A priori comparisons in a repeated measures design

Question

I'm interested in finding out more about the use of a priori planned contrasts within a one-way repeated measures ANOVA design.

Predictions:

• Grps 2+3 < Grp 1
• Grp 2 < Grp 3

My questions are:

1. If the data violates RM ANOVA assumptions (e.g., normality, sphericity), how does this affect the accuracy of the planned contrasts?

2. Following on from this, if transformations were considered but not successful, is there any way of performing the planned contrasts within a non-parametric alternative?

My sense is 'no', but where do others suggest to go from here? (e.g., is there a way of somehow combining variables in SPSS (e.g., for the first prediction where there are two groups in one cluster)?

Answer 1

There's no way to know how your specific violations impact your tests because different kinds of violations do different things. Your normality violation could be a lot of different things so I can't comment. Commonly sphericity raises the alpha rate over the nominal value. But for your contrasts sphericity isn't an issue because there are really only two levels in each so it cannot be violated (you need at least 3 levels to even have a concept of sphericity).

You can search on the web for how to do planned contrasts in SPSS. There are even youtube videos. When you enter your contrasts correctly the variables get combined for you.

Note, if you've already run an ANOVA and have a significant effect you might be best off just describing the pattern of data. The pattern of values means something, that's what your ANOVA effect means. Doing contrasts afterwards, even planned ones, may not be necessary if the pattern is clear.

Answer 2

In addition to John's excellent points, if you want to use something else than ANOVA/t-tests (e.g. non-parametric, rank-based or permutation test…), you can always perform separate tests and use some general multiple testing adjustment (the Bonferroni-Holm procedure or techniques based on the false discovery rate don't have any particular affinity with ANOVA or the linear model and apply to any kind of test).