Testing Assumptions in One-Way ANOVA: Monte Carlo Study of Preliminary Tests for Normality and Homoscedasticity

• In Event: Division D: Multiple Linear Regression: The General Linear Model SIG

Abstract

Like other General Linear Model statistical methods, researchers are encouraged to test assumptions for one-way ANOVA. Kolmogorov-Smirnov-Lilliefors and Shapiro-Wilk statistics are often used to test the normality of the dependent variable conditionally by group (with potential inflation of Type I error rates due to multiple hypothesis testing), but can also be used to test normality of residuals. Levene's test is commonly used to test homoscedasticity. Our purpose is to examine, through a Monte Carlo study, (a) multiple hypothesis testing and heteroscedasticity as they impact tests of normality and (b) how non-normality impacts tests of homogeneity of variances. Finally, we will examine the impact of these combined violations on the one-way ANOVA F, Welch F, and the Kruskal-Wallis test.

Authors

• Gordon P. Brooks, Ohio University

• Nina Adjanin, Ohio University

• Marsha S. Lewis, Ohio University