Editing Noncentral F-distribution (section)

{{Short description|Probability distribution generalizing the F-distribution with a noncentrality parameter}}
{{DISPLAYTITLE:Noncentral ''F''-distribution}}
In [[probability theory]] and [[statistics]], the '''noncentral ''F''-distribution''' is a [[continuous  probability distribution]] that is a [[noncentral distribution|noncentral generalization]] of the (ordinary) [[F-distribution|''F''-distribution]]. It describes the distribution of the quotient (''X''/''n''<sub>1</sub>)/(''Y''/''n''<sub>2</sub>), where the numerator ''X'' has a [[noncentral chi-squared distribution]] with ''n''<sub>1</sub> degrees of freedom and the denominator ''Y'' has a central [[chi-squared distribution]] with ''n''<sub>2</sub> degrees of freedom. It is also required that ''X'' and ''Y'' are [[statistical independence|statistically independent]] of each other.

It is the distribution of the [[test statistic]] in [[analysis of variance]] problems when the [[null hypothesis]] is false.  The noncentral ''F''-distribution is used to find the [[statistical power|power function]] of such a test.