Type-I Error Rate

Definition

Let $\varphi$ be a test, the probability of a Type-I Error under a given probabilistic model is central to the quality of a test. The probability of a Type-I Error is called the size of the test and is denoted by $\alpha \in [0,1]$. It is defined as

\begin{equation}\tag{test size}\alpha:=p_{\Theta_0}(\phi(y)=1)\;,\end{equation}

and referred as Type I error rate of the test. Its complementary probability

$p_{{\Theta }_0}(y=0)=1-\alpha$

is known as the specificity of the test.

Reference

D. Ostwald - The general linear model 20_21 pp 117