Holm step-down on 5 p-values

Question

You test m = 5 hypotheses and want the family-wise error rate held at \alpha = 0.05. Sorted smallest to largest, the p-values are 0.008,\ 0.011,\ 0.020,\ 0.030,\ 0.6. How many does the Holm step-down procedure reject?

Accepted Answer

Holm's widening cutoffs. Compare the k-th smallest p-value to \frac{\alpha}{m-k+1}, which grows as you move down the list. Reject in order until the first failure, then stop. Walk down. With \alpha = 0.05 and m = 5: k p{(k)} cutoff \frac{\alpha}{m-k+1} decision ------------ 1 0.008 0.05/5 = 0.010 reject, continue 2 0.011 0.05/4 = 0.0125 reject, continue 3 0.020 0.05/3 = 0.0167 fail, stop Stop. The first failure is at k = 3 (0.020 0.0167), so Holm rejects the first two and stops. Holm rejects 2 hypotheses. Compare to Bonferroni. Bonferroni's cutoff is 0.05/5 = 0.01; only 0.008 clears it, so Bo…

Holm step-down on 5 p-values

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