# How should I analyze data with repeated measures variables and integer between-subject factors?

I ran a study, where a single variable was measured repeatedly for each participant, under different conditions. Analyzing this data with SPSS has been rather straightforward, by using the General Linear Model -> Repeated Measures ANOVA, and specifying each measure in the within-subject factors.

My problem arises when I try to include some post-experiment data I collected, like a test that all participants completed after the experiment, with integral scores ranging from 0-24. I want to include this to see how these scores relate to the within-subjects measures, and adding this data as a between-subject factor makes sense, but due to the nature of the test score variable I have up to 25 categories that make the data impossible to work with.

It seems like this should be a common issue, and my Googling has helped me a bit, but most of the examples I have seen use categorical variables like gender for the between-subject factors. What do I do if the between-subject factor isn't categorical?

I will be very grateful for any insight, comments and tips you have. Thanks!

• I'm thinking that your concern is that the scores are ordinal data instead of interval, is that right? Jul 23, 2012 at 14:04
• @gung I will admit that I sometimes have trouble discerning between ordinal, interval and discrete data. In this case the scores are integers ranging from 0 to 24, and represent the number of problems the participant answered correctly. For reference, the test is the MRT-A mental rotations test, described here: link. Jul 23, 2012 at 14:55

You could treat the test score as an interval between subjects predictor in a full model of that and the within effects. You really should be doing multi-level modelling at this point and I'd strongly encourage you look at some tutorials on that for SPSS.

There is an alternative, that is not as good but might be simpler to understand. Let's say your primary question is whether the repeated measures effect is dependent on (interacts with) a linear effect of the test score. Calculate the repeated measures effect score for each participant and then perform a regression on the resulting effect scores. In general, once you have each subject with a single score you're interested in then you could analyze the continuous test score predictor how you'd handle any continuous variable.

• Thank you for a helpful response. As for using a continuous factor, I have seen some papers where the authors convert the integer scores in this test (MRT-A, referenced in a comment on the original post) to percentages (or an arcsine in one case) to make it continuous. But is that really enough? I will also look into multi-level modelling, and thanks for bringing that up. Jul 23, 2012 at 14:58
• Converting it to another scale doesn't make it continuous. That's actually kind of an absurd idea. Then you'd just have intervals in a different scale. You have a variable that you can treat continuously as long as you don't take fractional scores as meaningful in discussion. In practice no variables are continuous since there is always some limit to the ability to measure. This is a relatively course continuous variable is all.
– John
Jul 23, 2012 at 18:18
• The scores might be converted when they're response variables because they're known not to be distributed normally and the arcsine fixes that. But there's not requirement for normality as a predictor variable.
– John
Jul 23, 2012 at 18:28
• thanks for your comments. I felt that simply changing the scale was weird, but wasn't sure enough. The fact that I've seen some papers do it didn't help. I'm reading up on multi-level modelling right now. Jul 23, 2012 at 19:22

I would agree with John. Another simpler approach might be to say four or five categories such as very poor [0,x1] poor[x1,x2] average [x2,x3] good [x3,x4] and excellent [x4,24]. Known the test you should be able to pick reasonable break points. I raise this idea because it just seems to me that the difference between a score 24 and 25 say probably does add much useful information regarding the relationships you are trying to look at,

• Thanks. That thought did cross my mind, and I'm glad to see it wasn't too crazy. I'll have to comb the literature though, since I haven't seen any such categorization in any papers that use this particular test (MRT-A, referenced in a comment on the original post) yet. Jul 23, 2012 at 15:02
• I think that the argument at the end of your answer is problematic. You're not just throwing out small differences with broad categorizations of the test, you're potentially throwing out the pattern of the relationship between the test and the effect score (or whatever the questioner uses). There could be a curvilinear pattern that is quite dependent upon all those individual points to reveal adequately. I only used linear as an example. There are so many good options for dealing with non-linear these days that breaking it into categories is never a good idea.
– John
Jul 23, 2012 at 18:31

To use MRT-A as a continuous variable, you should add it to the model as a covariate. Then from the button Model in SPSS, choose under specify model Custom, drag the within- and between-subjects to the corresponding Model.