Mimicking Properties of Nonparametric Rank Tests Using Scores that are not Ranks

Abstract

In a computer simulation study, random samples from a uniform density were substituted for each of two independent samples from normal and various nonnormal densities. This procedure was compared with conventional ranking and with Bell and Doksum's (1965) procedure, which substituted random normal deviates for initial sample values. After performing the Student t test, the program transformed the initial scores and performed additional t tests on ranks, random uniform scores, and random normal scores. For several distributions, the test on random normal scores was more powerful than the others, consistent with known asymptotic results. The probabilities of Type I and Type II errors of the test on random uniform scores were nearly the same as those of the Mann-Whitney-Wilcoxon test, for all distributions examined.