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Education And Debate

# What's wrong with Bonferroni adjustments

BMJ 1998; 316 (Published 18 April 1998) Cite this as: BMJ 1998;316:1236
1. Thomas V Perneger (perneger@cmu.unige.ch), medical epidemiologist
1. Institute of Social and Preventive Medicine, University of Geneva, CH-1211 Geneva 4, Switzerland
1. Correspondence to: Dr Perneger
• Accepted 16 January 1998

When more than one statistical test is performed in analysing the data from a clinical study, some statisticians and journal editors demand that a more stringent criterion be used for “statistical significance” than the conventional P<0.05.1 Many well meaning researchers, eager for methodological rigour, comply without fully grasping what is at stake. Recently, adjustments for multiple tests (or Bonferroni adjustments) have found their way into introductory texts on medical statistics, which has increased their apparent legitimacy. This paper advances the view, widely held by epidemiologists, that Bonferroni adjustments are, at best, unnecessary and, at worst, deleterious to sound statistical inference.

#### Summary points

Adjusting statistical significance for the number of tests that have been performed on study data—the Bonferroni method—creates more problems than it solves

The Bonferroni method is concerned with the general null hypothesis (that all null hypotheses are true simultaneously), which is rarely of interest or use to researchers

The main weakness is that the interpretation of a finding depends on the number of other tests performed

The likelihood of type II errors is also increased, so that truly important differences are deemed non-significant

Simply describing what tests of significance have been performed, and why, is generally the best way of dealing with multiple comparisons

## Adjustment for multiple tests

Bonferroni adjustments are based on the following reasoning.1-3 If a null hypothesis is true (for instance, two treatment groups in a randomised trial do not differ in terms of cure rates), a significant difference (P<0.05) will be observed by chance once in 20 trials. This is the type I error, or α. When 20 independent tests are performed (for example, study groups are compared with regard to 20 unrelated variables) and the null hypothesis holds for all 20 comparisons, the chance of at least one test being significant is no longer 0.05, but 0.64. …

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