Evaluation of Six Effect Size Measures of Measurement Non-Invariance for Continuous Outcomes

Measurement invariance is assessed in the factor analytic framework by testing differences in model fit of a sequential series of models; however, the statistical significance of these differences is influenced by many factors, including sample size. Effect sizes are independent of sample size and can be used to determine the magnitude and practical importance of an effect. We developed four new effect size measures of measurement non-invariance for continuous outcomes. To test the properties of these effect sizes and of two existing effect sizes of non-invariance, we conducted a simulation study. We varied group sample sizes, location of the latent distributions, magnitude of non-invariance and type of non-invariance (e.g., metric invariance). Three of the effect sizes were unbiased in all conditions and all six were consistent. Recommendations for their use and future directions are discussed.