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Unbiased Estimators of Ability Parameters, of their Variance, and of their Parallel-Forms Reliability

Published online by Cambridge University Press:  01 January 2025

Frederic M. Lord
Frederic M. Lord*
Affiliation:
Educational Testing Service
*
Requests for reprints should be addressed to: Frederic M. Lord, Educational Testing Service, Princeton, New Jersey, 08541.
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Abstract

Given known item parameters, unbiased estimators are derived i) for an examinee's ability parameter θ and for his proportion-correct true score ς, ii) for the variances of θ and ς across examinees in the group tested, and iii) for the parallel-forms reliability of the maximum likelihood estimator\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\hat \theta$$\end{document}.

Keywords

item response theorytrue scorelatent trait theorymaximum likelihood
Type
Original Paper
Information
Psychometrika , Volume 48 , Issue 2 , June 1983 , pp. 233 - 245
Copyright
Copyright © 1983 The Psychometric Society

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Footnotes

This work was supported in part by contract N00014-80-C-0402, project designation NR 150-453 between the Office of Naval Research and Educational Testing Service. Reproduction in whole or in part is permitted for any purpose of the United States Government.

References

Reference Note

Sympson, J. B. Estimating the reliability of adaptive tests from a single test administration. Paper presented at the meeting of the American Educational Research Association, Boston, April 1980.Google Scholar

References

Bradley, R. A. & Gart, J. J. The asymptotic properties of ML estimators when sampling from associated populations. Biometrika, 1962, 49, 205–214.Google Scholar
Jordan, C. Calculus of finite differences 2nd ed., New York: Chelsea, 1947.Google Scholar
Lord, F. M. Applications of item response theory to practical testing problems, Hillsdale, N.J.: Lawrence Erlbaum Associates, 1980.Google Scholar
Lord, F. M. & Novick, M. R. Statistical theories of mental test scores, Reading, Mass.: Addison-Wesley, 1968.Google Scholar
Shenton, L. R. & Bowman, K. O. Maximum likelihood estimation in small samples, New York: Macmillan, 1977.Google Scholar