Heterogeneity of Variance

Heterogeneity of variance refers to the violation of the homogeneity of variance assumption, one of the main assumptions underlying the analysis of grouped data in the univariate and multivariate contexts (i.e., independent samples t-test, analysis of variance [ANOVA], and multivariate analysis of variance [MANOVA]). Broadly speaking, heterogeneity of variance means that the population variances of the groups or cells being compared are not homogenous or equal. Because variances are averaged in the calculation of standard error and error terms, under the assumption they are roughly equal, heterogeneity will create bias and inconsistencies in significance tests and confidence intervals for the model under consideration. Heterogeneity of variance is a special instance of what is known as heteroscedasticity in the context of regression, the only difference being due to the nature of the predictors—categorical in procedures of group means comparisons and continuous in regression-based procedures.

Generally, the impact of heterogeneous variance will depend on the ratio of largest to smallest variance between groups, and on whether the sample sizes for the groups being compared are equal or not. If the ratio of largest to smallest variance does not exceed 4:1, and the sample sizes are about equal, heterogeneity is not considered a threat to validity of the analyses. However, if the sample sizes are not roughly equal, the test statistic will be biased, resulting in an increased likelihood of Type I or Type II Error. Thus, corrections may be required to ensure that test statistics and confidence intervals are correct.

The impact of heterogeneity on the analyses being performed, as well as the procedures to test for its presence, and how to correct it when necessary, varies depending on the analytical context. Thus, this entry discusses heterogeneity of variance separately for each of the analytical contexts in which it may occur: t-test, ANOVA, and MANOVA. For each, a definition of heterogeneity is provided, followed by a discussion of the tests and procedures to assess it, its likely consequences, and the available corrections.