Does FDR control cap the chance of any false positive?

Question

You ran a procedure controlling the false discovery rate at 5% and it flagged 50 discoveries. A colleague concludes: "Great, so there's only a 5% chance that even one of these 50 is a false positive."

Is the colleague right?

Accepted Answer

Two different guarantees. The colleague is confusing two distinct error rates. - False discovery rate (FDR), what you controlled, is the expected proportion of your discoveries that are false. Controlling it at 5% means on average about 5% of your 50 discoveries (roughly 2 to 3) are fake. - Family-wise error rate (FWER) is the chance of even one false positive anywhere. That is the far stricter guarantee the colleague described. Why the colleague is wrong. Controlling FDR at 5% does not cap the probability of any single false positive at 5%. In fact, when you make 50 discoveries under FDR con…

Does FDR control cap the chance of any false positive?

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