A Generalization of Wilcoxon Rank Sum Test
نویسنده
چکیده
In this paper, we consider applying the Wilcoxon’s idea for the construction of the one-sample problem to the two-sample case. For this, we show that the location translation parameter becomes a median of the distribution of the difference of two independent random variables under the location translation model. Based on this fact, we construct generalized signed-rank statistics for the two sample problem and consider to apply the permutation principle to obtain the null distribution. Then we compare the efficiency of the proposed test with that of the Wilcoxon test. We discuss some interesting features which are related with the generalized signed-rank statistics. Finally, we derive the asymptotic normality for the generalized signed-rank statistics with the U-statistics theorem. Mathematics Subject Classification: 62G10
منابع مشابه
The Two-sample Rank-sum Test: Early Development
The historical development of the two-sample rank-sum test is explored. While most textbooks and journal articles attribute the origin of the two-sample rank-sum test to Wilcoxon (1945) and/or Mann and Whitney (1947), the test was independently developed by at least six researchers in the late 1940s and early 1950s. In addition to Wilcoxon and Mann and Whitney, Festinger (1946), Whitfield (1947...
متن کاملAn extension of the Wilcoxon Rank-Sum test for complex sample survey data.
In complex survey sampling, a fraction of a finite population is sampled. Often, the survey is conducted so that each subject in the population has a different probability of being selected into the sample. Further, many complex surveys involve stratification and clustering. For generalizability of the sample to the finite population, these features of the design are usually incorporated in the...
متن کاملIncorporation of clustering effects for the Wilcoxon rank sum test: a large-sample approach.
The Wilcoxon rank sum test is frequently used in statistical practice for the comparison of measures of location when the underlying distributions are far from normal or not known in advance. An assumption of the ordinary rank sum test is that individual sampling units are independent. In many ophthalmologic clinical trials, the Early Treatment for Diabetic Retinopathy Scale (ETDRS) is a princi...
متن کاملRank-Sum Tests for Clustered Data
The Wilcoxon rank-sum test is widely used to test the equality of two populations, because it makes fewer distributional assumptions than parametric procedures such as the t-test. However, the Wilcoxon rank-sum test can be used only if data are independent. When data are clustered, tests based on generalized estimating equations (GEEs) that generalize the t-test have been proposed. Here we deve...
متن کاملSocial choice violations in rank sum scoring: A formalization of conditions and corrective probability computations
Rank sum scoring is a popular manner by which to obtain group rankings from events that are individual in nature. For example, rank sum scoring is employed in cross country team competition, the Putnam Mathematics Team Competition, snowboard cross team competition, snowboard half-pipe team competition, and snowboard slopestyle team competition. It also forms the basis for a non-parametric stati...
متن کامل