Demonstrating the Consequences of Violations of Assumptions in between-Subjects Analysis of Variance

Abstract

This article describes how to use a personal computer to conduct a classroom demonstration of the effects of violations of the assumptions of analysis of variance (ANOVA) on the probability of Type I error. The demonstration is based on the idea that if many data sets of randomly selected numbers are submitted to an ANOVA, then the frequency distribution of empirical F values should approximate the probability density curve of the F statistic for the specified degrees of freedom. If violations of the assumptions do not impair the approximation, then the test is robust. Results obtained in various trials were consistent with the statistical literature in showing that violations of the assumptions of normality and homogeneity of variances have a measurable but small effect on the probability of Type I error, especially when all groups are the same size.