Multi-group comparison of means for single-factor experiment with small sample size under normality and heteroscedasticity

The design of single-factor experiment is commonly used to compare multiple groups in non-clinical studies, where groups generally have small size and different variances. The classical F test tends to inflate type I error rate in this scenario. Many alternative tests have been proposed in the literature to manage heteroscedasticity. Several papers compared these alternative tests, among which is heterogeneous-variance mixed-effects model. The mixed-effects model approach has at least 2 advantages over other tests: (1) allowing different group variance structures (e.g. homogeneous-variance or heterogeneous-variance); and (2) the capacity to do model diagnosis via residual analysis. In this article, we conducted comprehensive simulation experiments to evaluate both type I error rate and power of the 13 tests investigated in Pham et al. (Citation2020) spanning ANOVA-based tests, structured means modeling (SMM), and mixed-effects models—under diverse conditions, including (un)equal variances, (non-)normal distributions, and (un)balanced designs. Two additional mixed-effects models (homogeneous-variance mixed-effects model and adaptive mixed-effects model) were introduced and assessed alongside the 13 tests. We also considered the Kenward-Roger approximation of degrees of freedom for the 3 mixed-effects models, which generally offers more reliable type I error rate than the Satterthwaite approximation. Results suggested that no single method consistently outperforms across all scenarios.