Empirical power of F and normality tests under different experimental conditions

The assumption of normality holds significant importance in inferential methods, such as the F-test of Analysis of Variance (ANOVA), which finds extensive application across various fields such as agricultural and clinical trials. Consequently, normality tests serve the purpose of evaluating the distribution of experimental errors for normality. However, prior studies aiming to compare the power of these tests should have considered the experimental design employed for simulated studies and assessed the impact of varying experimental conditions on the test powers. This study, therefore, focuses on assessing the effects of symmetry (or asymmetry) in the empirical distributions of the response variable for each treatment, the equality (or inequality) of their means, and the homogeneity (or heterogeneity) of their variances on the empirical power of both normality tests and the F-test, considering a Completely Randomized Design (CRD). To achieve this objective, normality tests were applied to 10,000 simulated sets of experimental residuals, while the F-test was applied to 10,000 simulated sets of response variable values. The findings of this study indicate that, in the majority of scenarios, power increases with an increasing number of replications per treatment. Furthermore, it was observed that the presence of symmetry tends to diminish the power of normality tests, while the F-test exhibits remarkable robustness to violations of normality assumptions. However, the power of the F-test can be influenced when the homogeneity of variances is compromised in conjunction with the asymmetry of non-normally distributed empirical data.