Linking and Aligning Scores and Scales

In their preface to the second edition of Test Equating, Scaling, and Linking, Mike Kolen and Bob Brennan (2004) made the following observation: “Prior to 1980, the subject of equating was ignored by most people in the measurement community except for psychometricians, who had responsibility for equating” (p. vii). The authors went on to say that considerably more attention is now paid to equating, indeed to all forms of linkages between tests, and that this increased attention can be attributed to several factors: 1. An increase in the number and variety of testing programs that use multiple forms and the recognition among professionals that these multiple forms need to be linked. 2. Test developers and publishers, in response to critics, often refer to the role of linking in reporting scores. 3. The accountability movement and fairness issues related to assessment have become much more visible. Those of us who work in this field know that ensuring comparability of scores is not an easy thing to do. Nonetheless, our customers―the te- takers and score users―either assume that scores on different forms of an assessment can be used interchangeably or, like the critics above, ask us to justify our comparability assumptions. And they are right to do this. After all, the test scores that we provide have an impact on decisions that affect people’s choices and their future plans. From an ethical point of view, we are obligated to get it right.

The comparability of measurements made in differing circumstances by different methods and investigators is a fundamental pre-condition for all of science. Successful applications of technology require comparable measurements. While the applications herefocus on educational tests, score linking issues are directly applicable to medicine and many branches of behavioral science.

Since the 1980s, the fields of educational and psychological measurement have enhanced and widely applied techniques for producing linked scores that are comparable. The interpretation attached to a linkage depends on how the conditions of the linkage differ from the ideal. In this book, experts in statistics and psychometrics describe classes of linkages, the history of score linkings, data collection designs, and methods used to achieve sound score linkages. They describe and critically discuss applications to a variety of domains including equating of achievement exams, linkages between computer-delivered exams and paper-and-pencil exams, concordances between the current version of the SAT® and its predecessor, concordances between the ACT® and the SAT®, vertical linkages of exams that span grade levels, and linkages of scales from high-stakes state assessments to the scales of the National Assessment of Educational Progress (NAEP).

Dr. Neil J. Dorans is a Distinguished Presidential Appointee at Educational Testing Service. During his 27 years at ETS, he has had primary responsibility for the statistical work associated with the AP®, PSAT/NMSQT®, and SAT® exams. He was the architect for the recentered SAT scales. He has guest edited special issues on score linking for Applied Measurement in Education, Applied Psychological Measurement, and the Journal of Educational Measurement.

Dr. Mary Pommerich is a psychometrician in the Personnel Testing Division of the Defense Manpower Data Center, where she works with theASVAB (Armed Services Vocational Aptitude Battery) testing program. She guest edited a special issue on concordance for Applied Psychological Measurement. Her research is typically generated by practical testing problems and has focused on a wide variety of issues, including linking and concordance.

Dr. Paul W. Holland is the Frederic M. Lord Chair in Measurement and Statistics at Educational Testing Service and before that professor in the School of Education and the department of Statistics at the University of California, Berkeley. His books include Discrete Multivariate Analysis, Differential Item Functioning, Perspectives on Social Network Research , and two books on test score equating. He is a fellow of the American Statistical Association and the Institute for Mathematical Statistics, was designated a National Associate of the National Academies, was awarded for his career contributions by the National Council on Measurement in Education, and was elected to the National Academy of Education.