I understand that false discovery rate (FDR) is $\leq$ familywise error rate (FWE). I have read this means that controlling FDR is hence "more powerful" than controlling FWE. What does more powerful mean in this multiple testing context?
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kjetil b halvorsen
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Golden_Ratio
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It means you can allow a looser threshold to declare significance with FDR-controlling procedures, thereby rejecting more hypotheses, thereby having higher power. – BigBendRegion Jan 21 '22 at 13:01
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@BigBendRegion Thanks for the comment. I have since thought about this. But from what I gather, I don't see how the looser threshold implies an FDR controlling procedure necessarily rejects more hypotheses than an FWE controlling procedure. I asked about this here: https://stats.stackexchange.com/questions/555877/does-a-procedure-controlling-fdr-at-level-alpha-always-reject-at-least-as-muc – Golden_Ratio Jan 21 '22 at 19:36
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Eg, p< .03 happens more often than p< .01. – BigBendRegion Jan 21 '22 at 20:02