When Holm rejects nothing at all

Question

You test m = 4 hypotheses and want the family-wise error rate held at \alpha = 0.05. Sorted smallest to largest, the p-values are 0.02,\ 0.03,\ 0.04,\ 0.045. How many does the Holm step-down procedure reject?

Accepted Answer

Holm's first step is the strictest. The smallest p-value faces the tightest cutoff, \frac{\alpha}{m} = \frac{0.05}{4} = 0.0125, identical to Bonferroni's. Only if it clears this does Holm move on to the looser cutoffs. Check the first step. The smallest p-value is 0.02, and 0.02 0.0125. It fails immediately. Stop at once. Because Holm halts at the first failure and cannot reject anything larger than a p-value that already failed, the procedure stops right away and rejects 0 hypotheses. The intuition. All four p-values sit between 0.02 and 0.045. Individually each would pass a lone 5% test, bu…

When Holm rejects nothing at all

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