Holm-Bonferroni Correction

The Holm-Bonferroni correction is a stepwise multiple-testing procedure that adjusts p-values to control the familywise error rate while being uniformly more powerful than the ordinary Bonferroni correction.

Holm-Bonferroni 보정은 p값을 단계적으로 조정하여 가족별 오류율을 통제하면서도 일반 Bonferroni 보정보다 항상 검정력이 같거나 높은 다중검정 보정 방법이다.

How do I adjust p-values when I run many pairwise comparisons?

여러 쌍의 비교를 할 때 p값을 어떻게 보정하나요?

The Holm-Bonferroni (Holm) procedure ranks the p-values from smallest to largest and compares each against an increasingly lenient threshold, stopping at the first non-significant result. It fits any set of comparisons, such as pairwise group tests, where you need to control the familywise error rate without the conservatism of plain Bonferroni.

When to use Holm-Bonferroni Correction

• Several pairwise comparisons between groups on one outcome
• A planned family of hypothesis tests that must share one familywise alpha
• Comparisons where Tukey-type procedures do not apply, such as nonparametric pairwise tests

When to use something else

• Controlling the proportion of false discoveries is acceptable, as with many exploratory tests: use the Benjamini-Hochberg procedure
• All pairwise mean comparisons with equal variances: use the Tukey HSD test

Assumptions and requirements

• The family of tests is defined before testing
• Each individual test is valid on its own
• Valid under any dependence structure among the tests

What the analysis reports

• Unadjusted p-value per comparison
• Holm-adjusted p-value per comparison
• Rejection decision at the familywise alpha (commonly .05)
• Test statistic and effect size for each comparison

How to report it

Pairwise comparisons with Holm-Bonferroni correction showed that [group 1] differed from [group 2], t([df]) = [value], p_adj = [value].

Related methods

• Bonferroni Correction
• Benjamini-Hochberg Procedure
• Tukey HSD Post Hoc Test

Run Holm-Bonferroni Correction on Quorant