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Estimating True-Score Distributions in Psychological Testing (an Empirical Bayes Estimation Problem)

Published online by Cambridge University Press:  01 January 2025

Frederic M. Lord
Frederic M. Lord*
Affiliation:
Educational Testing Service
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Abstract

The following problem is considered: Given that the frequency distribution of the errors of measurement is known, determine or estimate the distribution of true scores from the distribution of observed scores for a group of examinees. Typically this problem does not have a unique solution. However, if the true-score distribution is “smooth,” then any two smooth solutions to the problem will differ little from each other. Methods for finding smooth solutions are developed a) for a population and b) for a sample of examinees. The results of a number of tryouts on actual test data are summarized.

Type
Original Paper
Information
Psychometrika , Volume 34 , Issue 3 , September 1969 , pp. 259 - 299
Copyright
Copyright © 1969 The Psychometric Society

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Footnotes

*

The writer wishes to thank Diana Lees and Virginia Lennon, who wrote the computer programs, carried out some of the mathematical derivations, and helped with other important aspects of the work. This work was supported in part by contract Nonr-2752(00) between the Office of Naval Research and Educational Testing Service. Reproduction, translation, use and disposal in whole or in part by or for the United States Government is permitted.

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