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I have a 2x2 study design to test the interaction between two drugs, with a single variable outcome. The data are very much non-parametric and it seems that a good alternative to the traditional two-way ANOVA is to use a permutation ANOVA, e.g. aovp(outcome ~ drugA * drugB) from the lmperm package.

My question is what is the most appropriate way to run a post-hoc test on the resulting aovp object, to make adjusted comparisons between specific drug combinations? Any advice is appreciated.

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  • $\begingroup$ The only way I know to do this would be to use pairwise comparisons of treatments. That is, if drugA is significant, compare, e.g. A1 to A2, A1 to A3, and A2 to A3. Each with a permutation test. I don't particularly like doing this kind of pairwise comparison because each comparison ignores all the rest of the data that's not in that comparison. $\endgroup$
    – Sal Mangiafico
    Commented Nov 22, 2021 at 14:21

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Answer from comments:

The only way I know to do this would be to use pairwise comparisons of treatments. That is, if drugA is significant, compare, e.g. A1 to A2, A1 to A3, and A2 to A3. Each with a permutation test. I don't particularly like doing this kind of pairwise comparison because each comparison ignores all the rest of the data that's not in that comparison.

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