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Family-Wise Error Rate (FWER)

Family-wise error rate (FWER) is the probability of making one or more Type I errors (false rejections of a true null hypothesis) across a family of mm hypothesis tests H1,,HmH_1, \dots, H_m considered jointly. Formally, if VV is the number of true null hypotheses that are rejected, then FWER=Pr(V1)\mathrm{FWER} = \Pr(V \geq 1). A multiple-testing procedure is said to control FWER in the strong sense at level α\alpha when FWERα\mathrm{FWER} \leq \alpha for every configuration of true and false nulls. FWER control is the standard error guarantee invoked when reporting paired comparisons within a family of related tests, because it bounds the chance that any of the highlighted differences is spurious.

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Updated 2026-05-16

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