Module 33: Population Invariance in Linking and Equating

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A goal for any linking or equating of two or more tests is that the linking function be invariant to the population used in conducting the linking or equating. Violations of population invariance in linking and equating jeopardize the fairness and validity of test scores, and pose particular problems for test-based accountability programs that require schools, districts, and states to report annual progress on academic indicators disaggregated by demographic group membership. This instructional module provides a comprehensive overview of population invariance in linking and equating and the relevant methodology developed for evaluating violations of invariance. A numeric example is used to illustrate the comparative properties of available methods, and important considerations for evaluating population invariance in linking and equating are presented.

Keywords: equating, fairness, group-to-overall method, invariance, linking, linking function, omnibus method, pairwise method, validity

Anne C. Huggins

Research and Evaluation Methodology, University of Florida

Randall D. Penfield

Professor, Educational Research Methodology, University of North Carolina at Greensboro, NC

Dr. Penfield is Dean of the School of Education and a Professor of educational measurement and assessment. His research focuses on issues of fairness in testing, validity of test scores, and the advancement of methods and statistical models used in the field of assessment. In recognition of his scholarly productivity he was awarded the 2005 early career award by the National Council on Measurement in Education, and was named a Fellow of the American Educational Research Association in 2011. In addition, he has served as co-principal investigator or consultant on a numerous federal grants funded by the National Science Foundation and the Department of Education.


Module 33: An NCME Instructional Module on Population Invariance in Linking and Equating
Open to download resource.
Open to download resource.