Performance of Non-Parametric Maximum Test for Location Testing between Two Populations with Skewed Distributions and Unequal Variances

Montri Sangthong

Authors

Montri Sangthong Division of Mathematics, Faculty of Science and Technology, Rajamangala University of Technology Suvarnabhumi, Phra Nakhon Si Ayutthaya, Thailand

Keywords:

Maximum Test, Location Testing, Nonparametric Statistics

Abstract

This research aimed to study the efficiency of the non-parametric Maximum test for location testing between two populations with skewed distributions and unequal variances; the Maximum test is a new statistical technique and was evaluated in comparison with the Brunner-Munzel test, Welch Based on Rank test and Yuen-Welch test. All the tests were performed with positive skewed distributions in both populations, which were identically distributed and non-identically distributed; the variances were set under six different conditions. The results illustrated that under the conditions of log-normal distribution and exponential distribution at a significant level of 0.05, the ability of the Maximum test to control type I error was lower than those of the Brunner-Munzel test and the Yuen-Welch test but higher than tha of the Welch Based on Rank test. When considering the highest test power of all the techniques, Welch Based on Rank test exhibited the highest capacity; this was followed in descending order by the Brunner-Munzel test and Maximum test. At a significant level of 0.01, the ability to control type I error of the Maximum test was lower than that of the Yuen-Welch test but higher than those of the Brunner-Munzel test and Welch based on rank test. When considering the highest test power at this significant level, the highest powers were achieved by the Yuen-Welch test and Welch Based on Rank test. In the case that the first population exhibited exponential distribution and the second population exhibited log-normal distribution, the ability of the Maximum test, at 0.05 significant level, to control type I error was lower than those of the Brunner-Munzel test and the Yuen-Welch test but higher than that of the Welch Based on Rank test. When considering the highest test power at this condition, Welch Based on Rank test had the highest capacity; this was followed in descending oredr by the Maximum test, Yuen-Welch test and Brunner-Munzel test. Furthermore, at a significant level of 0.01, the ability of the Maximum test to control type I error was lower than that of Yuen-Welch test but higher than those of Brunner-Munzel test and Welch Based on Rank test. When considering the test method with the highest test power that can control type I error, Welch based on rank test had the highest capacity; this was followed by the Yuen-Welch test and the Maximum test.

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