Abstract We have considered equicorrelated observations from normal distribution for simultaneous testing problem. In this article, we have shown that FWER asymptotically is a convex function of the correlation ( ρ ) and hence an upper bound on the FWER of Bonferroni- α procedure is α ( 1 − ρ ) . This implies that Bonferroni’s method actually controls the FWER at a much smaller level than the desired level of significance under the positively correlated case and necessitates a correlation correction.

中文翻译：

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相关正态的 FWER 约束

摘要 我们已经为同时测试问题考虑了正态分布的等相关观测值。在本文中，我们已经证明 FWER 渐近地是相关性 ( ρ ) 的凸函数，因此 Bonferroni-α 过程的 FWER 的上限是 α ( 1 − ρ ) 。这意味着 Bonferroni 的方法实际上将 FWER 控制在比正相关情况下所需的显着性水平小得多的水平上，并且需要进行相关校正。