Definition: Critical value

Index: The Book of Statistical Proofs ▷ General Theorems ▷ Frequentist statistics ▷ Hypothesis testing ▷ Critical value

Definition: In a statistical hypothesis test, the critical value $t_\mathrm{crit}$ is that value of the test statistic $T(Y)$ which partitions the set of possible test statistics into “acceptance region” and “rejection region” based on a significance level $\alpha$. Put differently, if the observed test statistic $t_\mathrm{obs} = T(y)$ computed from actually measured data $y$ is as extreme or more extreme than the critical value, the test rejects the null hypothesis $H_0$ in favor of the alternative hypothesis.

 

Sources:

• Wikipedia (2021): "Statistical hypothesis testing"; in: Wikipedia, the free encyclopedia, retrieved on 2021-03-19; URL: https://en.wikipedia.org/wiki/Statistical_hypothesis_testing#Definition_of_terms.

Metadata: ID: D134 | shortcut: cval | author: JoramSoch | date: 2021-03-19, 14:54.