Computing Probabilties for Rank Statistics Used with Block Design Nonparametric Subset Selection Rules

Abstract This article addresses the issue of computing an implementation constant required to apply a nonparametric subset selection procedure. Specifically, several approximations to the cumulative distribution function (cdf) of a statistic, based on ranks assigned randomly to continuous data arising from a randomized block designed experiment, are given and compared to the exact cdf. One of these approximations is simulation based using an R code. The second is based on a normal approximation to the rank sums. In the special case of comparing two populations, algebraic properties of the cdfs are derived and validated with the exact tabulations previously given in the literature. An application of these approximation methods is given for a published study of state traffic fatality rates for the years 1994 through 2012.