The F test is used for hypotheses concerning variances. It is used to test whether two variances are equal and is also used in the analysis of variance (ANOVA).

Let U and V be two independent chi-square random variables having m and n degrees of freedom (df), respectively. The ratio F = (U= m)/(V= n)hasan F distribution with numerator df equal to m and denominator df equal to n. Two properties of the F distribution are as follows

• If X ∼ Fm,n, then 1/X ∼ Fn,m, that is, the reciprocal of an F random variable is again an F random variable.
• If X ∼ tm (X has a t distribution with df = m), then X2 ∼ F1,m.