Holm–Bonferroni method

In statistics, the Holm–Bonferroni method (also called the Holm method or Bonferroni-Holm method) is used to counteract the problem of multiple comparisons. It is intended to control the familywise error rate and offers a simple test uniformly more powerful than the Bonferroni correction. It is one of the earliest usages of stepwise algorithms in simultaneous inference. It is named after Sture Holm, who codified the method, and Carlo Emilio Bonferroni.

When considering several hypotheses, the problem of multiplicity arises: the more hypotheses we check, the higher the probability of a Type I error (false positive). The Holm–Bonferroni method is one of many approaches that control the family-wise error rate (the probability that one or more Type I errors will occur) by adjusting the rejection criteria of each of the individual hypotheses or comparisons.

The method is as follows:

The Holm–Bonferroni method ensures that this method will control the ${\displaystyle FWER\leq \alpha }$, where ${\displaystyle FWER}$ is the Familywise error rate

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