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Statistical Theory for Logistic Mental Test Models With a Prior Distribution of Ability

Birnbaum, Allan
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Ability Distribution, Mathematical Models, Statistics, Test Theory


The logistic model of a mental test was introduced by the present writer in Chapters 17 through 20 of Lord and Novick, Statistical Theories of Mental Test Scores, where statistical inference methods were developed without assumption of a prior distribution of ability. Such a distribution is assumed in this paper, and corresponding statistical inference methods and distribution theory are developed. Results include detailed investigation of posterior distributions, given observed response patterns; point-estimation of ability, and its mean-squared error; and distributions of test scores and their moments. Some computational methods and detailed examples are given.

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