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: Template:Math 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
Template:Rh | Test is declared significant	Template:Mvar	Template:Mvar	Template:Mvar
Template:Rh | Test is declared non-significant	Template:Mvar	Template:Mvar	$m-R$
Template:Rh | Total	$m_0$	$m-m_0$	Template:Mvar

• Template:Mvar 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
• Template:Mvar is the number of false positives (Type I error) (also called "false discoveries")
• Template:Mvar is the number of true positives (also called "true discoveries")
• Template:Mvar is the number of false negatives (Type II error)
• Template:Mvar is the number of true negatives
• $R=V+S$ is the number of rejected null hypotheses (also called "discoveries", either true or false)

In Template:Mvar hypothesis tests of which $m_0$ are true null hypotheses, Template:Mvar is an observable random variable, and Template:Mvar, Template:Mvar, Template:Mvar, and Template:Mvar are unobservable random variables. Template:Documentation