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标题：A Note on the Assumption of Identical Distributions for Nonparametric Tests of Location.
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作者：David W. Nordstokke ; S. Mitchell Colp
期刊名称：Practical Assessment, Research and Evaluation
印刷版ISSN：1531-7714
电子版ISSN：1531-7714
出版年度：2018
卷号：23
出版社：ERIC: Clearinghouse On Assessment and Evaluation
摘要：Often, when testing for shift in location, researchers will utilize nonparametric statistical tests in placeof their parametric counterparts when there is evidence or belief that the assumptions of theparametric test are not met (i.e., normally distributed dependent variables). An underlying and oftenunattended to assumption of nonparametric tests of location is that of identical distributions. Theassumption of identical distributions requires that distributions conform to one another in terms ofvariability and shape (i.e., variance, skew and kurtosis). The purpose of the current study is todemonstrate, via the use of Monte Carlo simulation, the assumption of identical distribution usingthe Wilcoxon-Mann-Whitney (WMW) test and the Student t-test for comparison. For each of theconditions, there are several levels of sample size, variance ratio, group sample size ratio, and degreeof skew in the parent distribution. Empirical Type I error rates are compared to nominal Type I errorrates to determine the validity of the result for each run of the simulation. Violation of the assumptionof identical distributions lead to bias in the result of the WMW test and the Student t-test. Practicalimplications are also discussed.