Estimating an effect size in one-way multivariate analysis of variance (MANOVA)

When two or more univariate population means are compared, the proportion of variation in the dependent variable accounted for by population group membership is eta-squared. This effect size can be generalized by using multivariate measures of association, based on the multivariate analysis of variance (MANOVA) statistics, to establish whether population mean vectors are practically significant different. In the case of random samples from populations, approximate and asymptotically unbiased estimators of these effect sizes as well as confidence intervals are suggested under the assumptions of equal covariance matrices and normality. Statistical properties of these estimators are studied by Monte Carlo simulations. The accuracy and spread of the proposed effect sizes are also compared with those of other multivariate measures of association in Monte Carlo simulations. The proposed effect sizes are also illustrated by applying them in an empirical example using college admission test data obtained from StatSoft (2007).