Skip directly to site content Skip directly to page options Skip directly to A-Z link Skip directly to A-Z link Skip directly to A-Z link
Volume 21, Number 2—February 2015

Etymologia: Bonferroni Correction

Article Metrics
citations of this article
EID Journal Metrics on Scopus

Cite This Article

Bonferroni [bonʹfər-ōʺni] Correction

Named after Italian mathematician Carlo Emilio Bonferroni (1892–1960) but first attributed to Olive Jean Dunn, the Bonferroni correction compensates for multiple comparisons by dividing the significance level by the number of comparisons. The significance level is the probability that a given test will incorrectly find a difference in the sample that is not present in the population (false positive). A significance level of 0.05 is a commonly accepted significance level. If a study tested 5 comparisons, there would be up to a 25% likelihood (0.05 + 0.05 + 0.05 + 0.05 + 0.05) that any one of them would show a significant difference by chance. The Bonferroni correction adjusts for this by dividing the significance level by the number of tests. In this case, the significance level for a given comparison would be 0.01, for an overall risk no larger than 0.05 of falsely detecting a difference.

This technique has been criticized as too conservative, particularly when a large number of tests are used, and it may increase the risk for a false negative. Other tests, such as the Tukey-Kramer and Scheffe method, may reduce this risk.



  1. Bland  JM, Altman  GD. Multiple significance tests: the Bonferroni method. BMJ. 1995;310:170 . DOIPubMedGoogle Scholar
  2. Dunn  OJ. Multiple comparisons among means. J Am Stat Assoc. 1961;56:5264. DOIGoogle Scholar
  3. Perneger  TV. What’s wrong with Bonferroni adjustments. BMJ. 1998;316:12368. DOIPubMedGoogle Scholar
  4. Sedgwick  P. Multiple hypothesis testing and Bonferroni’s correction. BMJ. 2014;349:g6284. DOIPubMedGoogle Scholar


Cite This Article

DOI: 10.3201/eid2102.et2102

Related Links


Table of Contents – Volume 21, Number 2—February 2015

Page created: January 20, 2015
Page updated: January 20, 2015
Page reviewed: January 20, 2015
The conclusions, findings, and opinions expressed by authors contributing to this journal do not necessarily reflect the official position of the U.S. Department of Health and Human Services, the Public Health Service, the Centers for Disease Control and Prevention, or the authors' affiliated institutions. Use of trade names is for identification only and does not imply endorsement by any of the groups named above.