Improving the Welch-Satterthwaite Approximation

The Welch-Satterthwaite (WS) methodology is typically used in medicine, biology and economic courses to make inferences about the difference between two population means. Despite his wide-spreading applications, it has been pointing out in many references the multiple limitations of the inferences based on it. In this work, we propose three simple ways to improve the classical WS approach. Under balanced samples scenarios, we give exact inference results of two of the proposed estimators. Additionally, under unbalanced samples scenarios, we offer first-order approximation results and through several Monte Carlo simulations, we assess the mean and variance of the proposed estimators under (very) small and moderate sample sizes. Nonetheless, the simplicity of the proposed approach we obtain a much better performance than the WS proposal. Lastly, one application is presented in which the proposed estimators potentially improve the performance of t-student interval estimation and hypothesis testing procedures.