Benjamini-Hochberg on 10 p-values at q = 0.10

Question

You test m = 10 hypotheses and control the false discovery rate at q = 0.10. Sorted smallest to largest, the p-values are 0.001,\ 0.004,\ 0.006,\ 0.02,\ 0.03,\ 0.06,\ 0.08,\ 0.09,\ 0.3,\ 0.4. How many does the Benjamini-Hochberg procedure reject?

Accepted Answer

Build the ladder. BH compares p{(k)} to \frac{k}{m}q = \frac{k}{10}(0.10) = k 	imes 0.01, giving 0.01,\ 0.02,\ 0.03,\ 0.04,\ 0.05,\ 0.06,\ 0.07,\ 0.08,\ 0.09,\ 0.10. Compare. k p{(k)} ladder pass? ------------ 1 0.001 0.01 Yes 2 0.004 0.02 Yes 3 0.006 0.03 Yes 4 0.02 0.04 Yes 5 0.03 0.05 Yes 6 0.06 0.06 Yes 7 0.08 0.07 No 8 0.09 0.08 No 9 0.3 0.09 No 10 0.4 0.10 No Mind the tie. At k = 6, the p-value equals its rung exactly (0.06 \le 0.06), which counts as a pass, the rule uses "less than or equal." The largest passing rung is k = 6, so reject the six smallest. So BH rejects 6 hypotheses. Co…

Benjamini-Hochberg on 10 p-values at q = 0.10

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