bonferroni bonferroni_correction dissertation genetics genomewide_association_studies globalwarming math mathematics methodology scholarship statistics stats test

My tags:

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 one way of maintaining the familywise error rate is to test each individual hypothesis at a statistical significance level of 1/n times what it would be if only one hypothesis were tested (α/n). Statistically significant simply means that a given result is unlikely to have occurred by chance assuming your hypothesis is correct. Another correction that is often used is

1 − (1 − α)^1/n (corrected for n comparisons)

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 equal to the square root of 0.05. Notably one can derive valid confidence intervals matching the test decision using the Bonferroni correction by using 100(1 − α^1/n)% confidence intervals.

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 is expected to be significant at the α = 0.05 level purely due to chance. Furthermore, the probability of getting a significant result with n tests at this level of significance is 1 − 0.95ⁿ (1 − probability of not getting a significant result with n tests).

It was developed by Italian mathematician Carlo Emilio Bonferroni.

A uniformly more powerful test procedure (i.e. more powerful regardless of the values of the unobservable parameters) 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.

[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. 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
• Shaffer, J. P. "Multiple Hypothesis Testing." Ann. Rev. Psych. 46, 561–584, 1995.
• Strassburger, K, Bretz, Frank. "Compatible simultaneous lower confidence bounds for the Holm procedure and other Bonferroni-based closed tests". Stat Med, 2008.

This article is in need of attention from an expert on the subject. WikiProject Statistics or the Statistics Portal may be able to help recruit one. (November 2008)