Improving the Power of Bonferroni Adjustments under Joint Normality and Exchangeability

TL;DR

This paper introduces a practical modification to Bonferroni's correction for dependent tests, improving power while maintaining error control under joint normality and exchangeability.

Contribution

It proposes a new, intuitive adjustment to Bonferroni correction that enhances power in dependent test scenarios with proven error rate control.

Findings

Achieves higher power in sparse alternatives

Controls family-wise error rate at any significance level

Effective under joint normality and exchangeability

Abstract

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.