Template:Classification of multiple hypothesis tests

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The following table defines the possible outcomes when testing multiple null hypotheses. Suppose we have a number m of null hypotheses, denoted by: H1H2, ..., Hm. 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:

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 <math>m - R</math>
Template:Rh | Total <math>m_0</math> <math>m - m_0</math> Template:Mvar

In Template:Mvar hypothesis tests of which <math>m_0</math> 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.