Solution
Holm Beats Bonferroni
Show the problem again
Eight hypotheses are tested with p-values 0.0005, 0.0060, 0.0070, 0.0090, 0.0105, 0.0200, 0.2000, 0.6000. Apply Holm's step-down procedure at family-wise error rate 0.05: sort the p-values, compare the smallest with 0.05/8, the next with 0.05/7, then 0.05/6, and so on, rejecting in order and stopping at the first failure. How many hypotheses does Holm reject? Give an integer.
Worked solution
The thresholds are 0.00625, 0.00714, 0.00833, 0.01, 0.0125, 0.01667, ... The first five sorted p-values pass: 0.0005, 0.0060, 0.0070, 0.0090 and 0.0105 are below 0.00625, 0.00714, 0.00833, 0.01 and 0.0125 respectively. The sixth, 0.0200, exceeds 0.05/3 ≈ 0.0167, so Holm stops with 5 rejections. Plain Bonferroni (0.00625 for every test) would reject only the first two. Holm controls the family-wise error rate under any dependence and is uniformly more powerful.
Source: Holm (1979) step-down procedure, standard in multiple-testing texts. Statement written for AxiomIQ.