Skip to content

A Simple Sequentially Rejective Multiple Test Procedure

Why this mattered

Before Holm’s 1979 paper, Bonferroni correction gave researchers a simple way to control familywise Type I error, but often at a severe cost in power: every hypothesis was tested against the same conservative threshold. Holm’s key move was to make the correction sequential. By ordering the observed p-values and testing them one at a time against progressively less stringent Bonferroni bounds, the procedure retained strong familywise error control for any configuration of true and false hypotheses while allowing more rejections than ordinary Bonferroni.

This mattered because it turned multiplicity control from a blunt penalty into an adaptive procedure. After Holm, researchers could use a method that was nearly as simple and assumption-light as Bonferroni, yet uniformly more powerful, making rigorous multiple testing practical across experimental psychology, biomedicine, genomics, economics, and other fields where many hypotheses are tested at once.

The paper also helped establish the stepwise logic that later multiple-testing theory built on. Procedures such as Hochberg’s step-up method, closed testing interpretations, gatekeeping methods, and later false-discovery-rate approaches all belong to the broader shift toward ordered, data-dependent error control. Holm’s contribution was not just a better correction; it showed that strong error guarantees and practical power could coexist in a transparent algorithm.

Abstract

This paper presents a simple and widely ap- plicable multiple test procedure of the sequentially rejective type, i.e. hypotheses are rejected one at a tine until no further rejections can be done. It is shown that the test has a prescribed level of significance protection against error of the first kind for any combination of true hypotheses. The power properties of the test and a number of possible applications are also discussed.

Sources