2025/05/05 by Mark H. C. Lai, Yichi Zhang, Meltem Özcan +2 · 1 voice
Decision Sciences · Mathematics · #Psychometric Methodologies and Testing #Statistical Methods and Bayesian Inference #Advanced Statistical Methods and Models
paper · pdf · doi:10.1080/10705511.2025.2484812
openalex publication_date 2025/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22
With the increase in empirical studies evaluating measurement invariance of psychological measures, 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. As researchers increasingly explore invariance across more than two groups (e.g., race and ethnicity) and multiple grouping variables (e.g., race and gender), we propose the fMACS (and fMACS2) statistic as a natural extension to the dMACS effect size by Nye and Drasgow (Citation2011) for multiple groups, similar to how Cohen’s f is an extension of Cohen’s d for standardized mean differences of more than two groups. Using two empirical examples, we illustrate how fMACS can be computed using parameter estimates of a partial invariance model, and show how fMACS can quantify noninvariance due to both main effects and interactions when there are multiple grouping variables. We also provide suggestions for improving reporting practices of measurement invariance analyses to facilitate the computation of effect sizes in secondary research, making it easier to evaluate the replicability of invariance studies and synthesize findings from such studies.