Statistics Graduate Level Quiz
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HYPOTHESIS TESTING
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A study estimates mm treatment effects θ1,…,θm\theta_1,\ldots,\theta_m. For each coordinate and candidate value, pj(θj)p_j(\theta_j) is a valid p-value for H0j:θj=θj0H_{0j}:\theta_j=\theta_j^0. Define Cj={θj:pj(θj)>αm}C_j=\left\{\theta_j:p_j(\theta_j)>\frac{\alpha}{m}\right\} and the rectangular set C=C1×⋯×CmC=C_1\times\cdots\times C_m.
Without assuming independence among the p-values, which coverage claim follows from test inversion?
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