Bonferroni correction

From Wikipedia, the free encyclopedia

In statistics, the Bonferroni correction states that if an experimenter is testing n dependent or independent hypotheses on a set of data, then the statistical significance level that should be used for each hypothesis separately is 1/n times what it would be if only one hypothesis were tested. Statistically significant simply means that a given result is unlikely to have occurred by chance.

For example, to test two independent hypotheses on the same data at 0.05 significance level, instead of using a p value threshold of 0.05, one would use a stricter threshold of 0.025.

The Bonferroni correction is a safeguard against multiple tests of statistical significance on the same data falsely giving the appearance of significance, as 1 out of every 20 hypothesis-tests will appear to be significant at the α = 0.05 level purely due to chance.

It was developed by Italian mathematician Carlo Emilio Bonferroni.

A less restrictive criterion is the rough false discovery rate giving (3/4)0.05 = 0.0375 for n = 2 and (21/40)0.05 = 0.02625 for n = 20.

[edit] See also

• Bonferroni inequalities
• Holm-Bonferroni method
• Multiple testing

[edit] References

• Abdi, H (2007). "Bonferroni and Sidak corrections for multiple comparisons", in N.J. Salkind (ed.): Encyclopedia of Measurement and Statistics. Thousand Oaks, CA: Sage. 
• Manitoba Centre for Health Policy (MCHP) 2003, Bonferroni Correction, <http://www.umanitoba.ca/centres/mchp/concept/dict/Statistics/bonferroni.html>.
• Perneger, Thomas V, What's wrong with Bonferroni adjustments, BMJ 1998;316:1236-1238 ( 18 April ) <http://www.bmj.com/cgi/content/full/316/7139/1236>
• School of Psychology, University of New England, New South Wales, Australia, 2000, <http://www.une.edu.au/WebStat/unit_materials/c5_inferential_statistics/bonferroni.html>
• Weisstein, Eric W. "Bonferroni Correction." From MathWorld--A Wolfram Web Resource. <http://mathworld.wolfram.com/BonferroniCorrection.html>

This article or section is in need of attention from an expert on the subject. WikiProject Statistics may be able to help recruit one. If a more appropriate WikiProject or portal exists, please adjust this template accordingly.