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Empirical Bayes Point Estimates of True Score Using a Compound Binomial Error Model

Kearns, Jack
Publication Year:
Report Number:
ETS Research Memorandum
Document Type:
Page Count:
Subject/Key Words:
Error Patterns, Mathematical Models, Statistical Analysis, True Scores


Empirical Bayes point estimates of true score may be obtained if the distribution of observed score for a fixed examinee is approximated in one of several ways by a well-known compound binomial model. The Bayes estimates of true score may be expressed in terms of the observed score distribution and the distribution of a hypothetical binomial test. The latter distribution is found by use of the compound binomial approximation formula and from relationships which exist between Bayes estimates and unconditional probabilities of observed score. Empirical Bayes point estimates are obtained by use of the sample observed score distribution.

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