Holm step-down at a 10% family level, six tests

Question

You test m = 6 hypotheses and want the family-wise error rate held at \alpha = 0.10. Sorted smallest to largest, the p-values are 0.01,\ 0.03,\ 0.04,\ 0.2,\ 0.3,\ 0.4. How many does the Holm step-down procedure reject?

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Holm's cutoffs. Compare the k-th smallest p-value to \frac{\alpha}{m-k+1}, rejecting in order until the first failure. Walk down. With \alpha = 0.10 and m = 6: k p{(k)} cutoff \frac{\alpha}{m-k+1} decision ------------ 1 0.01 0.10/6 = 0.0167 reject, continue 2 0.03 0.10/5 = 0.020 fail, stop Stop early. The very first cutoff (0.0167) clears the smallest p-value, but at k = 2 the p-value 0.03 exceeds its cutoff of 0.020, so Holm stops. Everything from k = 2 onward is retained (not rejected). Holm rejects 1 hypothesis. Why stopping is mandatory. Once a p-value fails, Holm cannot reject anything …

Holm step-down at a 10% family level, six tests

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