The Bonferroni correction is the simplest single-step procedure for controlling the family-wise error rate when $m$ hypotheses $H_1, \dots, H_m$ are tested simultaneously. Each individual test is conducted at the reduced significance level

$\alpha_{\text{per-test}} = \frac{\alpha}{m},$

so a null hypothesis $H_i$ is rejected when its p-value satisfies $p_i \leq \alpha/m$. By Boole's (Bonferroni's) inequality, $\Pr\!\left(\bigcup_{i: H_i \text{ true}} \{p_i \leq \alpha/m\}\right) \leq \alpha$, so the procedure strongly controls $\mathrm{FWER}$ at level $\alpha$ under any joint distribution of the test statistics. Its drawback is that it uses the same constant threshold $\alpha/m$ for every hypothesis, which makes it conservative and motivates step-down refinements such as Holm's procedure.