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An Interval Estimate for making Statistical Inferences about True Scores

Published online by Cambridge University Press:  01 January 2025

Frederic M. Lord  and
Martha L. Stocking
Frederic M. Lord*
Affiliation:
Educational Testing Service
Martha L. Stocking
Affiliation:
Educational Testing Service
*
Requests for reprints should be sent to Dr. Frederic M. Lord, Educational Testing Service, Princeton, New Jersey 08540.
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Abstract

A numerical procedure is outlined for obtaining an interval estimate of the regression of true score on observed score. Only the frequency distribution of observed scores is needed for this. The procedure assumes that the conditional distribution of observed scores for fixed true score is binomial. The procedure is applied to several sets of test data.

Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 1 , March 1976 , pp. 79 - 87
Copyright
Copyright © 1976 The Psychometric Society

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Footnotes

This research was sponsored in part by the Personnel and Training Research Programs, Psychological Sciences Division, Office of Naval Research, under Contract No. N00014-69-C-0017, Contract Authority Identification Number, NR No. 150-303, and Educational Testing Service. Reproduction in whole or in part is permitted for any purpose of the United States Government.

References

Copas, J. B. Compound decisions and empirical Bayes. Journal of the Royal Statistical Society, 1969, 31, 397–425.CrossRefGoogle Scholar
Fiacco, A. V. and McCormick, G. P. Nonlinear programming: Sequential unconstrained minimization techniques, 1968, New York: Wiley.Google Scholar
Fletcher, R. and Powell, M. J. D. A rapidly convergent descent method for minimization. Computer Journal, 1963, 2, 163–168.CrossRefGoogle Scholar
Griffin, B. S. and Krutchkoff, G. Optimal linear estimators: An empirical Bayes version with application to the binomial distribution. Biometrika, 1971, 58, 195–201.CrossRefGoogle Scholar
Jöreskog, K. G. Some contributions to maximum likelihood factor analysis. Psychometrika, 1967, 32, 443–482.CrossRefGoogle Scholar
Karlin, S. and Shapley, L. S. Geometry of moment space. Memoirs of the American Mathematical Society, 1953, 12.Google Scholar
Lord, F. M. A strong true-score theory, with applications. Psychometrika, 1965, 30, 239–270.CrossRefGoogle Scholar
Lord, F. M. Estimating true-score distributions in psychological testing (an empirical Bayes estimation problem). Psychometrika, 1969, 34, 259–299.CrossRefGoogle Scholar
Lord, F. M. and Cressie, N. An empirical Bayes procedure for finding an interval estimate. Sankhyā, in press.Google Scholar
Lord, F. M. and Novick, M. R. Statistical theories of mental test scores, 1968, Reading, Mass.: Addison-Wesley.Google Scholar
Maritz, J. S. Smooth empirical Bayes estimation for one-parameter discrete distributions. Biometrika, 1966, 53, 417–429.CrossRefGoogle Scholar
Possé, C. Sur quelques applications des fractions continues algébriques, 1886, St. Petersbourg, Russie: L'Académie Impériale des Sciences.Google Scholar
Robbins, H. An empirical Bayes approach to statistics. In Neyman, J. (Eds.), Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. Berkeley: University of California Press. 1956, 157–164.Google Scholar