Sequential Rank Tests. I. Monte Carlo Studies of the Two-Sample Procedure

摘要

Monte Carlo studies of a sequential, two-sample, ranksum test developed earlier by Wilcoxon, Rhodes and Bradley are reported. Ranking is accomplished within groups of observations in the sequential procedures and the theory is based on a model suggested by Lehmann. Design parameters are alpha and beta probabilities of Type I or Type II errors, m and n, the numbers of X- and Y-observations in a group of observations, and k sub 1, the power in the Lehmann model wherein the alternative hypothesis states that the cdf of the Y-population is G(u) identical to F(k sub 1) (u), F(u) being the cdf of the Xpopulation. Studies are made for designs with alpha = beta = .05, m = n = 2(1)5, k sub 1 = 1.5, 2.33, 4 and 9. Data appropriate to the Lehmann model are generated and studies are also made when G(u-mu sub y) identical to F(u). Average sample numbers and powers of tests are estimated. The effects of truncation are examined. It is concluded that the Monte Carlo results substantiate the use of the usual Wald theory of sequential analysis and that the use of the sequential methods for data from normal populations differing only in locations is satisfactory for most practical applications. (Author)