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Family-Wise Error Rate in Multiple Hypothesis Testing

The family-wise error rate (FWER) is the probability of making at least one Type I error across a pre-specified family of mm null hypotheses H1,,HmH_1, \dots, H_m tested simultaneously. Formally, if VV is the number of true nulls that are rejected, then FWER=Pr(V1)\text{FWER} = \Pr(V \geq 1). A multiple-testing procedure is said to control FWER at level α\alpha when FWERα\text{FWER} \leq \alpha holds for every configuration of true and false nulls (strong control). Because a single per-test threshold of α\alpha inflates the chance of at least one false rejection as mm grows, families of tests require dedicated correction procedures whose guarantee is stated in terms of FWER rather than per-test error.

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Updated 2026-05-18

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