Understanding repeated measure ANOVA assumptions for correct interpretation of SPSS output I am investigating whether different reward conditions may affect task performance. I have data from a small study with two groups, each with n=20. I collected data on a task that involved performance in 3 different "reward" conditions. The task involved performance in each of the 3 conditions twice but in random order. I want to see if there is a mean difference in task performance for each group, in each of the different "reward" conditions.


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*IV= Group type

*DV = mean measure of task performance across 3 conditions


I have output from a repeated measures ANOVA and access to the raw data set in SPSS but am unsure how to proceed. I haven't been able to find a step-by-step guide for this interpretation, as the Pallant text is somewhat limited. My particular issues are in the following areas:


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*Do I check the normality of each of my variables individually or within combinations of each of the levels of the IV? If it within combinations, how do I check that?

*Do I check Mauchly's Test first? If it is violated, what does that mean? If it is not violated, what does that mean?

*When is it okay to look at the multivariate tests tables, or the tests of within-subjects effects? I'm not sure when it is appropriate to use either (or both?)?

*Is it always okay to look at the pairwise comparisons? It seems counterintuitive to do so if the multivariate or within-subjects effects don't indicate significance (ie P<0.05) but I am again unsure.

 A: General Resource on interpreting repeated measures ANOVA with SPSS
It sounds like you need a better general resource on repeated measures ANOVA. Here are a few web resources, but in general a search for "SPSS repeated measures ANOVA" will yield many useful options.


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*UCLA has an example of SPSS output with interpretation by a 2 by 3 mixed ANOVA along with several other examples.

*Andy Field on repeated measures ANOVA
1. Checking normality


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*From a practical perspective, tests of normality are often used to justify transformations. If you do apply a transformation, then you need to apply the same transformation to all cells of the design. 

*A common way to assess normality using SPSS is to set up your model and save the residuals and then examine the distribution of residuals.


2. Value of Mauchly's test


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*A common strategy is to look at Mauchly's test and if it is statistically significant, interpret either the univariate corrected tests or the multivariate tests.


3. Multivariate


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*I think @ttnphns has summed this up well.


4. Pairwise comparisons


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*I think @ttnphns has summed this up well. 

A: *

*Your dependent variables should be normal in each cell of between-subject design. You have 2 such cells: 2 groups, so normality should be in both groups. Also, variance-covariance matrix between your 3 DV should be same in the 2 groups. You could check normality by Shapiro-Wilk test or Kolmogorov-Smirnov (with Lilliefors correction) test in EXPLORE procedure. Variance-covariance homogeneity could be tested by Box's M test (found in Discriminant analysis). Note however that ANOVA is quite robust to violations to both assumptions.

*Mauchly's test checks the so called sphericity assumption which is necessary for univariate approach to repeated measures ANOVA. This assumption requires that, roughly speaking, differences between your repeated measure DVs don't intercorrelate. If the assumption is violated you should disregard "Spericity assumed" in Tests of Within-Subjects Effects table - there found some corrections (such as Greenhouse-Geisser) instead.

*While Tests of Within-Subjects Effects table reflects "univariate approach" in RM-ANOVA, Multivariate Tests table reflects "multivariate approach". These two are both useful and there's a little debate which is "better". Read a little here about them, a bit more here.

*Usually one won't check pairwise tests if overall effect is non-significant, it has little sense.
