An improved statistical approach to compare means

In many experiments, our interest lies in testing the significance of means from the grand mean of the study variable. Sometimes, an additional linearly related uncontrollable factor is also observed along with the main study variable, known as a covariate. For example, in Electrical Discharge Machining (EDM) problem, the effect of pulse current on the surface roughness (study variable) is affected by the machining time (covariate). Hence, covariate plays a vital role in testing means, and if ignored, it may lead to false decisions. Therefore, we have proposed a covariate-based approach to analyze the means in this study. This new approach capitalizes on the covariate effect to refine the traditional structure and rectify misleading decisions, especially when covariates are present. Moreover, we have investigated the impact of assumptions on the new approach, including normality, linearity, and homogeneity, by considering equal or unequal sample sizes. This study uses percentage type Ⅰ error and power as our performance indicators. The findings reveal that our proposal outperforms the traditional one and is more useful in reaching correct decisions. Finally, for practical considerations, we have covered two real applications based on experimental data related to the engineering and health sectors and illustrated the implementation of the study proposal.