Definition

Consider $m$ Multiple Testing problem $H_{0 i} : μ_{1 i} = μ_{2 i}, i = 1, 2, \dots, m$ , and let $E_{i}$ be an event of type 1 error for $H_{0 i}$ . Then, by the Bonferroni Inequality, $F W ER = P (V \geq 1) = P (i = 1 ⋃ m E_{i}) \leq i = 1 \sum m P (E_{i})$ Therefore, to control Family-Wise Error Rate $P (V \geq 1)$ at $α$ , we need to control $P (E_{i}) \leq \frac{α}{m}$

The Bonferroni method is too conservative and consequently, it is not a powerful test.