Template:Classification of multiple hypothesis tests

The following table defines the possible outcomes when testing multiple null hypotheses. Suppose we have a number m of null hypotheses, denoted by: $H 1, H 2, ..., H m .$ Using a statistical test, we reject the null hypothesis if the test is declared significant. We do not reject the null hypothesis if the test is non-significant. Summing each type of outcome over all H_i yields the following random variables:

	Null hypothesis is true (H₀)	Alternative hypothesis is true (H_A)	Total
Test is declared significant	$V$	$S$	$R$
Test is declared non-significant	$U$	$T$	$m-R$
Total	$m_{0}$	$m-m_{0}$	$m$

$m$ is the total number hypotheses tested
$m_{0}$ is the number of true null hypotheses, an unknown parameter
$m-m_{0}$ is the number of true alternative hypotheses
$V$ is the number of false positives (Type I error) (also called "false discoveries")
$S$ is the number of true positives (also called "true discoveries")
$T$ is the number of false negatives (Type II error)
$U$ is the number of true negatives
$R=V+S$ is the number of rejected null hypotheses (also called "discoveries", either true or false)

In $m$ hypothesis tests of which $m_{0}$ are true null hypotheses, $R$ is an observable random variable, and $S$ , $T$ , $U$ , and $V$ are unobservable random variables.