Comparing the Performance of Approaches for Testing the Homogeneity of Variance Assumption in One-Factor ANOVA Models

Area of Science:

• Statistics
• Statistical Methodology
• Data Analysis

Background:

• Homogeneity of variance is a critical assumption in ANOVA.
• Existing tests for this assumption lack consensus on robustness, especially when normality is violated.

Purpose of the Study:

• To evaluate the performance of 14 tests for homogeneity of variance in one-way ANOVA models.
• To determine robustness under violations of the normality assumption.

Main Methods:

• A simulation study manipulated seven factors: group number, sample size, variance patterns, distribution shape, and alpha level.
• Performance was assessed based on Type I error control and statistical power.

Main Results:

• Five tests demonstrated adequate Type I error control: Ramsey conditional, O'Brien, Brown-Forsythe, Bootstrap Brown-Forsythe, and Levene (squared deviations).
• These five tests performed better across various conditions compared to others.
• Acceptable statistical power was observed for these five tests, with subtle differences among them.

Conclusions:

• The Ramsey conditional, O'Brien, Brown-Forsythe, Bootstrap Brown-Forsythe, and Levene (squared deviations) tests are recommended for assessing homogeneity of variance when normality is not met.
• Guidelines for test selection are provided, considering average cell size.