On Bayesian formula scores for random guessing in multiple choice tests

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Abstract
Van der Ven (1974) identified defects of the classical formula score used to estimate the probability of chance success and the number of items on a multiple choice test for which the examinee truly knows the answer. He derived an estimator based upon the assumption of a uniform prior distribution for the number of known items. The present paper investigates properties of this estimator and compares it with the classical formula. More general models are presented of which the uniform prior is a special case. Further, it is shown that estimators of the prior distribution may be derived from the distribution of the total number of correct answers for a group of examinees. The fit of the models for some observed data is discussed.

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