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A Bayesian Approach to Tailored Testing

Owen, Roger J.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Bayesian Statistics, Individualized Tests, Mathematical Models, Scoring, Statistical Analysis, Test Construction


The sequential design and analysis of a test consisting of dichotomously scored items is approached from a Bayesian viewpoint. For a given examinee and for given items with known parameters, the scores on the items are taken to be independently distributed. Each item characteristic curve is taken to be a weighted average of 1 and a normal ogive function (to include the case where guessing is effective). Taking a normal prior distribution on the examinee ability, explicit expressions are derived for the posterior distribution and its mean and variance. In the Decision Theoretic framework of Wald, a quadratic loss function is taken and a simple, practical and approximately locally (or stepwise) optimum procedure is derived for sequentially choosing the (difficulties, discriminating powers and guessing constants of) items and analyzing the results.

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