Comparisons of approximations to the percentiles of the t , x 2 ,and F distributions

Appriximations for the percentiles at arbitrary levels of the t, X 2 and F distributions can be found in the literature, but with little information about the accuracy. This paper provides a single source of these approximations and contains tables of percent errors to aid int the selection of the simplest procedure yielding the required accuracy. For use in digital computers, approximations compared in this paper yield percentiles more rapidly than more exact iteration schemes with accuracy dependent on the complexity of the approximation. An approximation procedure may also be used to obtain percentiles for non-integral degrees of freedom.