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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