Size of Critical Region

Definition

if $\alpha ={\max }_{\theta \in {\omega }_0}{P}_{\theta }[(X_1,\dots ,X_n)\in C]$ Then

• We say critical region $C$ is of size $\alpha$
• We often say $\alpha$ is the significance level of the test associated with $C$
• The size/significance level $\alpha$ is the probability of making a type I error