An F approximation and its application

Abstract

Formulae for upper probabilities and for upper percentiles of statistics which follow approximately an F distribution are developed. Their accuracies are compared numerically with the usual ones adjusting only the first two cumulants, when applied to the noncentral F distribution, the statistic of a particular cumulative sum method and the studentized range. Furthermore, it is pointed out that the χ 2 approximation of the squared range from identically and independently distributed normal variables is more accurate than the well-known χ approximation by Patnaik (1950) so far as upper 1 and 5% points are concerned.