Definition: Statistical hypothesis test
Definition: Let $y$ be a set of measured data. Then, a statistical hypothesis test consists of the following:

an assumption about the distribution of the data, often expressed in terms of a statistical model $m$;

a null hypothesis $H_0$ and an alternative hypothesis $H_1$ which make specific statements about the distribution of the data;

a test statistic $T(Y)$ which is a function of the data and whose distribution under the null hypothesis is known;

a significance level $\alpha$ which imposes an upper bound on the probability of rejecting $H_0$, given that $H_0$ is true.
Procedurally, the statistical hypothesis test works as follows:

Given the null hypothesis $H_0$ and the significance level $\alpha$, a critical value $t_\mathrm{crit}$ is determined which partitions the set of possible values of $T(Y)$ into “acceptance region” and “rejection region”.

Then, the observed test statistic $t_\mathrm{obs} = T(y)$ is calculated from the actually measured data $y$. If it is in the rejection region, $H_0$ is rejected in favor of $H_1$. Otherwise, the test fails to reject $H_0$.
 Wikipedia (2021): "Statistical hypothesis testing"; in: Wikipedia, the free encyclopedia, retrieved on 20210319; URL: https://en.wikipedia.org/wiki/Statistical_hypothesis_testing#The_testing_process.
Metadata: ID: D130  shortcut: test  author: JoramSoch  date: 20210319, 14:36.