Performance of Seven Statistics for Mean Difference Testing Between Two Populations Under Combined Assumption Violations

Abstract

The objective of this research was to compare the performance of seven statistics for mean difference testing between two populations when data did not follow assumptions whereas the simulation conditions were determined as 5 distributions, variance, and sample size in both cases are equal and unequal. The results showed that when the population had log-normal distribution, gamma distribution andpoisson distribution and equal variance, the Welch Based on Rank test (WBR test) were most effective. When the population had log-normal distribution, gamma distribution,exponential distribution,poisson distribution and uniform distribution and unequal variance, the Welch t test was distinctively found to have a higher performance than others testing statistics. Keywords: Two-sample location test, Parametric test, Non-parametric test, Non-parametric bootstrap test, t test, Welch t test, Welch Based on Rank test, Brunner-Munzel test, Yuen-Welch test, Exact Wilcoxon signed-rank test