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Tutorial 3
Measurement Invariance: Conceptual and Data Analysis Issues

David Chan
National University of Singapore

In virtually all areas of I-O psychology, we often make direct comparisons between two or more groups of individuals (e.g., male vs. female, White vs. African American, supervisors vs. coworkers, Culture A vs. Culture B) in their responses to the same set of items/measures. On the basis of absolute differences in the scores on the measurement scale, substantive inferences are made about between-group differences in the level of the construct purportedly represented by the items/measures. The validity of these inferences is dependent on the often untested assumption that, across groups, the same items/measures are measuring the same construct and measuring it with the same precision. When this assumption of measurement invariance is in fact violated, absolute differences in scores between groups, and therefore inferences based on these differences, are likely to be misleading or not meaningful. Hence, measurement invariance is often a statistical hurdle that should be cleared before making direct between-groups comparisons of scores. On the other hand, measurement invariance or lack thereof may also reflect or represent substantive between-groups differences that are of theoretical interest. 

This tutorial will introduce the conceptual and data analysis issues involved in measurement invariance. The focus is on the logic of measurement invariance although numerical examples using structural equation modeling will be presented to illustrate the various issues, including how tests of measurement invariance can be performed. Measurement invariance of responses over time may also be discussed. 

David Chan (PhD, Michigan State University) is currently associate professor at the National University of Singapore and scientific advisor to the Center for Testing and Assessment in Singapore. He serves on the editorial boards for six journals. His research includes areas in personnel selection, longitudinal modeling, and adaptation to changes at work. He has received several scholarly awards including the Distinguished Early Career Contributions Award, the William Owens Scholarly Achievement Award, the Edwin Ghiselli Award for Innovative Research Design, the APA Dissertation Research Award, the Michigan State University Social Science College Award, and the Best Paper Award from the Human Resources Division of the Academy of Management. He has worked with several public and private organizations in Singapore and the United States on personnel selection and related projects. He is currently a consultant to the Prime Ministers Office in Singapore, the Ministry of Community Development and Sports, the Singapore Police Force, and the Singapore Prison Service.

Coordinator: Steve Scullen, North Carolina State University

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