Our goal with Prism has always been to make basic biostatistics very accessible and easy. Three-way ANOVA really is beyond "basic biostatistics". Multiple comparisons after three-way ANOVA stretch this definition even more. If you haven't taken the time to really understand three-way ANOVA, it is quite easy to be mislead by the results. Beware!
•Three-way ANOVA is not a topic that is easy to master. In addition to reading textbooks, also consider getting help from someone with more experience.
•Prism also offers to fit a mixed model to repeated measures data. Understanding this fully is even more complicated.
•Before getting lost in the many choices for multiple comparisons, first articulate clearly the scientific goals of the study. Don't articulate your goals in terms of ANOVA (looking for interactions). Figure out what you really want to know. Then figure out the best statistical approach to getting the answer.
•We can only provide limited technical support with understanding three-way ANOVA.