Is there any consensus on adjusting p-values for multiple tests? I'm confused as to when adjustments for multiple tests need to be used. I'm an undergrad who's familiarising himself with stats, so apologies if my question sounds dumb, but I haven't found any satisfactory answer myself. I understand the purpose of these corrections as well as that there are different approaches (controlling FWER vs. FDR). That being said, I have found many people not using any such corrections except for specific cases such as multiple comparisons in ANOVA. One of our lecturers said that you're adjusting when the tests are not independent. Others have told me that it doesn't really matter and as long as you're following NHST, you should control for all your tests performed on one sample (seems kinda strict). Some say that you should decide based on what your "family of tests" is. And also, others seem to highlight the importance of formulating the hypotheses a priori, in which case you don't always need to adjust. Is there some link between all of these views that I am missing? 
Also, suppose I'm using ANOVA with 2 categorical predictors and an interaction. Why don't I need to adjust my F-test p-values for each of the predictors and the interaction? Also, when we use multiple comparisons or contrasts, why do we adjust taking into account only these tests and not including the p-values from the F-tests? 
 A: Is there any consensus on adjusting p-values for multiple tests?
Not really.
This really depends on your field, your target audience, your question, and the opinion of the individual. There isn't one and only one accepted way of doing this and I've had conflicting opinions from reviewers from international peer-reviewed journal submissions, with being told the Bonferonni corrections is both necessary and overly conservative and we should use a FDR. Bonferonni / FWER type corrections tend to be better understood by non-statisticians though, which is sometimes relevant depending on your target audience and the actual purpose of your work.
Edit: A comment below seems to indicate this answer implied whether to correct is subject to opinion. The answer was never supposed to imply that, only that which specific control method you use is often subject to field / audience / question, and that FWER is more widely understood.
In general terms: FDR is more powerful than FWER but does allow for some false positives. I generally prefer FWER, because if I find a borderline significant p value and report it negative, someone else might repeat the study, meta-analyse our results, and find a positive result. But if I find a false positive, it's less likely to be checked, and even it is and found to be negative by someone else with bigger numbers, positive findings propagate faster than negative findings.
