We consider one of the most basic multiple testing problems that compares expectations of multivariate data among several groups. As a test statistic, a conventional (approximate) $t$-statistic is considered, and we determine its rejection region using a common rejection limit. When there are unknown correlations among test statistics, the multiplicity adjusted $p$-values are dependent on the unknown correlations. They are usually replaced with their estimates that are always consistent under any hypothesis. In this paper, we propose the use of estimates, which are not necessarily consistent and are referred to as spurious correlations, in order to improve statistical power. Through simulation studies, we verify that the proposed method asymptotically controls the family-wise error rate and clearly provides higher statistical power than existing methods. In addition, the proposed and existing methods are applied to a real multiple testing problem that compares quantitative traits among groups of mice and the results are compared.

我们考虑了最基本的多重测试问题之一，该问题可以比较多个组之间对多元数据的期望。作为测试统计数据，常规（近似）$Ť$考虑到-statistic，我们使用共同的拒绝限制来确定其拒绝区域。如果检验统计量之间的相关性未知，则调整多重性$p$-值取决于未知的相关性。通常将其替换为在任何假设下始终保持一致的估计。在本文中，我们建议使用估计值，这些估计值不一定是一致的，因此被称为虚假相关性，以提高统计能力。通过仿真研究，我们验证了所提出的方法渐近地控制了全族错误率，并且显然提供了比现有方法更高的统计能力。另外，将所提出的和现有的方法应用于实际的多重测试问题，该问题比较了各组小鼠之间的数量性状并比较了结果。