Index: The Book of Statistical ProofsGeneral Theorems ▷ Frequentist statistics ▷ Hypothesis testing ▷ Significance level

Definition: Let the size of a statistical hypothesis test be 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:

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

Then, the test is said to have significance level $\alpha$, if the size is less than or equal to $\alpha$:

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

Metadata: ID: D133 | shortcut: alpha | author: JoramSoch | date: 2021-03-19, 14:50.