A Comparison of Parametric and Nonparametric Test Statistics for Testing the Mean Difference of Two Independent Populations

Abstract

The purpose of this study is to compare parametric test statistics, t-test, and four nonparametric test statistics: median test, Wilcoxon rank sum test, Yuen Welch test, and bootstrap Yuen test for testing the mean difference of two independent populations at the significant level of 0.05 when the population has a normal distribution and non-normal distribution for nine combinations of population skewness and kurtosis. The Monte Carlo technique is used to simulate data with 15,000 iterations by determining the sample sizes from 2 populations (n₁, n₂): (5,10) (10,10) (20,25) (25,25) (40,50) and (50,50). The study found that all five test statistics have the ability to control the probability of Type 1 error for most of the cases. When the population is negatively skewed distribution, symmetrical and leptokurtic distribution, positively skewed and leptokurtic distribution, the Wilcoxon rank sum test statistic had the highest power of the test. When the population is symmetrical and platykurtic distribution, the Yuen Welch test statistic had the highest power of the test for almost all the cases. When the population is positively skewed and leptokurtic distribution, positively skewed and mesokurtic distribution, the bootstrap Yuen test statistic and the Wilcoxon rank sum test statistic had the highest power of the test, respectively, for small sample sizes.