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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)?

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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.

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  • $\begingroup$ Thanks for your response John. I feel pretty comfortable about how to run the planned contrasts in SPSS, but am less confident on the theoretical side of things. Unfortunately, I haven't found much on the web, in stats texts etc, that really addresses my question re: how to proceed with planned contrasts if normality is violated, if it's possible to run planned contrasts via nonparametric means, etc. $\endgroup$
    – user26473
    Commented Jul 17, 2013 at 5:35
  • $\begingroup$ If normality is really violated that much in the residuals of the ANOVA you shouldn't be doing the ANOVA in the first place. You should just be doing non-parametric tests. It's easy in repeated measures to combine variables because you can just get the mean of the two / subject. $\endgroup$
    – John
    Commented Jul 17, 2013 at 10:40
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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).

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