Comparing Performance of Tests for One-Factor ANOVA Models Under Heterogeneity and Non-Normality: A Monte Carlo Simulation Study

• Activity Number: 196
• Type: Contributed
• Date/Time: Monday, August 1, 2016 : 10:30 AM to 12:20 PM
• Sponsor: Social Statistics Section
• Author(s): Thanh Pham* and Yan Wang and Diep Nguyen and Eun Sook Kim and Jeffrey Kromrey and Yi-Hsin Chen
• Companies: University of South Florida and University of South Florida and University of South Florida and University of South Florida and University of South Florida and University of South Florida
• Keywords: Analysis of variance ; Homogeneity ; Heterogeneity ; Non-normality ; Type I error control ; Statistical power

Abstract

The Analysis of Variance (ANOVA) F test is one of the most common statistical methods to test the group mean equivalence. However, it is sensitive to the violation of the assumption of homogeneity of variance. Several alternative tests have been developed in response to this problem of ANOVA F test. These tests can be classified into two groups: a group of tests using ANOVA-typed approach and a group of tests using Structured Means Modeling (SMM) technique. This simulation study examines the performance of fourteen available tests in one-factor ANOVA models in terms of their Type I error rate and statistical power under comprehensive conditions (total of 48,384), especially, under the violation of the assumption of homogeneity of variance. The results show that when the assumption of equal variance was satisfied, the ANOVA F test with Ordinary Least Square (OLS) excelled the other methods in terms of both Type I error control and power. When the homogeneity assumption was violated, the Brown-Forsythe, the SMM with Bartlett, and SMM with Maximum Likelihood tests are strongly recommended for the omnibus test of group mean equality.