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The F Distribution / F-Distribution <Back to Last Page>     <Full Glossary>

Definition of The F Distribution / F-Distribution: The F distribution is defined in terms of two independent chi-squared variables. Let u and v be independently distributed chi-squared variables with u1 and v1 degrees of freedom, respectively.

Then the statistic: F=(u/u1)/(v/v1) has an F distribution with (u1,v1) degrees of freedom.

As can be computed from the definition of the t distribution, the square of a t statistic may be written:

t2=(z2/1)/(v/v1), where z2, being the square of a standard normal variable, has a chi-squared distribution. Thus the square of a t variable with v1 degrees of freedom is an F variable with (1,v1) degrees of freedom, that is:

t2=F(1,v1). (Econterms)

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