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)...