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Regarding multiple comparisons, could someone please explain me why the power of false discovery rate (FDR) is greater than the power of family-wise error rate (FWER)?

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Basically it is because controlling the FWER controls the probability of making a Type I error AT ALL and the FDR allows Type I Errors but controls how many of them you make in proporition to your true positives. The FDR has a higher power because it has a higher Type I error rate, which is a classical trade-off.

This is just a short answer, but I think it catches the essence.

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Ok and formally how do you prove it? I understand the intuition but searching for a formal proof. Furthermore why the fdr power is good when the number of samples is increased and the feet gets worse when increasing the number of samples? Thank you! – MLS Apr 19 '12 at 15:38

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