Difference between revisions of "Template:Classification of multiple hypothesis tests"

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The following table defines the possible outcomes when testing multiple null hypotheses.  
 
The following table defines the possible outcomes when testing multiple null hypotheses.  
Suppose we have a number ''m'' of multiple null hypotheses, denoted by: ''H''<sub>1</sub>,&nbsp;''H''<sub>2</sub>,&nbsp;...,&nbsp;''H''<sub>''m''</sub>.
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Suppose we have a number ''m'' of null hypotheses, denoted by: ''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.
 
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:
 
Summing each type of outcome over all ''H<sub>i</sub>''&nbsp; yields the following random variables:

Revision as of 21:48, 12 December 2016

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
Test is declared significant <math>V</math> <math>S</math> <math>R</math>
Test is declared non-significant <math>U</math> <math>T</math> <math>m - R</math>
Total <math>m_0</math> <math>m - m_0</math> <math>m</math>

In <math>m</math> hypothesis tests of which <math>m_0</math> are true null hypotheses, <math>R</math> is an observable random variable, and <math>S</math>, <math>T</math>, <math>U</math>, and <math>V</math> are unobservable random variables.