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: H₁, H₂, ..., 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 (HA)	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.