Power and precision in confirmatory factor analytic tests of measurement invariance

This study investigates the effects of sample size, factor overdetermination, and communality on the precision of factor loading estimates and the power of the likelihood ratio test of factorial invariance in multigroup confirmatory factor analysis. Although sample sizes are typically thought to be the primary determinant of precision and power, the degree of factor overdetermination and the level of indicator communalities also play important roles. Based on these findings, no single rule of thumb regarding the ratio of sample size to number of indicators can ensure adequate power to detect a lack of measurement invariance.