View source for 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: {{math|''H''<sub>1</sub>,&nbsp;''H''<sub>2</sub>,&nbsp;...,&nbsp;''H''<sub>''m''</sub>.}}
Using a [[Statistical hypothesis testing|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<sub>i</sub>''&nbsp; yields the following random variables:

{|class="wikitable"
| |
! Null hypothesis is true (H<sub>0</sub>)
! Alternative hypothesis is true (H<sub>A</sub>)
! | Total
|- align="center"
! {{rh}} | Test is declared significant
| {{mvar|V}}
| {{mvar|S}}
| {{mvar|R}}
|- align="center"
! {{rh}} | Test is declared non-significant
| {{mvar|U}}
| {{mvar|T}}
| <math>m - R</math>
|- align="center"
! {{rh}} | Total
| <math>m_0</math>
| <math>m - m_0</math>
| {{mvar|m}}
|}

* {{mvar|m}} is the total number hypotheses tested
* <math>m_0</math> is the number of true [[null hypothesis|null hypotheses]], an unknown parameter
* <math>m - m_0</math> is the number of true [[alternative hypothesis|alternative hypotheses]]
* {{mvar|V}} is the number of [[Type I and type II errors|false positives (Type I error)]] (also called "false discoveries")
* {{mvar|S}} is the number of [[Type I and type II errors|true positives]] (also called "true discoveries")
* {{mvar|T}} is the number of [[Type I and type II errors|false negatives (Type II error)]]
* {{mvar|U}} is the number of [[Type I and type II errors|true negatives]]
* <math>R=V+S</math> is the number of rejected null hypotheses (also called "discoveries", either true or false)
In {{mvar|m}} hypothesis tests of which <math>m_0</math> are true null hypotheses, {{mvar|R}} is an observable random variable, and {{mvar|S}}, {{mvar|T}}, {{mvar|U}}, and {{mvar|V}} are unobservable [[random variable]]s.