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I'm running a 3-factor (Between by Between by Within) ANOVA with the correlation structure modeled using a Random Intercept and Gaussian Serial Correlation. I have the following variables:

Dependent variable: Bodyweight

Independent:

Size - size of the subject (between). 2 levels: normal and large
Diet - diet given (between). 2 levels: normal or experimental diet.
Time - weekly bodyweight measurements (within). 12 levels: 1:12

I have a significant 3-way interaction and all 2-way interactions(p<0.05), and so I am stratifying the 3-factors to test all pairwise differences between Normal and Large Size, on each Diet, and at each week. I'm doing these specific comparisons because I'm interested in whether Size further increases the weight gain known to occur on the experimental diet. Using this approach, I have a total of 24 post-hoc comparisons.

I would like to improve power by using Hochberg's procedure rather than Holm's to adjust for multiple comparisons, but I'm unclear whether my data meet the assumption of independent or positively associated test statistics/p-values (as per Simes' test and multcomp documentation in R).

I'm employing the mixed model because of the positively correlated repeated measures, so I'm tempted to conclude that the post-hoc/pairwise test statistics at each time would also be positively correlated. But I could very well be wrong.

Here are my questions:

  1. Would the pairwise test statistics/p-values of these repeated measures data meet the independence/positive assumption of Hochberg's procedure?

  2. Is there a way to test or at least calculate/extract the correlations of the test statistics/p-values to empirically validate the assumption?

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