Bonferroni inequalities

Carlo Emilio Bonferroni

Carlo Emilio Bonferroni (January 28, 1892August 18, 1960) was an Italian mathematician who worked on probability theory.

Bonferroni is famous for the Bonferroni correction, which 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. For example, when testing two hypotheses, instead of a p value of 0.05, one would use a stricter p value of 0.025. The Bonferroni correction is a safeguard against multiple tests of statistical significance on the same data, when the are no true systematic associations. Multiple tests in this case will lead to 1/20 of the hypotheses tested at the p = 0.05 level to be significant purely due to chance.

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