How many of your 80 discoveries are probably fake?

Question

You ran the Benjamini-Hochberg procedure controlling the false discovery rate at $q = 0.10$ , and it flagged 80 signals as significant.

Roughly how many of these 80 discoveries should you expect to be false?

Accepted Answer

What FDR control promises. Controlling the false discovery rate at 10% means the expected proportion of false discoveries among your flagged results is held to about 10%. In words: on average, no more than a tenth of what you flag is fake. Turn the proportion into a count. If about 10% of your discoveries are false, then out of 80 discoveries the expected number of false ones is roughly q 	imes R = 0.10 	imes 80 = 8. So expect about 8 of the 80 to be false, leaving roughly 72 genuine. A caveat on "roughly." FDR control bounds the expected proportion, not the exact count in any single run, a…

How many of your 80 discoveries are probably fake?

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