Open AccessA BAYESIAN APPROACH TO TAILORED TESTING
Author(s) -
Owen Roger J.
Publication year - 1969
Publication title -
ets research bulletin series
Language(s) - English
Resource type - Journals
eISSN - 2333-8504
pISSN - 0424-6144
DOI - 10.1002/j.2333-8504.1969.tb00772.x
Subject(s) - bayesian probability , mathematics , variance (accounting) , quadratic equation , function (biology) , prior probability , simple (philosophy) , statistics , computer science , philosophy , geometry , accounting , epistemology , evolutionary biology , business , biology
ABSTRACT 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.