Which method controls the family-wise error rate and is performed in a stepwise fashion?

• A. Bonferroni
• B. Holm-Bonferroni
• C. Tukey's HSD
• D. Sidak correction

Answer: (B)

Controlling the family-wise error rate with a stepwise procedure. The Holm-Bonferroni method is a sequential, rejective approach to multiple testing that preserves strong control of the FWER while usually offering more power than the plain Bonferroni rule. You start by ordering all p-values from smallest to largest, then compare the smallest p-value to alpha divided by the total number of tests, the next smallest to alpha divided by one less than the total, and so on. If a p-value is smaller than its corresponding threshold, you reject that hypothesis and move on; as soon as a p-value fails to meet its progressively less stringent threshold, you stop rejecting further hypotheses. This stepwise refinement ensures that the probability of making at least one false-positive claim across all tests stays at or below the chosen alpha level.

Bonferroni on the other hand uses a single fixed threshold for all tests (alpha divided by the number of tests) without ordering, which is simpler but more conservative. Tukey’s HSD is designed for all pairwise comparisons after an ANOVA and relies on a different distribution, not a stepwise rejection procedure. Sidak correction adjusts p-values based on an independence assumption to achieve a slightly less conservative overall threshold but is not implemented in a stepwise manner.