Empirical Comparison of Tests for One-Factor ANOVA Under Heterogeneity and Non-Normality: A Monte Carlo Study

Authors

Diep Nguyen, University of South FloridaFollow
Eunsook Kim, University of South FloridaFollow
Yan Wang, University of MassachusettsFollow
Thanh Vinh Pham, University of South FloridaFollow
Yi-Hsin Chen, University of South FloridaFollow
Jeffrey D. Kromrey, University of South FloridaFollow

Abstract

Although the Analysis of Variance (ANOVA) F test is one of the most popular statistical tools to compare group means, it is sensitive to violations of the homogeneity of variance (HOV) assumption. This simulation study examines the performance of thirteen tests in one-factor ANOVA models in terms of their Type I error rate and statistical power under numerous (82,080) conditions. The results show that when HOV was satisfied, the ANOVA F or the Brown-Forsythe test outperformed the other methods in terms of both Type I error control and statistical power even under non-normality. When HOV was violated, the Structured Means Modeling (SMM) with Bartlett or SMM with Maximum Likelihood was strongly recommended for the omnibus test of group mean equality.

DOI

10.22237/jmasm/1604190000

Recommended Citation

Nguyen, D., Kim, E., Wang, Y., Pham, T. V., Chen, Y.-H., & Kromrey, J. D. (2019). Empirical comparison of tests for one-factor ANOVA under heterogeneity and non-normality: A Monte Carlo study. Journal of Modern Applied Statistical Methods, 18(2), eP2906. doi: 10.22237/jmasm/1604190000