When to use the Bonferroni correction

Abstract

Purpose: The Bonferroni correction adjusts probability (p) values because of the increased risk of a type I error when making multiple statistical tests. The routine use of this test has been criticised as deleterious to sound statistical judgment, testing the wrong hypothesis, and reducing the chance of a type I error but at the expense of a type II error; yet it remains popular in ophthalmic research. The purpose of this article was to survey the use of the Bonferroni correction in research articles published in three optometric journals, viz. Ophthalmic & Physiological Optics, Optometry & Vision Science, and Clinical & Experimental Optometry, and to provide advice to authors contemplating multiple testing.

Recent findings: Some authors ignored the problem of multiple testing while others used the method uncritically with no rationale or discussion. A variety of methods of correcting p values were employed, the Bonferroni method being the single most popular. Bonferroni was used in a variety of circumstances, most commonly to correct the experiment-wise error rate when using multiple 't' tests or as a post-hoc procedure to correct the family-wise error rate following analysis of variance (anova). Some studies quoted adjusted p values incorrectly or gave an erroneous rationale.

Summary: Whether or not to use the Bonferroni correction depends on the circumstances of the study. It should not be used routinely and should be considered if: (1) a single test of the 'universal null hypothesis' (Ho ) that all tests are not significant is required, (2) it is imperative to avoid a type I error, and (3) a large number of tests are carried out without preplanned hypotheses.

Keywords: Bonferroni correction; Clinical & Experimental Optometry; Ophthalmic & Physiological Optics; Optometry & Vision Science; statistical guidelines.