A New Effect Size Statistic for Measurement Non-Invariance With Multiple Groups and Multiple Grouping Variables

• In Event: Evaluating Model Fit in Structural Equation Models

Abstract

Psychometricians and methodologists have called for more attention to effect size when invariance is violated---that is, the practical significance of noninvariance. However, most existing effect sizes are limited to two-group designs. Given that researchers are increasingly interested in examining invariance across more than two groups, we propose the f_MACS (and f^2_MACS) statistic as a natural extension to the d_MACS effect size by Nye et al. (2011) for multiple groups, analogous to how Cohen's f extends Cohen's d for standardized mean differences. Using two empirical examples, we illustrate how f_MACS can be computed using parameter estimates of a partial invariance model, and show how f_MACS can quantify noninvariance due to both main effects and interactions when there are multiple grouping variables.

Authors

• Hok Chio Mark Lai, University of Southern California

• Yichi Zhang, American Institutes for Research

• Meltem Ozcan, University of Southern California

• Winnie Wing-Yee Tse, University of Southern California