An accurate, non-iterative approximation for studentized range quantiles

Abstract

Several statistical procedures require upper quantiles of the studentized range distribution, but few environments for statistical analysis offer on-line calculation of those quantiles. This is because available algorithms require high-precision numerical integration, applied iteratively, to achieve accurate results. Consider instead a simple non-iterative approximate transformation from student t quantiles, which are easily computed and generally available, to studentized range quantiles. Given an accurate quantile from the student t distribution, only a few arithmetic operations yield a studentized range quantile with accuracy sufficient for most data analytic and other practical purposes; in fact, the accuracy is nearly as good as that of the studentized range table that has been in use since 1960. This approach also yields methods for interpolating studentized range quantiles that are more accurate than methods in current use.