Conditional and Unconditional ANOVA Tests: An Empirical Comparison of Type I Error Control and Statistical Power under Variance Heterogeneity and Non-Normality

• Activity Number: 473 - Tools of Inferential Decision Making in Education and Behavioral Sciences
• Type: Contributed
• Date/Time: Wednesday, August 2, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Social Statistics Section
• Author(s): Zhiyao Yi* and Yan Wang and Thanh Pham and Diep Nguyen and Yue Yin and Jeffrey Kromrey and Eun Sook Kim 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 and University of South Florida and University of South Florida
• Keywords: Analysis of variance ; Homogeneity of variance ; Non-normality ; Type I error control ; Statistical power

Abstract

The analysis of variance (ANOVA) F test is a commonly used method to test the mean equality among two or more populations. A critical assumption of ANOVA is homogeneity of variance (HOV), that is, the compared groups have equal population variances. Although it is encouraged to test HOV as part of the regular ANOVA procedure, the efficacy of the initial HOV screening that leads to the choice between the ANOVA F test and robust ANOVA methods (namely, conditional ANOVA) has not been investigated systematically. This simulation study examined the efficacy of conditional ANOVA methods under various research conditions. Results suggested that under a small sample size (e.g., 5 per group) the combination of the Brown-Forsythe test of means with the Levene or O'Brien test of variances is the best choice; with large sample sizes, structured means modeling with maximum likelihood or the Bartlett's correction coupled with Levene or O'Brien are the best combinations; and alpha levels between .20 and .30 for the test of variances are most appropriate.