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How should I do the p-value adjustment for several post hoc comparisions. Should I adjust them all at once. Or should I adjutment per comparsion. Suppose

            Anova-pvalue            Pvalue:A1-A2      Pvalue:A1-A3      Pvalue:A2-A3
Colostrol:     0.04                  0.1                    0.03             0.02
Height         0.01                  0.01                   0.03              0.1

Should I adjust by taking into account all possible multiple comparisons (Post Hoc) (6 tests) or should I adjust just for A1-A2, which would be two tests, and then separately for A1-A3 (two tests) and A2-A3? Thanks for the advice

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  • $\begingroup$ "Tukey's HSD (Honest Significant Difference)" is one effective approach. $\endgroup$
    – whuber ♦
    Commented May 22, 2023 at 13:52

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In this context, it appears you are doing two separate 1-way ANOVA (with a single factor with three levels). Thus, standard/conventional protocol would be to do the post hoc adjustment for each triple (if the omnibus ANOVA clears the significance threshold).

One additional note, "adjusting all at once" is not actually the best way to describe this process for some protocols (like the Holm-Bonferroni process, which adjusts successive p-values based on their ordered magnitude). While I'm happy to share more on this, I don't believe this is the heart of your question here.

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