Observed-Score Test Equating: Illustration using the Gaussian Kernel Method

Pre-conference workshop with Alina von Davier, Educational Testing Service, Princeton, USA

20th July, 9.00 - 13.00, Boys Smith Room, Fisher Building

Alina von DavierTest equating methods are used to produce scores that are comparable across different test forms. The Kernel Method of Test Equating (KE) is a unified approach to test equating based on a flexible family of equipercentile-like equating functions that contains the linear equating function as a special case. Any observed-score test equating is viewed as having five steps: 1) pre-smoothing; 2) estimation of the score probabilities on the target population; 3) continuization; 4) computing the equating function; 5) computing the standard error of equating and related accuracy measures. KE brings together these steps into an organized whole rather than treating them as disparate problems. KE exploits pre-smoothing by fitting log-linear models to score data, and incorporates it into step 5) above. KE provides new tools for comparing two or more equating functions and to rationally choose between them.

In this session, theoretical issues will be considered along with numerical examples and software demonstration using real data. The session will provide an overview of the observed-score equating methods, their assumptions, and the relevant data collection designs. The book “The Kernel Method of Test Equating” of von Davier, Holland, and Thayer (2004) is the basis of this training session. Recent research results described in the book “Statistical Models for Test Equating, Linking, and Scaling” (in press) edited by the presenter are also incorporated.

References

von Davier, A.A. (Ed.) (in press). Statistical Models for Equating, Linking, and Scaling. New York: Springer Verlag.

von Davier, A. A., Holland, P. W., & Thayer, D. T. (2004). The Kernel Method of Test Equating.   New York: Springer Verlag.