Bonferroni and Holm Corrections

Overview

Bonferroni Correction

Reject \(H_i\) if \(p_i \leq \alpha/m\). Simple but conservative.

Holm's Step-Down Procedure

1. Order p-values: \(p_{(1)} \leq p_{(2)} \leq \cdots \leq p_{(m)}\)
2. Reject \(H_{(i)}\) if \(p_{(i)} \leq \alpha/(m-i+1)\) for all prior hypotheses
3. Stop at first non-rejection

Holm's method is uniformly more powerful than Bonferroni while still controlling FWER.