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A Test Theory Model for Ordinal Measurements

Published online by Cambridge University Press:  01 January 2025

Robert S. Schulman  and
Richard L. Haden
Robert S. Schulman
Affiliation:
Virginia Polytechnic Institute and State University
Richard L. Haden
Affiliation:
The University of North Carolina
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Abstract

A model is proposed for the description of ordinal test scores based on the definition of true score as expected rank. Derivations from the model are compared with results from clasiscal test theory as developed by Lord and Novick, in particular with respect to parallel tests and composites. An unbiased estimator of population true score from sample data is derived and its variance is shown to decrease with increasing sample size. Population reliability is shown to be analytically related to expected sample reliability, and methods of reliability estimation are discussed.

Type
Original Paper
Information
Psychometrika , Volume 40 , Issue 4 , December 1975 , pp. 455 - 472
Copyright
Copyright © 1975 The Psychometric Society

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Footnotes

*

This investigation was supported in part by PHS traineeship and research grants, MH-08258 and MH-10006, from the National Institute of Mental Health, Public Health Service. Also partial support was received from the National Science Foundation science development grant GU-2059.

†

The authors are indebted to Dr. Amnon Rapoport for a thorough reading of this manuscript and for his many helpful suggestions.

References

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Lord, F. M., Novick, M. R.. Statistical theories of mental test scores, 1968, Reading, Mass.: Addison-Wesley.Google Scholar
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Parzen, E.. Stochastic processes, 1962, San Francisco: Holden-Day.Google Scholar