An important probability distribution used to test the significance of estimated mean squares in an analysis of variance and in regression analysis. Theoretically the F distribution is the distribution of the ratio of two independent random variables S1\\f1 and S2\\f2, where S1 has the chi-squared distribution on f1 degrees of freedom and S2 has the chi-squared distribution on f2 degrees of freedom. Tables of critical values of the F distribution for ranges of f1 and f2 are widely available, but direct computation requires lengthy algorithms to compute the incomplete beta function.