Descriptive Statistics for Nonparametric Models. III. Dispersion

Abstract

It is now coming to be generally agreed that in testing for shift in the two-sample problem, certain tests based on ranks have considerable advantage over the classical t-test. From the beginning, rank tests were recognized to have one important advantage: their significance levels are exact under the sole assumption that the samples are randomly drawn (or that the assignment of treatments to subjects is performed at random), whereas the t-test in effect is exact only when we are dealing with random samples from normal distributions. On the other hand, it was felt that this advantage had to be balanced against the various optimum properties possessed by the t-test under the assumption of normality. It is now being recognized that these optimum properties are somewhat illusory and that, under realistic assumptions about extreme observations or gross errors, the t-test in practice may well be less efficient than such rank tests as the Wilcoxon or normal scores test [6], [7]. Rank tests were naturally develo...