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In statistics, the Bonferroni correction is a method used to counteract the problem of multiple comparisons. It is named after Italian mathematician Carlo Emilio Bonferroni for the use of Bonferroni inequalities,〔Bonferroni, C. E., Teoria statistica delle classi e calcolo delle probabilità, Pubblicazioni del R Istituto Superiore di Scienze Economiche e Commerciali di Firenze 1936〕 but modern usage is often credited to Olive Jean Dunn, who described the procedure in a pair of articles written in 1959 and 1961. ==Informal introduction== Statistical inference logic is based on rejecting the null hypotheses if the likelihood of the observed data under the null hypotheses is low. The problem of multiplicity arises from the fact that as we increase the number of hypotheses being tested, we also increase the likelihood of a rare event, and therefore, the likelihood of incorrectly rejecting a null hypothesis (i.e., make a Type I error). The Bonferroni correction is based on the idea that if an experimenter is testing hypotheses, then one way of maintaining the familywise error rate (FWER) is to test each individual hypothesis at a statistical significance level of times the desired maximum overall level. So, if the desired significance level for the whole family of tests is , then the Bonferroni correction would test each individual hypothesis at a significance level of . For example, if a trial is testing hypotheses with a desired , then the Bonferroni correction would test each individual hypothesis at . ''Statistically significant'' simply means that a given result is unlikely to occur if the null hypothesis is true (i.e., no difference among groups, no effect of treatment, no relation among variables). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bonferroni correction」の詳細全文を読む スポンサード リンク
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