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I would like to know if it is necessary to correct the "overall" tests ofmain-effects/interaction effect for multiple comparisons in a 2x2 mixed-effects repeated-measures ANOVA.

Simple example: Imagine a model with a (between-subject) factor of "group" (2 levels), a (within-subject) factor of "time" (2 levels) and an interaction factor of group x time. If you just want to investigate the main-effects ("group" and "time", 2 tests) and the interaction-effect (1 test) at alpha=0.05 would you need to adjust alpha via (e.g.) Bonferroni to alpha=0.05/3?

Please note that I am not talking about posthoc tests following a significant interaction effect (which have to be corrected). I am just talking about what the significance threshold should be to determine if the interaction is significant in the first place.

I was always thinking that such a correction is not necessary (alpha=0.05 is sufficient) but was recently told that I absolutely need to correct for multiple comparisons on the factor-level already (alpha=0.05/3)...

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If you want to control the type 1 error rate across the three null hypotheses, then an adjustment is necessary in the scenario you describe.

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  • $\begingroup$ But is that actually necessary in the case of the RM-ANOVA/is it normally done? Do you maybe have a reference/tutorial mentioning this? $\endgroup$ – Paul Aug 1 '19 at 13:13
  • $\begingroup$ It is, if you wish to control the familywise type 1 error. Multiple tests except in some very special cases (e.g. nested hypotheses) simply do. $\endgroup$ – Björn Aug 1 '19 at 13:19
  • $\begingroup$ OK. Can you point me to any reference (book/paper/tutorial/statistical package description) describing this in more detail? (Not trying to argue against you just would like to see an "official" reference stating that) $\endgroup$ – Paul Aug 1 '19 at 13:25
  • $\begingroup$ What about: en.m.wikipedia.org/wiki/… $\endgroup$ – Björn Aug 1 '19 at 13:35
  • $\begingroup$ Hmm... but that does not really address the issue of the RM-ANOVA? The only paragraph in there about ANOVA in general is: "Methods which rely on an omnibus test before proceeding to multiple comparisons. Typically these methods require a significant ANOVA, MANOVA, or Tukey's range test. These methods generally provide only "weak" control of Type I error, except for certain numbers of hypotheses." But I think I get your point. Thanks! $\endgroup$ – Paul Aug 1 '19 at 13:46

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