Sidak Method

Definition

Consider $m$ Multiple Testing problem $H_{0i}:{\mu }_{1i}={\mu }_{2i},i=1,2,\dots ,m$, and let $E_i$ be an event of type 1 error for $H_{0i}$ By the definition of the type 1 error in $m$ multiple testing, $FWER=P(V\ge 1)=P(\bigcup _{i=1}^m{E}_i)\le 1-(1-\alpha {)}^m$ Therefore, to control Family-Wise Error Rate $P(V\ge 1)$ at $\alpha$, Sidak method uses ${\alpha }^{\ast }=1-(1-\alpha {)}^{1/m}$ instead of the $\alpha$