Bonferroni correction

In statistics, the Bonferroni correction is one of several methods used to counteract the problem of multiple comparisons.

The Bonferroni correction is named after Italian mathematician Carlo Emilio Bonferroni for its use of Bonferroni inequalities, but modern usage is often credited to Olive Jean Dunn, who described the procedure's application to confidence intervals.

Statistical hypothesis testing is based on rejecting the null hypothesis if the likelihood of the observed data under the null hypotheses is low. If multiple comparisons are done or multiple hypotheses are tested, the chance of a rare event increases, and therefore, the likelihood of incorrectly rejecting a null hypothesis (i.e., making a Type I error) increases.

The Bonferroni correction compensates for that increase by testing each individual hypothesis at a significance level of ${\displaystyle \alpha /m}$, where ${\displaystyle \alpha }$ is the desired overall alpha level and ${\displaystyle m}$ is the number of hypotheses. For example, if a trial is testing ${\displaystyle m=20}$ hypotheses with a desired ${\displaystyle \alpha =0.05}$, then the Bonferroni correction would test each individual hypothesis at ${\displaystyle \alpha =0.05/20=0.0025}$.

...
Wikipedia