Interval Estimates of Multivariate Effect Sizes

Abstract

Monte Carlo methods were used to examine techniques for constructing confidence intervals around multivariate effect sizes. Using interval inversion and bootstrapping methods, confidence intervals were constructed around the standard estimate of Mahalanobis distance ( D2), two bias-adjusted estimates of D2, and Huberty’s I. Interval coverage and width were examined across conditions by adjusting sample size, number of variables, population effect size, population distribution shape, and the covariance structure. The accuracy and precision of the intervals varied considerably across methods and conditions; however, the interval inversion approach appears to be promising for D2, whereas the percentile bootstrap approach is recommended for the other effect size measures. The results imply that it is possible to obtain fairly accurate coverage estimates for multivariate effect sizes. However, interval width estimates tended to be large and uninformative, suggesting that future efforts might focus on investigating design factors that facilitate more precise estimates of multivariate effect sizes.