Bonferroni correction

Bonferroni correction

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 uniformly more powerful test procedure is the Holm-Bonferroni method, however current methods for obtaining confidence intervals for the Holm-Bonferroni method do not guarantee confidence intervals that are contained within those obtained using the Bonferroni correction. A less restrictive criterion that does not control the familywise error rate 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.

ee also

*Bonferroni inequalities
*Holm-Bonferroni method
*Multiple testing

References

*cite book | author=Abdi, H | chapter=Bonferroni and Sidak corrections for multiple comparisons | editor=N.J. Salkind (ed.) | title=Encyclopedia of Measurement and Statistics | year=2007 | location=Thousand Oaks, CA | publisher=Sage | url=http://www.utdallas.edu/~herve/Abdi-Bonferroni2007-pretty.pdf
*Manitoba Centre for Health Policy (MCHP) 2008, Concept: Multiple Comparisons, http://mchp-appserv.cpe.umanitoba.ca/viewConcept.php?conceptID=1049
*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
*Strassburger, K, Bretz, Frank. "Compatible simultaneous lower confidence bounds for the Holm procedure and other Bonferroni-based closed tests". Stat Med, 2008.


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