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.
