Familywise error rate (FWER)

The familywise error rate is the probability of making at least one false rejection in a family of hypothesis tests.

For nonempty index sets forming a laminar family of sets, reject an intersection hypothesis when the displayed adjusted value is at most $\alpha$. The inclusion-maximal true sets are disjoint and have total size at most $m$. Any false rejection forces some maximal true $J$ to have $p_J\le \alpha |J|/m$. Validity and the union bound control the familywise error rate by $\alpha$, without independence or a complete closure.