= Familywise error control for a laminar hypothesis family
{title2=$p_I^{\mathrm{adj}}=\max_{J\supseteq I}\frac m{|J|}p_J$}
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 $p_J\leq\alpha|J|/m$. Validity and the <union bound> control the <familywise error rate> by $\alpha$, without independence or a complete closure.
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