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

Definition: Let there be a statistical hypothesis test with null hypothesis $H_0$ and alternative hypothesis $H_1$. Then, the power of the test is the probability of a true-positive result or not making a type II error, i.e. the probability of rejecting $H_0$, given that $H_1$ is actually true.

For given null and alternative hypothesis, the size is determined by the following conditional probability:

\[\label{eq:power} \mathrm{Pr}(\text{test rejects } H_0 \vert H_1) \; .\]

Metadata: ID: D137 | shortcut: power | author: JoramSoch | date: 2021-03-31, 09:01.