Question: Rather than finding multiple tests that control the FWER, consider the k-FWER, the probability of rejecting k or more false hypotheses. For a given k,
Rather than finding multiple tests that control the FWER, consider the k-FWER, the probability of rejecting k or more false hypotheses. For a given k, if there are s hypotheses, consider the procedure that rejects any hypothesis whose p-value is ≤ kα/s. Show that the resulting procedure controls the k-FWER. [Additional stepdown procedures that control the number of false rejections, as well as the probability that the proportion of false rejections exceeds a given bound, are obtained in Lehmann and Romano (2005).]
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