Index: The Book of Statistical ProofsGeneral Theorems ▷ Frequentist statistics ▷ Hypothesis testing ▷ Size of a test

Definition: Let there be a statistical hypothesis test with null hypothesis $H_0$. Then, the size of the test is the probability of a false-positive result or making a type I error, i.e. the probability of rejecting the null hypothesis $H_0$, given that $H_0$ is actually true.

For a simple null hypothesis, the size is determined by the following conditional probability:

\[\label{eq:size-h0-simp} \mathrm{Pr}(\text{test rejects } H_0 \vert H_0) \; .\]

For a composite null hypothesis, the size is the supremum over all possible realizations of the null hypothesis:

\[\label{eq:size-h0-comp} \operatorname*{sup}_{h \in H_0} \mathrm{Pr}(\text{test rejects } H_0 \vert h) \; .\]

Metadata: ID: D132 | shortcut: size | author: JoramSoch | date: 2021-03-19, 14:46.