 Weighted interval testing for a piecewise-constant mean

Given valid p-values $q_J$ for constancy on intervals of length at least two, reject $I$ when ${\max }_{J\supseteq I}n{q}_J/|J|\le \alpha$. Every rejected true interval forces rejection of its maximal constant block. A union bound over the non-singleton maximal blocks gives familywise error rate at most $\alpha$, since their lengths sum to at most $n$. Singleton blocks have no tested interval in this formulation.