Holm’s Method

Synonyms

Holm’s procedure; Holm-Bonferroni method; Sequentially rejective Bonferroni test

Definition

Designed for multiple hypothesis testing, the Holm’s method iteratively accepts and rejects hypotheses. The Holm’s method is a close relative to the Bonferroni correction with slightly different threshold levels.

Let α be the determined significance threshold for rejecting the null hypotheses and k be the number of hypotheses. Begin by ordering the k hypotheses by their respective p-values. Select the lowest p-value and compare it to α/k. If the p-value is lower, then reject that hypothesis and perform the same selection with the remaining k−1 hypotheses and a threshold of α/(k−1). Repeat the process until the selected p-value is not smaller, at which time all remaining hypotheses should be accepted.

By progressively adapting the threshold values, the Holm’s method gains power over the Bonferroni correction. Whereas in the Bonferroni correction all values are thresholded relative to a/k...