Bonferroni Correction

The Bonferroni correction is a multiple-comparison adjustment that controls the familywise error rate by testing each of m comparisons at alpha divided by m, or equivalently multiplying each p-value by m.

본페로니 교정은 m개의 비교 각각을 유의수준 α/m에서 검정하거나 각 p값에 m을 곱하여 집단전체 오류율을 통제하는 다중비교 보정 방법이다.

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

집단 간 쌍별 비교를 여러 번 할 때 p값을 어떻게 보정하나요?

The Bonferroni correction adjusts for multiple comparisons by dividing the significance level by the number of tests, which keeps the chance of any false positive at or below alpha. It fits a small number of planned comparisons, but it becomes conservative as the number of tests grows.

When to use Bonferroni Correction

• A small set of planned pairwise comparisons between groups on one outcome
• Several separate tests where any single false positive must be controlled
• Follow-up comparisons when a simple, widely accepted adjustment is required

When to use something else

• Many comparisons where power matters; use the Holm procedure or the Benjamini-Hochberg false discovery rate
• All pairwise mean comparisons after ANOVA with equal variances; use Tukey's HSD test

Assumptions and requirements

• The comparisons form a defined family of tests
• Valid unadjusted p-values from the underlying tests
• Valid under any dependence among tests, at the cost of being conservative

What the analysis reports

• Unadjusted and adjusted p-values
• Adjusted significance threshold
• Pairwise mean differences with confidence intervals

How to report it

Pairwise comparisons with Bonferroni correction showed that [Group A] differed from [Group B], adjusted p = [value].

Related methods

• Holm-Bonferroni Method
• Benjamini-Hochberg Procedure
• Tukey HSD Post Hoc Test

Run Bonferroni Correction on Quorant