Abstract
Consider an old testX consisting ofs sections and two new testsY andZ similar toX consisting ofp andq sections respectively. All subjects are given testX plus two variable sections from either testY orZ. Different pairings of variable sections are given to each subsample of subjects. We present a method of estimating the covariance matrix of the combined test (X 1, ...,X s ,Y 1, ...,Y p ,Z 1, ...,Z q ) and describe an application of these estimation techniques to linear, observed-score, test equating.
Similar content being viewed by others
References
Angoff, W. H. Scales, norms, and equivalent scores. In R. Thorndike (Ed.)Educational measurement, second edition. Washington, D.C.: American Council on Education, 1971, pp. 508–600.
Beaton, A. E.The use of special matrix operations in statistical calculus. Princeton, N.J.: Educational Testing Service, Research Bulletin No. 64-51, 1964.
Braun, H. I. & Holland, P. W. Observed score test equating: A mathematical analysis of some ETS equating procedures. In P. W. Holland and D. B. Rubin (Eds.),Test equating. New York: Academic Press, Inc., 1982.
Dempster, A. P., Laird, N. M., & Rubin, D. B. Maximum likelihood from incomplete data via the EM algorithm.Journal of the Royal Statistical Society Series B, 1977,39, pp. 1–38.
Holland, P. W. & Thayer, D. T.Section pre-equating the Graduate Record Examination. Princeton, N.J.: Educational Testing Service, Program Statistics Research Technical Report No. 81-13, 1981.
Holland, P. W. & Wightman, L. E. Section pre-equating: A preliminary investigation. In P. W. Holland and D. B. Rubin (eds.),Test equating. New York: Academic Press, Inc., 1982.
Rubin, D. B. Characterizing the estimation of parameters in incomplete-data problems.Journal of the American Statistical Association, 1974,69, pp. 467–474.
Rubin, D. B. Inference and missing data.Biometrika, 1976,63, pp. 581–592.
Rubin, D. B. & Thayer, D. T. Relating tests given to different samples.Psychometrika, 1978,43, pp. 3–10.
Author information
Authors and Affiliations
Additional information
The author is indebted to Paul W. Holland and Donald B. Rubin for their encouragement and many helpful comments and suggestions that contributed significantly to the development of this paper.
This research was supported by the Program Statistics Research Project of the ETS Research Statistics Group.
Rights and permissions
About this article
Cite this article
Thayer, D.T. Maximum likelihood estimation of the joint covariance matrix for sections of tests given to distinct samples with application to test equating. Psychometrika 48, 293–297 (1983). https://doi.org/10.1007/BF02294023
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02294023