Ten fakes among two hundred hits

Question

A large screen flags 200 candidate signals as significant. A careful follow-up finds that 10 of them were actually worthless. What fraction of the flagged signals were false discoveries?

Accepted Answer

Divide false by total. The false discovery proportion is 	ext{FDP} = \frac{10}{200} = 0.05, so 5% of the discoveries were false. Reading it in context. A 5% false discovery proportion is a healthy outcome for a screen: nineteen out of every twenty flagged signals are real. Note that this "5%" is about the discoveries, not the nulls, it is a coincidence that the number equals a common significance level, and the two mean entirely different things. How you would target this on purpose. To aim for a false discovery proportion around 5% on average, you would run the Benjamini-Hochberg procedure …

Ten fakes among two hundred hits

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