Definition: pvalue
Definition: Let there be a statistical test of the null hypothesis $H_0$ and the alternative hypothesis $H_1$ using the test statistic $T(Y)$. Let $y$ be the measured data and let $t_\mathrm{obs} = T(y)$ be the observed test statistic computed from $y$. Moreover, assume that $F_T(t)$ is the cumulative distribution function (CDF) of the distribution of $T(Y)$ under $H_0$.
Then, the pvalue is the probability of obtaining a test statistic more extreme than or as extreme as $t_\mathrm{obs}$, given that the null hypothesis $H_0$ is true:

$p = F_T(t_\mathrm{obs})$, if $H_1$ is a leftsided onetailed hypothesis;

$p = 1  F_T(t_\mathrm{obs})$, if $H_1$ is a rightsided onetailed hypothesis;

$p = 2 \cdot \min \left( \left[ F_T(t_\mathrm{obs}), \, 1  F_T(t_\mathrm{obs}) \right] \right)$, if $H_1$ is a twotailed hypothesis.
 Wikipedia (2021): "Statistical hypothesis testing"; in: Wikipedia, the free encyclopedia, retrieved on 20210319; URL: https://en.wikipedia.org/wiki/Statistical_hypothesis_testing#Definition_of_terms.
Metadata: ID: D135  shortcut: pval  author: JoramSoch  date: 20210319, 14:58.