Assessing Univariate and Multivariate Homogeneity of Variance: A Guide For Practitioners

Abstract

Most statistical methods assume constant variance and the validity of result from some of the methods highly rely on constant variance. However, a very high number of practitioners and researchers publications do not check the constant variance assumptions and hence the results are very prone to error. With aim of reducing this, both graphical and formal methods of assessing constant variance assumption are presented and illustrated in this paper. In univariate data several methods have been proposed. The graphical methods of assessing constancy of variance include plot of residuals against the fitted values, residuals against the fitted value square, and residual versus predictor variable are widely used. In addition, formal tests of assessing this assumption are Bartlett’s, Levene’s, Breusch-Pagan, Brown and Forsythe, O’Brien’s, White’s and Fligner-Killeen are commonly used and also applicable in most of statistical software. For multivariate data, the two common tests in practice are Box’s M teste and Bartlett’s. Finally, when the constancy of variance assumption not satisfied, it is very important to find a variance-stabilizing transformation.

Keywords: Homogeneity of variance, Bartlett’s test, Breusch-Pagan test, Brown and Forsythe test, Levene’s test.