Often, when testing for shift in location, researchers will utilize nonparametric statistical tests in place of their parametric counterparts when there is evidence or belief that the assumptions of the parametric test are not met (i.e., normally distributed dependent variables). An underlying and often unattended to assumption of nonparametric tests of location is that of identical distributions. The assumption of identical distributions requires that distributions conform to one another in terms of variability and shape (i.e., variance, skew and kurtosis). The purpose of the current study is to demonstrate, via the use of Monte Carlo simulation, the assumption of identical distribution using the Wilcoxon-Mann-Whitney (WMW) test and the Student t-test for comparison. For each of the conditions, there are several levels of sample size, variance ratio, group sample size ratio, and degree of skew in the parent distribution. Empirical Type I error rates are compared to nominal Type I error rates to determine the validity of the result for each run of the simulation. Violation of the assumption of identical distributions lead to bias in the result of the WMW test and the Student t-test. Practical implications are also discussed. Accessed 1,139 times on https://pareonline.net from April 05, 2018 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right.
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Nordstokke, David W. and Colp, S. Mitchell
"A Note on the Assumption of Identical Distributions for Nonparametric Tests of Location,"
Practical Assessment, Research, and Evaluation: Vol. 23
, Article 3.
Available at: https://scholarworks.umass.edu/pare/vol23/iss1/3