A Comparison of Nonparametric Statistics and Bootstrap Methods for Testing Two Independent Populations with Unequal Variance

The common parametric statistics used for testing two independent populations have often required the assumptions of normality and equal variances. Nonparametric tests have been used when assumptions of parametric tests cannot be achieved. However, some studies found nonparametric tests to be too conservative and less powerful than parametric tests. Bootstrap methods are also alternative tests when assumptions of parametric tests are violated, but they have small size limitations. Later, nonparametric tests when pooled with the bootstrap methods may overcome the powerful test and small sample sizes issue. Thus, the purpose of this study was to apply the bootstrap method together with nonparametric statistics and compare the efficiency of nonparametric tests and bootstraps methods when pooled with nonparametric tests for testing the mean difference between two independent populations with unequal variance. The Yuen Welch Test (YW), Brunner-Munzel Test (BM), Bootstrap Yuen Welch Test (BYW) and Bootstrap Brunner-Munzel Test (BBM) were studied via Monte Carlo simulation with non-normal population distributions. The results show that the probability of a type I error of all four test statistics could be controlled for all situations. The Brunner-Munzel test (BM) had the highest power and the best efficiency in the case of mean difference ratio increases. The Bootstrap Yuen Welch Test (BYW) had the highest power when the sample size was small.