Relative Efficiency of Some Tests of Two Population Means under Violation of Homoscedacity Assumptions

Abstract

 Researchers have been using statistical tools for data analysis that are based on the assumption of normality and other assumptions related to specific tools. When the researchers have developed the theoretical aspects related to these methods, they have assumed that the population from where the sample has been drawn follows a normal law. But, in reality the population need not be always normal or homoscedastic. When these methods are used for non-normal population, they may lead to unreliable results and also inferences with low power. This study therefore investigates two parametric tests (t and Welch's t tests) and their performances are compared with nonparametric counterparts of testing two independent population of unequal variances from normal, uniform, gamma and exponential distributions at different sample sizes. The results of the analysis revealed that the Welch's t- test is the best on data from normal distribution, Mann-Whitney from uniform, and Median from gamma and exponential distributions.