The Exact FDR of a Screen
A screen tests 1000 hypotheses, of which exactly 800 are true nulls (with independent, exactly uniform p-values) and 200 are real effects. The p-values are mutually independent. The Benjamini-Hochberg procedure is run at nominal level q = 0.05. The false discovery rate is the expected value of (false rejections) / max(1, total rejections). What is the exact FDR of this procedure? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
- The Smallest of Ten p-values 5.0/10
- Simultaneous Intervals by Bonferroni 5.0/10
- Two Hits Among Twenty Nulls 4.0/10
Source: Benjamini and Hochberg (1995) show that the BH procedure has FDR equal to pi0 q under independence. Statement written for AxiomIQ.