Bonferroni's correction is a popular tool to address multiplicity but is notorious for its low power when tests are dependent. This paper proposes a practical modification of Bonferroni's correction when test statistics are jointly normal and exchangeable. This method is intuitive to practitioners and achieves higher power in sparse alternatives, as our simulations suggest. We also prove that this method successfully controls the family-wise error rate at any significance level.

翻译：Bonferroni校正是处理多重性问题的常用工具，但在检验统计量存在依赖性时，其统计功效低下的问题广受诟病。本文针对检验统计量满足联合正态性与可交换性的情形，提出了一种实用的Bonferroni校正改进方法。该方法对实践者而言直观易懂，且模拟研究表明其在稀疏备择假设下能获得更高的统计功效。我们同时证明，该方法能在任意显著性水平上有效控制族错误率。