Benjamini-Hochberg on 5 p-values

Question

You test m = 5 hypotheses and control the false discovery rate at q = 0.05. Sorted smallest to largest, the p-values are 0.008,\ 0.011,\ 0.025,\ 0.5,\ 0.6. How many does the Benjamini-Hochberg procedure reject?

Accepted Answer

Build the ladder. BH compares the k-th smallest p-value to \frac{k}{m}q = \frac{k}{5}(0.05) = k 	imes 0.01, giving 0.01,\ 0.02,\ 0.03,\ 0.04,\ 0.05. Compare. k p{(k)} ladder pass? ------------ 1 0.008 0.01 Yes 2 0.011 0.02 Yes 3 0.025 0.03 Yes 4 0.5 0.04 No 5 0.6 0.05 No Find the largest passing rung. The largest k with p{(k)} \le \frac{k}{m}q is k = 3 (since 0.025 \le 0.03). Reject the three smallest. So BH rejects 3 hypotheses. Compare to Bonferroni. Bonferroni's cutoff is 0.05/5 = 0.01; only the smallest p-value (0.008) clears it, so Bonferroni rejects just one. BH's rising ladder recover…

Benjamini-Hochberg on 5 p-values

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