A Chi-Square Approximation for the F Distribution

Abstract

F distribution is one of the most frequently used distributions in statistics. For example, it is used for testing: equality of variances of two independent normal distributions, equality of means in the one-way ANOVA setting, overall significance of a normal linear regression model, and so on. In this paper, a simple chi-square approximation for the cumulative distribution of the F-distribution is obtained via an adjusted log-likelihood ratio statistic. This new approximation exhibits remarkable accuracy even when the degrees of freedom of the F distribution are small.