Power and Type I Error for ANOVA Under Random Mixtures of Normal Distributions

This study investigates the performance of the classical one-way ANOVA F-test under random mixtures of normal distributions. Using extensive simulation studies, we assess Type I error rates and statistical power across various conditions, including different group sizes, sample sizes, mixture proportions, and within-group variance structures. Results show that when group distributions are balanced and variances are equal, ANOVA maintains nominal Type I error rates. However, with increased mixture imbalance and heterogeneous variances, Type I errors inflate and statistical power decreases, particularly in small samples or when more groups are involved. The findings underscore the sensitivity of ANOVA to violations of its assumptions and highlight the need for alternative methods in the presence of complex, non-normal data structures.