The use of multiple comparisons tests after repeated measures ANOVA is a tricky topic that many statistics texts avoid. We follow methods suggested by Maxwell and Delaney(1).

With one way ANOVA, Prism computes the multiple comparisons tests in two different ways, depending on whether you ask Prism (on the first tab of the ANOVA dialog) to assume sphericity.

If you assume sphericity

The multiple comparisons tests performed by Prism use the mean square residual for all comparisons. This is a pooled value that assess variability in all the groups. If you assume that variability really is the same in all groups (with any differences due to chance) this gives you more power. This makes sense, as you get to use data from all time points to assess variability, even when comparing only two times.

If you do not assume sphericity

If you check the option to not assume sphericity, Prism does two things differently.

•It applies the Geisser-Greenhouse correction when computing the P values for the main effect.

•It computes the multiple comparisons differently. For each comparison of two groups, it uses only the data in those two groups (essentially performing a paired t test). This makes sense when scatter increases with time, so later treatments give a more variable response than earlier treatments. It uses the method described on pages 552-555 of Maxwell(1).

When you choose not to assume sphericity, some multiple comparisons will have more power (and narrower confidence intervals) than they would if you did not assume sphericity. But others will have less power (and wider confidence intervals).

Reference

1. Scott E. Maxwell, Harold D. Delaney, Designing Experiments and Analyzing Data: A Model Comparison Perspective, Second Edition. IBSN:0805837183