Walk the Benjamini-Hochberg ladder for 8 p-values

Question

You test m = 8 signals and want to control the false discovery rate at q = 0.05. Sorted from smallest to largest, the p-values are 0.003,\ 0.013,\ 0.017,\ 0.026,\ 0.030,\ 0.031,\ 0.20,\ 0.35. How many signals does the Benjamini-Hochberg procedure reject?

Accepted Answer

Build the ladder. Benjamini-Hochberg compares the k-th smallest p-value to a rising cutoff \frac{k}{m}q. Here \frac{k}{8}(0.05) = k 	imes 0.00625, giving the ladder 0.00625,\ 0.0125,\ 0.01875,\ 0.025,\ 0.03125,\ 0.0375,\ 0.04375,\ 0.05. Compare term by term. k p{(k)} ladder \frac{k}{m}q pass? ------------ 1 0.003 0.00625 Yes 2 0.013 0.0125 No 3 0.017 0.01875 Yes 4 0.026 0.025 No 5 0.030 0.03125 Yes 6 0.031 0.0375 Yes 7 0.20 0.04375 No 8 0.35 0.05 No Find the largest passing rung, then reject everything below it. This is the "step-up" rule: you do not stop at the first failure. Scan for the l…

Walk the Benjamini-Hochberg ladder for 8 p-values

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