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Estimating True Measurements From Fallible Measurements (Binomial Case) - Expansion in a Series of Beta Distributions

Lord, Frederic M.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Office of Naval Research, Binomial Distribution, Estimation (Mathematics), Mathematical Models, Scoring, True Scores


In mental-test theory, a useful mathematical model specifies the relation of the examinee's observed score, x, to his or her "true score," zeta. The present paper is concerned with a model for the number-right scores on a test composed of n questions or "items." The basic problem in the use of this model may be thought of as the problem of estimating the unknown frequency distribution of true scores. Once this is done, the bivariate distribution of zeta and x has also been estimated. All important properties of the test score can thus be investigated. Although it might at first seem otherwise, the model has empirically verifiable implications. The first section of the present paper discusses various methods for estimating g(zeta). The second section outlines the method to be reported here. The third section presents and discusses the results of applying this method to widely different sets of mental test data.

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