Bonferroni correction

The Bonferroni correction tests each of $m$ hypotheses at level $\alpha /m$. The union bound then controls the familywise error rate by $\alpha$ under arbitrary dependence.

The Holm–Bonferroni method orders p-values and compares the $j$th smallest with $\alpha /(m-j+1)$, stopping at the first failed comparison. It controls the familywise error rate under arbitrary dependence.