Bonferroni correction

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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.

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