Comparative Simulation of Homoskedasticity Tests on Modern Test Statistical Methods: Wilcox Keselman, Yuce, Carapeto Holt, Rackauskas Zuokas, Li Yao

Abstract

This study investigates the sensitivity of modern test statistics to heteroscedasticity in the context of linear regression models, specifically focusing on the Wilcox and Keselman's, Yuce, Carapeto-Holt, Rackauskas-Zuokas, and Li-Yao methods. Using both small (n=30) and large (n=100) sample sizes, random normally distributed data were generated to assess the empirical alpha values of these tests at various significance levels (α = 0.05, 0.10, and 0.50). The results show that Wilcox and Keselman's method consistently exhibits high sensitivity to heteroscedasticity, with empirical alpha values closely matching the predefined significance levels, particularly at 5% and 10%. In contrast, other methods, such as Yuce, Carapeto-Holt, Rackauskas-Zuokas, and Li-Yao, demonstrated less consistent performance, especially at lower significance levels. The Wilcox and Keselman's test was found to be the most reliable method for detecting heteroscedasticity, with empirical alpha values aligning closely with the intended alpha across both small and large samples. These findings emphasize the importance of selecting appropriate statistical tests when evaluating the assumption of homoscedasticity in linear regression models. The study concludes that Wilcox and Keselman's method is the most effective for identifying heteroscedasticity, offering valuable insights for robust regression analysis.