A Generalization of the Rank Transform in the Two-Sample Location Problem

The t-statistic computed as a function of the scores of a two-sampie linear rank statistic, rather than the observations them-selves, yields a statistic TCR which can be used to test for the equality of locations of two populations. For the Wilcoxon scores, the statistic TcR reduces to the f, rank transform” statistic T. By assuming the appropriate regularity conditions on the scores, TCR is shown to have approximately a t-distribution. The asymptotic relative efficiency (ARE) of T is the same as that of the corre-CR sponding linear rank statistic. The robustness of TCR, with respect to significance level and power, is studied by Monte Carlo simulation when the distributions are normal, uniform, double exponential Cauchy, and exponential.