The Step-Up Surprise
Ten hypotheses are tested, with p-values 0.720, 0.049, 0.001, 0.205, 0.060, 0.008, 0.390, 0.045, 0.074, 0.021 (in no particular order). Apply the Benjamini-Hochberg procedure at false discovery rate level q = 0.10: sort the p-values as p(1) ≤ ... ≤ p(10), find the largest k with p(k) ≤ 0.10 k / 10, and reject the k hypotheses with the smallest p-values. How many hypotheses are rejected? Give an integer.
Related problems & prerequisites
Worth solving first
- The Smallest of Ten p-values 5.0/10
- Two Hits Among Twenty Nulls 4.0/10
- The Peeking Problem 4.0/10
Source: Benjamini and Hochberg (1995) step-up procedure for false discovery rate control. Statement written for AxiomIQ.