This question is for simple data structure that involves one main effect only. I can definitely see ANOVA's usefulness in more complicated data containing multiple effects.

Aside from being a "convenient" omnibus test (which may give you some ideas whether something is worth further investigating), ANOVA added quite a few assumptions and so what you find would be more less an approximate indication (and to say the least, far too many people are too lazy to check the validity of assumptions for their data). And to my honest experience, it does not inform me anything more than I simply eyeballing the data graphically. By doing a Welch t-test multiple comparisons directly, we omitted some assumptions which also give you the ranks and differences directly (if I am not wrong, even student t-test has fewer assumptions than ANOVA). Any post-hoc multiple comparisons done following ANOVA also inherit its assumptions.

From a programming perspective, I honestly don't think a direct multiple comparisons done before ANOVA is any less easy to automate. So, why are we so fixated on ANOVA?



Browse other questions tagged or ask your own question.