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 Hi yields the following random variables:

In $V$ hypothesis tests of which $$m_0$$ are true null hypotheses, $S$ is an observable random variable, and $R$, $U$, $T$, and $m$ are unobservable random variables.
 * $m$ 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)