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• Assumptions of repeated measures ANOVA
• When can I use a repeated measurements ANOVA?
• How can I do post hoc tests for a two-way repeated measures ANOVA?
• Where do I find the repeated measurements ANOVA in SPSS?

Repeated measurements ANOVA is a somewhat older term for special forms of mixed models for analyzing repeated measurements of a quantitative dependent variable that is normally distributed. Within SPSS this technique is referred to as GLM - repeated. As noted earlier, this procedure is a specific variant of mixed models, but is only available for continuous, normally distributed dependent variables that are measured at fixed and identical time points in all patients.

Repeated measures ANOVA as implemented in SPSS provides two types of analyses, namely under the assumption that the correlations between the repeated measurements all have the same value (compound symmetry), or without assumptions about the correlations (unstructured). In the SPSS output, the compound-symmetry results are reported under the heading Tests of Within-Subjects Effects and the unstructured results under the heading Multivariate Tests. It is useful that Mauchly's Test of Sphericity is given; this is a statistical test of the null hypothesis that the compound symmetry assumption holds (small p-values for this test indicate that compound symmetry does not fit the data well). If sphericity (i.e. compound symmetry) is rejected, then either the multivariate test results can be used, or a Greenhouse-Geisser or a Huynh-Feldt correction can be applied to the Tests of Within-Subjects Effects.

You can use a repeated measurements ANOVA if:

• the dependent variable is continuous and (per level of the independent predictor) normally distributed,
• the repeated measurements were made at fixed time points in all patients,
• there are no missing values.

I have two independent groups (patient/control is the between-subjects factor) where for both, data was collected at 5 time points (5 timepoints as the within-subjects factor). Now I run a two-way repeated measures ANOVA to look at the interaction effect between group and time. If this is significant, I would like to know at which time points the control group differed from the patient group. There is no option in SPSS to do a Tukey post hoc test. May I use an independent t-test at each time point in this situation to determine at which time points the two groups differed from each other?

If not, then I would like to calculate a Tukey by hand; I have already done this for the one-way repeated measures ANOVA in which I looked, within the patient group, at which time points the data differed from the baseline measurement. But can this also be done for a two-way ANOVA with 2 independent groups?

You can do the separate (t-)tests (t0 patient minus t0 control, t1 patient minus t1 control, etc.). And then you need to correct the results of those tests for the fact that you are doing multiple comparisons. I would not immediately see how to apply Tukey here myself, because that assumes a number of means with the hypothesis that they are all equal (to each other). Now it is a different case, namely you want to check whether the means are equal to each other pairwise, two at a time. I would therefore use a different correction method (such as Bonferroni or Bonferroni-Holm).

In your earlier analysis (post hoc on the within factor), also make sure that you perform the comparisons in a paired manner. Incidentally, you can have SPSS do this (within) comparison for you. Namely by moving the factor 'time' to 'Display means for' under 'Options' and then clicking 'compare main effects', with the desired correction method.

On this site by David Howell there is a great deal of advice about the sense and nonsense of post hoc tests for repeated measurements ANOVAs.

You will find the repeated measurements ANOVA in SPSS 16 under Analyze->General Linear Model->Repeated measures.

For the repeated measurements ANOVA, the repeated measurements of the patients must be in separate columns next to each other in the SPSS file. Suppose there are three repeated measurements from three patients, then the data file looks as follows with four columns:

patientnumber	measurement1	measurement2	measurement3
1	10	9	11
2	8	11	12
3	5	8	9

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