The F-distribution reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

F-distribution

In statistics, the F-distribution is the probability distribution of a random variable of the form

where

• U₁ and U₂ have chi-square distributions with d₁ and d₂ degrees of freedom respectively, and

• U₁ and U₂ are independent (see Cochran's theorem for an application).

The F-distribution arises frequently as the null distribution of a test statistic, especially in likelihood-ratio tests, perhaps most notably in the analysis of variance.

If d₂ > 2, then the mean is d₂/(d₂ − 2) and if d₂ > 4 the variance is given by

The F-distribution always ranges from zero to infinity; if d₁ > 2, it is a unimodal with mode

External links

• Table of critical values of the F-distribution
• Online significance testing with the F-distribution

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