Evaluating the Robustness of Some Two-Sample inferential Statistics in the Presence of Mixture Distributions: A Simulation study

This study investigates the robustness of two-sample inferential statistics when datasets are derived from mixture distributions, where traditional methods like the t-test may fail due to violated assumptions. Using R software, random variables from Standard Normal, Gamma, and Exponential distributions were generated and analyzed using four inferential tests: Rank Transformation t-test (Rt), Wilcoxon Sum Rank Test (WSD and its Asymptotic version WSA), and Trimmed t-test (Tt-test). Robustness was evaluated based on Type I error rates across varying levels of multicollinearity and sample sizes (n=10, 20, 30, 40, 50, 60, 70, 80 and100). A test was deemed robust if it maintained acceptable error rates (α=0.1, 0.05, and 0.01) and demonstrated consistency across multicollinearity levels and sample sizes. At α=0.1, the WSD and Tt-test exhibited the highest robustness. At α=0.05, the Tt-test was the most robust, while at α=0.01, both the Tt-test and WSD were robust, with the Tt-test slightly outperforming. Overall, the Tt-test and WSD consistently demonstrated robustness across all significance levels, suggesting they are reliable alternatives for two-sample problems involving mixture distributions. These findings underscore the importance of selecting robust statistical methods to ensure accurate inferences in complex data scenarios.