Index: The Book of Statistical ProofsGeneral Theorems ▷ Frequentist statistics ▷ Hypothesis testing ▷ p-value

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 p-value 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:


Metadata: ID: D135 | shortcut: pval | author: JoramSoch | date: 2021-03-19, 14:58.