An approximation of F distribution by binomial probabilities
It is well known that the F distribution function can be expressed as an incomplete beta function. In particular when both degrees of freedom are even, the F distribution function may be simply expressed as a sum of binomial probabilities. In this note we consider the F distribution with at least one odd degree of freedom. By relating the F distribution to a generalized logistic distribution we obtain an approximation of the F distribution in terms of binomial probabilities. Because it is very close to the exact at the tails, the approximation is particularly suitable for estimating P-values of F ratio tests. All the computations involved can be carried out easily with only a hand calculator. © 1987.
Statistics and Probability Letters
George, E., & Singh, K. (1987). An approximation of F distribution by binomial probabilities. Statistics and Probability Letters, 5 (3), 169-173. https://doi.org/10.1016/0167-7152(87)90033-2