Title: Measurement Invariance Using Equivalence Testing: An Introduction and Applied Example

Abstract: Measurement invariance (MI) is an important concept for scale developers and researchers who would like to compare data from multiple populations on some trait or construct. It is the idea that observed differences between populations are a function of group membership rather than bias in how a scale measures the target trait. A common practice to test levels of MI is through comparison of nested confirmatory factor analysis models after adding equality constraints on parameters across the groups. Statistically nonsignificant results from a chi square difference test are typically used as an indication of MI since the additional constraints do not statistically worsen the model fit. Yuan and Chan (2016) proposed to use equivalence testing approaches instead of this method to avoid the logical and statistical issues with “accepting” the null hypothesis. In this presentation, I will introduce Yuan and Chan’s equivalence testing approach to MI and illustrate its application using data from the Generic Conspiracist Beliefs Scale. Specifically I will test MI by gender and discuss the differences between the results obtained under the traditional and equivalence testing methods for MI.