The two-sample independent problem remains a persistent challenge in statistical analysis. Parametric tests, such as Student's t-test and Welch's t-test, are commonly employed to assess the significance of differences between the means of two groups. However, these methods rely on the assumption of normally distributed populations. When this assumption is violated, nonparametric alternatives like the Wilcoxon-Mann-Whitney, Yuen-Welch, Brunner-Munzel, and Baumgartner tests offer robust solutions. This study introduces an adaptive framework for nonparametric two-sample tests, building upon the foundation of Baumgartner-type tests. To enhance statistical power, we incorporate a recently proposed relative rank transformation method that is more resilient to scale differences between the two samples. The adaptive tests are suitable for both location and scale comparisons. Through extensive Monte Carlo simulations, we evaluate the power performance of our adaptive tests under diverse distributional scenarios. Our results demonstrate that adaptive tests offer a substantial advantage over traditional nonparametric methods. To illustrate the practical application of our approaches, we apply the adaptive tests along their competitors to six real-world biomedical datasets. These examples highlight the reliability and effectiveness of the proposed methodology in addressing the two-sample independent location-scale testing problem.
Aslam et al. (Thu,) studied this question.