping
variables, the order in which they appear on the Groups Based on list determines the manner in which
cases are grouped.
If you select Compare groups, results from all split-file groups will be included in the same table(s), as
shown in the following table of summary statistics that is generated by the Frequencies procedure.
Figure 81. Split-file output with single pivot table
If you select Organize output by groups and run the Frequencies procedure, two pivot tables are
created: one table for females and one table for males.
Figure 82. Split-file output with pivot table for females
68 IBM SPSS Statistics V27 Brief Guide
Figure 83. Split-file output with pivot table for males
Sorting Cases for Split-File Processing
The Split File procedure creates a new subgroup each time it encounters a different value for one of the
grouping variables. Therefore, it is important to sort cases based on the values of the grouping variables
before invoking split-file processing.
By default, Split File automatically sorts the data file based on the values of the grouping variables. If the
file is already sorted in the proper order, you can save processing time if you select File is already sorted.
Turning Split-File Processing On and Off
After you invoke split-file processing, it remains in effect for the rest of the session unless you turn it off.
• Analyze all cases. This option turns split-file processing off.
• Compare groups and Organize output by groups. This option turns split-file processing on.
If split-file processing is in effect, the message Split File on appears on the status bar at the bottom of
the application window.
Selecting Subsets of Cases
You can restrict your analysis to a specific subgroup based on criteria that include variables and complex
expressions. You can also select a random sample of cases. The criteria used to define a subgroup can
include:
• Variable values and ranges
• Date and time ranges
• Case (row) numbers
• Arithmetic expressions
• Logical expressions
• Functions
To select a subset of cases for analysis:
1. From the menus choose:
Data > Select Cases…
This opens the Select Cases dialog box.
Chapter 9. Sorting and Selecting Data 69
Figure 84. Select Cases dialog box
Selecting Cases Based on Conditional Expressions
To select cases based on a conditional expression:
1. Select If condition is satisfied and click If in the Select Cases dialog box.
This opens the Select Cases If dialog box.
Figure 85. Select Cases If dialog box
70 IBM SPSS Statistics V27 Brief Guide
The conditional expression can use existing variable names, constants, arithmetic operators, logical
operators, relational operators, and functions. You can type and edit the expression in the text box just
like text in an output window. You can also use the calculator pad, variable list, and function list to paste
elements into the expression. See the topic “Using Conditional Expressions” on page 63 for more
information.
Selecting a Random Sample
To obtain a random sample:
1. Select Random sample of cases in the Select Cases dialog box.
2. Click Sample.
This opens the Select Cases Random Sample dialog box.
Figure 86. Select Cases Random Sample dialog box
You can select one of the following alternatives for sample size:
• Approximately. A user-specified percentage. This option generates a random sample of approximately
the specified percentage of cases.
• Exactly. A user-specified number of cases. You must also specify the number of cases from which to
generate the sample. This second number should be less than or equal to the total number of cases in
the data file. If the number exceeds the total number of cases in the data file, the sample will contain
proportionally fewer cases than the requested number.
Selecting a Time Range or Case Range
To select a range of cases based on dates, times, or observation (row) numbers:
1. Select Based on time or case range and click Range in the Select Cases dialog box.
This opens the Select Cases Range dialog box, in which you can select a range of observation (row)
numbers.
Figure 87. Select Cases Range dialog box
• First Case. Enter the starting date and/or time values for the range. If no date variables are defined,
enter the starting observation number (row number in the Data Editor, unless Split File is on). If you
do not specify a Last Case value, all cases from the starting date/time to the end of the time series
are selected.
• Last Case. Enter the ending date and/or time values for the range. If no date variables are defined,
enter the ending observation number (row number in the Data Editor, unless Split File is on). If you
do not specify a First Case value, all cases from the beginning of the time series up to the ending
date/time are selected.
Chapter 9. Sorting and Selecting Data 71
For time series data with defined date variables, you can select a range of dates and/or times based on
the defined date variables. Each case represents observations at a different time, and the file is sorted
in chronological order.
Figure 88. Select Cases Range dialog box (time series)
To generate date variables for time series data:
2. From the menus choose:
Data > Define Dates…
Treatment of Unselected Cases
You can choose one of the following alternatives for the treatment of unselected cases:
• Filter out unselected cases. Unselected cases are not included in the analysis but remain in the
dataset. You can use the unselected cases later in the session if you turn filtering off. If you select a
random sample or if you select cases based on a conditional expression, this generates a variable
named filter_$ with a value of 1 for selected cases and a value of 0 for unselected cases.
• Copy selected cases to a new dataset. Selected cases are copied to a new dataset, leaving the original
dataset unaffected. Unselected cases are not included in the new dataset and are left in their original
state in the original dataset.
• Delete unselected cases. Unselected cases are deleted from the dataset. Deleted cases can be
recovered only by exiting from the file without saving any changes and then reopening the file. The
deletion of cases is permanent if you save the changes to the data file.
Note: If you delete unselected cases and save the file, the cases cannot be recovered.
Case Selection Status
If you have selected a subset of cases but have not discarded unselected cases, unselected cases are
marked in the Data Editor with a diagonal line through the row number.
Figure 89. Case selection status
72 IBM SPSS Statistics V27 Brief Guide
Chapter 10. Sample Files
The sample files installed with the product can be found in the Samples subdirectory of the installation
directory. There is a separate folder within the Samples subdirectory for each of the following languages:
English, French, German, Italian, Japanese, Korean, Polish, Russian, Simplified Chinese, Spanish, and
Traditional Chinese.
Not all sample files are available in all languages. If a sample file is not available in a language, that
language folder contains an English version of the sample file.
Descriptions
Following are brief descriptions of the sample files used in various examples throughout the
documentation.
• accidents.sav. This is a hypothetical data file that concerns an insurance company that is studying age
and gender risk factors for automobile accidents in a given region. Each case corresponds to a cross-
classification of age category and gender.
• adl.sav. This is a hypothetical data file that concerns efforts to determine the benefits of a proposed
type of therapy for stroke patients. Physicians randomly assigned female stroke patients to one of two
groups. The first received the standard physical therapy, and the second received an additional
emotional therapy. Three months following the treatments, each patient’s abilities to perform common
activities of daily life were scored as ordinal variables.
• advert.sav. This is a hypothetical data file that concerns a retailer’s efforts to examine the relationship
between money spent on advertising and the resulting sales. To this end, they have collected past sales
figures and the associated advertising costs.
• aflatoxin.sav. This is a hypothetical data file that concerns the testing of corn crops for aflatoxin, a
poison whose concentration varies widely between and within crop yields. A grain processor has
received 16 samples from each of 8 crop yields and measured the alfatoxin levels in parts per billion
(PPB).
• anorectic.sav. While working toward a standardized symptomatology of anorectic/bulimic behavior,
researchers 1 made a study of 55 adolescents with known eating disorders. Each patient was seen four
times over four years, for a total of 220 observations. At each observation, the patients were scored for
each of 16 symptoms. Symptom scores are missing for patient 71 at time 2, patient 76 at time 2, and
patient 47 at time 3, leaving 217 valid observations.
• bankloan.sav. This is a hypothetical data file that concerns a bank’s efforts to reduce the rate of loan
defaults. The file contains financial and demographic information on 850 past and prospective
customers. The first 700 cases are customers who were previously given loans. The last 150 cases are
prospective customers that the bank needs to classify as good or bad credit risks.
• bankloan_binning.sav. This is a hypothetical data file containing financial and demographic
information on 5,000 past customers.
• behavior.sav. In a classic example 2, 52 students were asked to rate the combinations of 15 situations
and 15 behaviors on a 10-point scale ranging from 0=”extremely appropriate” to 9=”extremely
inappropriate.” Averaged over individuals, the values are taken as dissimilarities.
• behavior_ini.sav. This data file contains an initial configuration for a two-dimensional solution for
behavior.sav.
1 Van der Ham, T., J. J. Meulman, D. C. Van Strien, and H. Van Engeland. 1997. Empirically based
subgrouping of eating disorders in adolescents: A longitudinal perspective. British Journal of Psychiatry,
170, 363-368.
2 Price, R. H., and D. L. Bouffard. 1974. Behavioral appropriateness and situational constraints as dimensions
of social behavior. Journal of Personality and Social Psychology, 30, 579-586.
• brakes.sav. This is a hypothetical data file that concerns quality control at a factory that produces disc
brakes for high-performance automobiles. The data file contains diameter measurements of 16 discs
from each of 8 production machines. The target diameter for the brakes is 322 millimeters.
• breakfast.sav. In a classic study 3, 21 Wharton School MBA students and their spouses were asked to
rank 15 breakfast items in order of preference with 1=”most preferred” to 15=”least preferred.” Their
preferences were recorded under six different scenarios, from “Overall preference” to “Snack, with
beverage only.”
• breakfast-overall.sav. This data file contains the breakfast item preferences for the first scenario,
“Overall preference,” only.
• broadband_1.sav. This is a hypothetical data file containing the number of subscribers, by region, to a
national broadband service. The data file contains monthly subscriber numbers for 85 regions over a
four-year period.
• broadband_2.sav. This data file is identical to broadband_1.sav but contains data for three additional
months.
• car_insurance_claims.sav. A dataset presented and analyzed elsewhere 4 concerns damage claims for
cars. The average claim amount can be modeled as having a gamma distribution, using an inverse link
function to relate the mean of the dependent variable to a linear combination of the policyholder age,
vehicle type, and vehicle age. The number of claims filed can be used as a scaling weight.
• car_sales.sav. This data file contains hypothetical sales estimates, list prices, and physical
specifications for various makes and models of vehicles. The list prices and physical specifications were
obtained alternately from edmunds.com and manufacturer sites.
• car_sales_uprepared.sav. This is a modified version of car_sales.sav that does not include any
transformed versions of the fields.
• carpet.sav. In a popular example 5, a company interested in marketing a new carpet cleaner wants to
examine the influence of five factors on consumer preference—package design, brand name, price, a
Good Housekeeping seal, and a money-back guarantee. There are three factor levels for package design,
each one differing in the location of the applicator brush; three brand names (K2R, Glory, and Bissell);
three price levels; and two levels (either no or yes) for each of the last two factors. Ten consumers rank
22 profiles defined by these factors. The variable Preference contains the rank of the average rankings
for each profile. Low rankings correspond to high preference. This variable reflects an overall measure
of preference for each profile.
• carpet_prefs.sav. This data file is based on the same example as described for carpet.sav, but it
contains the actual rankings collected from each of the 10 consumers. The consumers were asked to
rank the 22 product profiles from the most to the least preferred. The variables PREF1 through PREF22
contain the identifiers of the associated profiles, as defined in carpet_plan.sav.
• catalog.sav. This data file contains hypothetical monthly sales figures for three products sold by a
catalog company. Data for five possible predictor variables are also included.
• catalog_seasfac.sav. This data file is the same as catalog.sav except for the addition of a set of
seasonal factors calculated from the Seasonal Decomposition procedure along with the accompanying
date variables.
• cellular.sav. This is a hypothetical data file that concerns a cellular phone company’s efforts to reduce
churn. Churn propensity scores are applied to accounts, ranging from 0 to 100. Accounts scoring 50 or
above may be looking to change providers.
• ceramics.sav. This is a hypothetical data file that concerns a manufacturer’s efforts to determine
whether a new premium alloy has a greater heat resistance than a standard alloy. Each case represents
a separate test of one of the alloys; the heat at which the bearing failed is recorded.
• cereal.sav. This is a hypothetical data file that concerns a poll of 880 people about their breakfast
preferences, also noting their age, gender, marital status, and whether or not they have an active
3 Green, P. E., and V. Rao. 1972. Applied multidimensional scaling. Hinsdale,
Ill.: Dryden Press.
4 McCullagh, P., and J. A. Nelder. 1989. Generalized Linear Models, 2nd ed. London: Chapman & Hall.
5 Green, P. E., and Y. Wind. 1973. Multiattribute decisions in marketing: A measurement approach. Hinsdale,
Ill.: Dryden Press.
74 IBM SPSS Statistics V27 Brief Guide
lifestyle (based on whether they exercise at least twice a week). Each case represents a separate
respondent.
• clothing_defects.sav. This is a hypothetical data file that concerns the quality control process at a
clothing factory. From each lot produced at the factory, the inspectors take a sample of clothes and
count the number of clothes that are unacceptable.
• coffee.sav. This data file pertains to perceived images of six iced-coffee brands 6 . For each of 23 iced-
coffee image attributes, people selected all brands that were described by the attribute. The six brands
are denoted AA, BB, CC, DD, EE, and FF to preserve confidentiality.
• contacts.sav. This is a hypothetical data file that concerns the contact lists for a group of corporate
computer sales representatives. Each contact is categorized by the department of the company in
which they work and their company ranks. Also recorded are the amount of the last sale made, the time
since the last sale, and the size of the contact’s company.
• creditpromo.sav. This is a hypothetical data file that concerns a department store’s efforts to evaluate
the effectiveness of a recent credit card promotion. To this end, 500 cardholders were randomly
selected. Half received an ad promoting a reduced interest rate on purchases made over the next three
months. Half received a standard seasonal ad.
• customer_dbase.sav. This is a hypothetical data file that concerns a company’s efforts to use the
information in its data warehouse to make special offers to customers who are most likely to reply. A
subset of the customer base was selected at random and given the special offers, and their responses
were recorded.
• customer_information.sav. A hypothetical data file containing customer mailing information, such as
name and address.
• customer_subset.sav. A subset of 80 cases from customer_dbase.sav.
• debate.sav. This is a hypothetical data file that concerns paired responses to a survey from attendees
of a political debate before and after the debate. Each case corresponds to a separate respondent.
• debate_aggregate.sav. This is a hypothetical data file that aggregates the responses in debate.sav.
Each case corresponds to a cross-classification of preference before and after the debate.
• demo.sav. This is a hypothetical data file that concerns a purchased customer database, for the
purpose of mailing monthly offers. Whether or not the customer responded to the offer is recorded,
along with various demographic information.
• demo_cs_1.sav. This is a hypothetical data file that concerns the first step of a company’s efforts to
compile a database of survey information. Each case corresponds to a different city, and the region,
province, district, and city identification are recorded.
• demo_cs_2.sav. This is a hypothetical data file that concerns the second step of a company’s efforts to
compile a database of survey information. Each case corresponds to a different household unit from
cities selected in the first step, and the region, province, district, city, subdivision, and unit identification
are recorded. The sampling information from the first two stages of the design is also included.
• demo_cs.sav. This is a hypothetical data file that contains survey information collected using a complex
sampling design. Each case corresponds to a different household unit, and various demographic and
sampling information is recorded.
• diabetes_costs.sav. This is a hypothetical data file that contains information that is maintained by an
insurance company on policy holders who have diabetes. Each case corresponds to a different policy
holder.
• dietstudy.sav. This hypothetical data file contains the results of a study of the “Stillman diet” 7. Each
case corresponds to a separate subject and records his or her pre- and post-diet weights in pounds and
triglyceride levels in mg/100 ml.
6 Kennedy, R., C. Riquier, and B. Sharp. 1996. Practical applications of correspondence analysis to
categorical data in market research. Journal of Targeting, Measurement, and Analysis for Marketing, 5,
56-70.
7 Rickman, R., N. Mitchell, J. Dingman, and J. E. Dalen. 1974. Changes in serum cholesterol during the
Stillman Diet. Journal of the American Medical Association, 228:, 54-58.
Chapter 10. Sample Files 75
• dmdata.sav. This is a hypothetical data file that contains demographic and purchasing information for a
direct marketing company. dmdata2.sav contains information for a subset of contacts that received a
test mailing, and dmdata3.sav contains information on the remaining contacts who did not receive the
test mailing.
• dvdplayer.sav. This is a hypothetical data file that concerns the development of a new DVD player.
Using a prototype, the marketing team has collected focus group data. Each case corresponds to a
separate surveyed user and records some demographic information about them and their responses to
questions about the prototype.
• german_credit.sav. This data file is taken from the “German credit” dataset in the Repository of
Machine Learning Databases 8 at the University of California, Irvine.
• grocery_1month.sav. This hypothetical data file is the grocery_coupons.sav data file with the weekly
purchases “rolled-up” so that each case corresponds to a separate customer. Some of the variables
that changed weekly disappear as a result, and the amount spent recorded is now the sum of the
amounts spent during the four weeks of the study.
• grocery_coupons.sav. This is a hypothetical data file that contains survey data collected by a grocery
store chain interested in the purchasing habits of their customers. Each customer is followed for four
weeks, and each case corresponds to a separate customer-week and records information about where
and how the customer shops, including how much was spent on groceries during that week.
• guttman.sav. Bell 9 presented a table to illustrate possible social groups. Guttman 10 used a portion of
this table, in which five variables describing such things as social interaction, feelings of belonging to a
group, physical proximity of members, and formality of the relationship were crossed with seven
theoretical social groups, including crowds (for example, people at a football game), audiences (for
example, people at a theater or classroom lecture), public (for example, newspaper or television
audiences), mobs (like a crowd but with much more intense interaction), primary groups (intimate),
secondary groups (voluntary), and the modern community (loose confederation resulting from close
physical proximity and a need for specialized services).
• health_funding.sav. This is a hypothetical data file that contains data on health care funding (amount
per 100 population), disease rates (rate per 10,000 population), and visits to health care providers (rate
per 10,000 population). Each case represents a different city.
• hivassay.sav. This is a hypothetical data file that concerns the efforts of a pharmaceutical lab to
develop a rapid assay for detecting HIV infection. The results of the assay are eight deepening shades of
red, with deeper shades indicating greater likelihood of infection. A laboratory trial was conducted on
2,000 blood samples, half of which were infected with HIV and half of which were clean.
• hourlywagedata.sav. This is a hypothetical data file that concerns the hourly wages of nurses from
office and hospital positions and with varying levels of experience.
• insurance_claims.sav. This is a hypothetical data file that concerns an insurance company that wants
to build a model for flagging suspicious, potentially fraudulent claims. Each case represents a separate
claim.
• insure.sav. This is a hypothetical data file that concerns an insurance company that is studying the risk
factors that indicate whether a client will have to make a claim on a 10-year term life insurance
contract. Each case in the data file represents a pair of contracts, one of which recorded a claim and the
other didn’t, matched on age and gender.
• judges.sav. This is a hypothetical data file that concerns the scores given by trained judges (plus one
enthusiast) to 300 gymnastics performances. Each row represents a separate performance; the judges
viewed the same performances.
• kinship_dat.sav. Rosenberg and Kim 11 set out to analyze 15 kinship terms (aunt, brother, cousin,
daughter, father, granddaughter, grandfather, grandmother, grandson, mother, nephew, niece, sister,
8 Blake, C. L., and C. J. Merz. 1998. “UCI Repository of machine learning databases.” Available at http://
www.ics.uci.edu/~mlearn/MLRepository.html.
9 Bell, E. H. 1961. Social foundations of human behavior: Introduction to the study of sociology. New York:
Harper & Row.
10 Guttman, L. 1968. A general nonmetric technique for finding the smallest coordinate space for
configurations of points. Psychometrika, 33, 469-506.
76 IBM SPSS Statistics V27 Brief Guide
http://www.ics.uci.edu/~mlearn/MLRepository.html
http://www.ics.uci.edu/~mlearn/MLRepository.html
son, uncle). They asked four groups of college students (two female, two male) to sort these terms on
the basis of similarities. Two groups (one female, one male) were asked to sort twice, with the second
sorting based on a different criterion from the first sort. Thus, a total of six “sources” were obtained.
Each source corresponds to a 15 x 15 proximity matrix, whose cells are equal to the number of people
in a source minus the number of times the objects were partitioned together in that source.
• kinship_ini.sav. This data file contains an initial configuration for a three-dimensional solution for
kinship_dat.sav.
• kinship_var.sav. This data file contains independent variables gender, gener(ation), and degree (of
separation) that can be used to interpret the dimensions of a solution for kinship_dat.sav. Specifically,
they can be used to restrict the space of the solution to a linear combination of these variables.
• marketvalues.sav. This data file concerns home sales in a new housing development in Algonquin, Ill.,
during the years from 1999–2000. These sales are a matter of public record.
• nhis2000_subset.sav. The National Health Interview Survey (NHIS) is a large, population-based survey
of the U.S. civilian population. Interviews are carried out face-to-face in a nationally representative
sample of households. Demographic information and observations about health behaviors and status
are obtained for members of each household. This data file contains a subset of information from the
2000 survey. National Center for Health Statistics. National Health Interview Survey, 2000. Public-use
data file and documentation. ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/Datasets/NHIS/2000/.
Accessed 2003.
• ozone.sav. The data include 330 observations on six meteorological variables for predicting ozone
concentration from the remaining variables. Previous researchers 12, 13, among others found
nonlinearities among these variables, which hinder standard regression approaches.
• pain_medication.sav. This hypothetical data file contains the results of a clinical trial for anti-
inflammatory medication for treating chronic arthritic pain. Of particular interest is the time it takes for
the drug to take effect and how it compares to an existing medication.
• patient_los.sav. This hypothetical data file contains the treatment records of patients who were
admitted to the hospital for suspected myocardial infarction (MI, or “heart attack”). Each case
corresponds to a separate patient and records many variables related to their hospital stay.
• patlos_sample.sav. This hypothetical data file contains the treatment records of a sample of patients
who received thrombolytics during treatment for myocardial infarction (MI, or “heart attack”). Each case
corresponds to a separate patient and records many variables related to their hospital stay.
• poll_cs.sav. This is a hypothetical data file that concerns pollsters’ efforts to determine the level of
public support for a bill before the legislature. The cases correspond to registered voters. Each case
records the county, township, and neighborhood in which the voter lives.
• poll_cs_sample.sav. This hypothetical data file contains a sample of the voters listed in poll_cs.sav. The
sample was taken according to the design specified in the poll.csplan plan file, and this data file records
the inclusion probabilities and sample weights. Note, however, that because the sampling plan makes
use of a probability-proportional-to-size (PPS) method, there is also a file containing the joint selection
probabilities (poll_jointprob.sav). The additional variables corresponding to voter demographics and
their opinion on the proposed bill were collected and added the data file after the sample as taken.
• property_assess.sav. This is a hypothetical data file that concerns a county assessor’s efforts to keep
property value assessments up to date on limited resources. The cases correspond to properties sold in
the county in the past year. Each case in the data file records the township in which the property lies,
the assessor who last visited the property, the time since that assessment, the valuation made at that
time, and the sale value of the property.
• property_assess_cs.sav. This is a hypothetical data file that concerns a state assessor’s efforts to keep
property value assessments up to date on limited resources. The cases correspond to properties in the
11 Rosenberg, S., and M. P. Kim. 1975. The method of sorting as a data-gathering procedure in multivariate
research. Multivariate Behavioral Research, 10, 489-502.
12 Breiman, L., and J. H. Friedman. 1985. Estimating optimal transformations for multiple regression and
correlation. Journal of the American Statistical Association, 80, 580-598.
13 Hastie, T., and R. Tibshirani. 1990. Generalized additive models. London: Chapman and Hall.
Chapter 10. Sample Files 77
state. Each case in the data file records the county, township, and neighborhood in which the property
lies, the time since the last assessment, and the valuation made at that time.
• property_assess_cs_sample.sav. This hypothetical data file contains a sample of the properties listed
in property_assess_cs.sav. The sample was taken according to the design specified in the
property_assess.csplan plan file, and this data file records the inclusion probabilities and sample
weights. The additional variable Current value was collected and added to the data file after the sample
was taken.
• recidivism.sav. This is a hypothetical data file that concerns a government law enforcement agency’s
efforts to understand recidivism rates in their area of jurisdiction. Each case corresponds to a previous
offender and records their demographic information, some details of their first crime, and then the time
until their second arrest, if it occurred within two years of the first arrest.
• recidivism_cs_sample.sav. This is a hypothetical data file that concerns a government law
enforcement agency’s efforts to understand recidivism rates in their area of jurisdiction. Each case
corresponds to a previous offender, released from their first arrest during the month of June, 2003, and
records their demographic information, some details of their first crime, and the data of their second
arrest, if it occurred by the end of June, 2006. Offenders were selected from sampled departments
according to the sampling plan specified in recidivism_cs.csplan; because it makes use of a probability-
proportional-to-size (PPS) method, there is also a file containing the joint selection probabilities
(recidivism_cs_jointprob.sav).
• rfm_transactions.sav. A hypothetical data file containing purchase transaction data, including date of
purchase, item(s) purchased, and monetary amount of each transaction.
• salesperformance.sav. This is a hypothetical data file that concerns the evaluation of two new sales
training courses. Sixty employees, divided into three groups, all receive standard training. In addition,
group 2 gets technical training; group 3, a hands-on tutorial. Each employee was tested at the end of
the training course and their score recorded. Each case in the data file represents a separate trainee
and records the group to which they were assigned and the score they received on the exam.
• satisf.sav. This is a hypothetical data file that concerns a satisfaction survey conducted by a retail
company at 4 store locations. 582 customers were surveyed in all, and each case represents the
responses from a single customer.
• screws.sav. This data file contains information on the characteristics of screws, bolts, nuts, and
tacks 14.
• shampoo_ph.sav. This is a hypothetical data file that concerns the quality control at a factory for hair
products. At regular time intervals, six separate output batches are measured and their pH recorded.
The target range is 4.5–5.5.
• ships.sav. A dataset presented and analyzed elsewhere 15 that concerns damage to cargo ships caused
by waves. The incident counts can be modeled as occurring at a Poisson rate given the ship type,
construction period, and service period. The aggregate months of service for each cell of the table
formed by the cross-classification of factors provides values for the exposure to risk.
• site.sav. This is a hypothetical data file that concerns a company’s efforts to choose new sites for their
expanding business. They have hired two consultants to separately evaluate the sites, who, in addition
to an extended report, summarized each site as a “good,” “fair,” or “poor” prospect.
• smokers.sav. This data file is abstracted from the 1998 National Household Survey of Drug Abuse and
is a probability sample of American households. (http://dx.doi.org/10.3886/ICPSR02934) Thus, the first
step in an analysis of this data file should be to weight the data to reflect population trends.
• stocks.sav This hypothetical data file contains stocks prices and volume for one year.
• stroke_clean.sav. This hypothetical data file contains the state of a medical database after it has been
cleaned using procedures in the Data Preparation option.
• stroke_invalid.sav. This hypothetical data file contains the initial state of a medical database and
contains several data entry errors.
14 Hartigan, J. A. 1975. Clustering algorithms. New York: John Wiley and Sons.
15 McCullagh, P., and J. A. Nelder. 1989. Generalized Linear Models, 2nd ed. London: Chapman & Hall.
78 IBM SPSS Statistics V27 Brief Guide
http://dx.doi.org/10.3886/ICPSR02934
• stroke_survival. This hypothetical data file concerns survival times for patients exiting a rehabilitation
program post-ischemic stroke face a number of challenges. Post-stroke, the occurrence of myocardial
infarction, ischemic stroke, or hemorrhagic stroke is noted and the time of the event recorded. The
sample is left-truncated because it only includes patients who survived through the end of the
rehabilitation program administered post-stroke.
• stroke_valid.sav. This hypothetical data file contains the state of a medical database after the values
have been checked using the Validate Data procedure. It still contains potentially anomalous cases.
• survey_sample.sav. This data file contains survey data, including demographic data and various
attitude measures. It is based on a subset of variables from the 1998 NORC General Social Survey,
although some data values have been modified and additional fictitious variables have been added for
demonstration purposes.
• tcm_kpi.sav. This is a hypothetical data file that contains values of weekly key performance indicators
for a business. It also contains weekly data for a number of controllable metrics over the same time
period.
• tcm_kpi_upd.sav. This data file is identical to tcm_kpi.sav but contains data for four extra weeks.
• telco.sav. This is a hypothetical data file that concerns a telecommunications company’s efforts to
reduce churn in their customer base. Each case corresponds to a separate customer and records
various demographic and service usage information.
• telco_extra.sav. This data file is similar to the telco.sav data file, but the “tenure” and log-transformed
customer spending variables have been removed and replaced by standardized log-transformed
customer spending variables.
• telco_missing.sav. This data file is a subset of the telco.sav data file, but some of the demographic data
values have been replaced with missing values.
• testmarket.sav. This hypothetical data file concerns a fast food chain’s plans to add a new item to its
menu. There are three possible campaigns for promoting the new product, so the new item is
introduced at locations in several randomly selected markets. A different promotion is used at each
location, and the weekly sales of the new item are recorded for the first four weeks. Each case
corresponds to a separate location-week.
• testmarket_1month.sav. This hypothetical data file is the testmarket.sav data file with the weekly
sales “rolled-up” so that each case corresponds to a separate location. Some of the variables that
changed weekly disappear as a result, and the sales recorded is now the sum of the sales during the
four weeks of the study.
• tree_car.sav. This is a hypothetical data file containing demographic and vehicle purchase price data.
• tree_credit.sav. This is a hypothetical data file containing demographic and bank loan history data.
• tree_missing_data.sav This is a hypothetical data file containing demographic and bank loan history
data with a large number of missing values.
• tree_score_car.sav. This is a hypothetical data file containing demographic and vehicle purchase price
data.
• tree_textdata.sav. A simple data file with only two variables intended primarily to show the default
state of variables prior to assignment of measurement level and value labels.
• tv-survey.sav. This is a hypothetical data file that concerns a survey conducted by a TV studio that is
considering whether to extend the run of a successful program. 906 respondents were asked whether
they would watch the program under various conditions. Each row represents a separate respondent;
each column is a separate condition.
• ulcer_recurrence.sav. This file contains partial information from a study designed to compare the
efficacy of two therapies for preventing the recurrence of ulcers. It provides a good example of interval-
censored data and has been presented and analyzed elsewhere 16.
• ulcer_recurrence_recoded.sav. This file reorganizes the information in ulcer_recurrence.sav to allow
you model the event probability for each interval of the study rather than simply the end-of-study event
probability. It has been presented and analyzed elsewhere 17.
16 Collett, D. 2003. Modelling survival data in medical research, 2 ed. Boca Raton: Chapman & Hall/CRC.
Chapter 10. Sample Files 79
• verd1985.sav. This data file concerns a survey 18. The responses of 15 subjects to 8 variables were
recorded. The variables of interest are divided into three sets. Set 1 includes age and marital, set 2
includes pet and news, and set 3 includes music and live. Pet is scaled as multiple nominal and age is
scaled as ordinal; all of the other variables are scaled as single nominal.
• virus.sav. This is a hypothetical data file that concerns the efforts of an Internet service provider (ISP)
to determine the effects of a virus on its networks. They have tracked the (approximate) percentage of
infected e-mail traffic on its networks over time, from the moment of discovery until the threat was
contained.
• wheeze_steubenville.sav. This is a subset from a longitudinal study of the health effects of air
pollution on children 19. The data contain repeated binary measures of the wheezing status for children
from Steubenville, Ohio, at ages 7, 8, 9 and 10 years, along with a fixed recording of whether or not the
mother was a smoker during the first year of the study.
• workprog.sav. This is a hypothetical data file that concerns a government works program that tries to
place disadvantaged people into better jobs. A sample of potential program participants were followed,
some of whom were randomly selected for enrollment in the program, while others were not. Each case
represents a separate program participant.
• worldsales.sav This hypothetical data file contains sales revenue by continent and product.
17 Collett, D. 2003. Modelling survival data in medical research, 2 ed. Boca Raton: Chapman & Hall/CRC.
18 Verdegaal, R. 1985. Meer sets analyse voor kwalitatieve gegevens (in Dutch). Leiden: Department of Data
Theory, University of Leiden.
19 Ware, J. H., D. W. Dockery, A. Spiro III, F. E. Speizer, and B. G. Ferris Jr.. 1984. Passive smoking, gas
cooking, and respiratory health of children living in six cities. American Review of Respiratory Diseases, 129,
366-374.
80 IBM SPSS Statistics V27 Brief Guide
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Index
A
Access (Microsoft) 11
B
bar charts 24
C
cases
selecting 69
sorting 67, 69
categorical data
summary measures 23
charts
bar 24, 27
creating charts 27
histograms 26
computing new variables 61
conditional expressions 63
continuous data 23
counts
tables of counts 23
create variable labels 19
D
Data Editor
entering non-numeric data 18
entering numeric data 17
data entry 17, 18
data types
for variables 20
database files
reading 11
Database Wizard 11
date and time variables 63
Date and Time Wizard 63
E
editing pivot tables 36
entering data
non-numeric 18
numeric 17
Excel (Microsoft)
exporting results to 46
Excel files
reading 8
exporting results
HTML 53
to Excel 46
to PowerPoint 46
to Word 46
F
frequency tables 23
functions in expressions 62
G
graphs
bar 27
creating graphs 27
H
hiding rows and columns in pivot tables 37
histograms 26
HTML
exporting results 53
I
interval data 23
L
layers
creating in pivot tables 36
level of measurement 23
M
measurement level 23
missing values
for non-numeric variables 22
for numeric variables 21
system-missing 21
moving
elements in pivot tables 35
items in the Viewer 33
N
nominal data 23
numeric data 17
O
ordinal data 23
P
pasting syntax
from a dialog box 55
pivot tables
accessing definitions 34
cell data types 37
Index 83
pivot tables (continued)
cell formats 37
editing 36
formatting 36
hiding decimal points 37
hiding rows and columns 37
layers 36
pivoting trays 35
transposing rows and columns 35
PowerPoint (Microsoft)
exporting results to 46
Q
qualitative data 23
quantitative data 23
R
ratio data 23
recoding values 59
S
sample files
location 73
scale data 23
scale variables
summary measures 25
selecting cases 69
sorting cases 67
split-file processing 67
spreadsheet files
reading 8
reading variable names 8
string data
entering data 18
subsets of cases
based on dates and times 71
conditional expressions 70
deleting unselected cases 72
filtering unselected cases 72
if condition is satisfied 70
random sample 71
selecting 69
summary measures
categorical data 23
scale variables 25
syntax 55
syntax files
opening 57
Syntax Help tool 56
syntax windows
auto-completion 56
breakpoints 57
color coding 56
editing commands 56
pasting commands 55
running commands 55, 57
system-missing values 21
T
text data files
reading 13
Text Import Wizard 13
transposing (flipping) rows and columns in pivot tables 35
V
value labels
assigning 20
controlling display in Viewer 20
numeric variables 20
variable labels
creating 19
variables
data types 20
labels 19
Viewer
hiding and showing output 33
moving output 33
W
Word (Microsoft)
exporting results to 46
84 IBM SPSS Statistics V27 Brief Guide
IBM®
-
Contents
- Chapter 1. Introduction
- Chapter 2. Reading Data
- Chapter 3. Using the Data Editor
- Chapter 4. Examining Summary Statistics for Individual Variables
- Chapter 5. Creating and editing charts
- Chapter 6. Working with Output
- Chapter 7. Working with Syntax
- Chapter 8. Modifying Data Values
- Chapter 9. Sorting and Selecting Data
- Chapter 10. Sample Files
Sample Files
Opening a Data File
Running an Analysis
Creating Charts
Basic Structure of IBM SPSS Statistics Data Files
Reading IBM SPSS Statistics Data Files
Reading Excel Data
Reading Data from a Database
Reading Data from a Text File
Entering Numeric Data
Entering String Data
Defining Data
Adding Variable Labels
Changing Variable Type and Format
Adding Value Labels
Handling Missing Data
Missing Values for a Numeric Variable
Missing Values for a String Variable
Level of Measurement
Summary Measures for Categorical Data
Charts for Categorical Data
Summary Measures for Scale Variables
Histograms for Scale Variables
Chart creation basics
Using the Chart Builder gallery
Defining variables and statistics
Adding text
Creating the chart
Using the Viewer
Using the Pivot Table Editor
Accessing Output Definitions
Pivoting Tables
Creating and Displaying Layers
Editing Tables
Hiding Rows and Columns
Changing Data Display Formats
TableLooks
Using Predefined Formats
Customizing TableLook Styles
Changing the Default Table Formats
Customizing the Initial Display Settings
Displaying Variable and Value Labels
Using Results in Other Applications
Pasting Results as Word Tables
Pasting Results as Text
Exporting Results to Microsoft Word, PowerPoint, and Excel Files
Exporting Results to PDF
Exporting Results to HTML
Pasting Syntax
Editing Syntax
Opening and Running a Syntax File
Using Breakpoints
Creating a Categorical Variable from a Scale Variable
Computing New Variables
Using Functions in Expressions
Using Conditional Expressions
Working with Dates and Times
Calculating the Length of Time between Two Dates
Adding a Duration to a Date
Sorting Data
Split-File Processing
Sorting Cases for Split-File Processing
Turning Split-File Processing On and Off
Selecting Subsets of Cases
Selecting Cases Based on Conditional Expressions
Selecting a Random Sample
Selecting a Time Range or Case Range
Treatment of Unselected Cases
Case Selection Status
Notices
Trademarks
Index
A
B
C
D
E
F
G
H
I
L
M
N
O
P
Q
R
S
T
V
W
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Turnitin Report
Formatting
Title Page
Citation
Outline
