13.4 Family Wise Error Rate (FWER)

Probability of making at least 1 type I error.

FWER is the probability of at least 1 type I error

\[FWER =Pr(V\geq1)=\] \[=1-Pr(V=0)=\] \[=1-\prod_{1}^{m}{(1-\alpha)}=\] \[1-(1-\alpha)^m\]

With hypothesis that m tests are independents.

\[FWER\leq m\frac{\alpha}{m}=\alpha\] We set a new \(\alpha\) value which is lower in proportion.

Bonferroni \(\frac{\alpha}{m}=\text{new } \alpha\)

Holm’s step down Holm’s \(L=min{j:p_j>\frac{\alpha}{m+1-j}}\) is less conservative, with fewer type II errors and greater power.

\[\text{min }\{p_j>\frac{\alpha}{m+1-j}\}\]

These other two are subsequent methods to apply for further investigations: