Holm step-down that rejects everything

Question

You test m = 3 hypotheses and want the family-wise error rate held at \alpha = 0.05. Sorted smallest to largest, the p-values are 0.001,\ 0.02,\ 0.03. How many does the Holm step-down procedure reject?

Accepted Answer

The cutoffs widen. Compare the k-th smallest p-value to \frac{\alpha}{m-k+1}, rejecting in order until the first failure. Walk down. With \alpha = 0.05 and m = 3: k p{(k)} cutoff \frac{\alpha}{m-k+1} decision ------------ 1 0.001 0.05/3 = 0.0167 reject, continue 2 0.02 0.05/2 = 0.025 reject, continue 3 0.03 0.05/1 = 0.05 reject, continue No failure. Every p-value clears its (widening) cutoff, so Holm rejects all 3 hypotheses. Notice the last step. By the final hypothesis, Holm's cutoff has relaxed all the way back to the full \alpha = 0.05. That is why the 0.03, which plain Bonferroni (cutoff…

Holm step-down that rejects everything

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