To resolve a recent controversy between Klein and Cleary and Levy, a model for dichotomous congeneric items is presented which has mean errors of zero, dichotomous true scores that are uncorrelated with errors, and errors that are mutually uncorrelated. (Author)

The problem of whether a precise connection exists between the stochastic processes considered in mathematical learning theory and the Guttman simplex is investigated. The approach used is to derive a set of conditions which a probabilistic model must satisfy in order to generate inter-trial correlations with the perfect simplex property.…

A modified beta binomial model is presented for use in analyzing random guessing multiple choice tests and taste tests. Detection probabilities for each item are distributed beta across the population subjects. Properties for the observable distribution of correct responses are derived. Two concepts of true score estimates are presented.…

Using the concepts of conditional probability, conditional expectation, and conditional independence, the main results of the classical test theory model can be derived in a very few steps with minimal assumptions. The present effort explores the possibility that present classical test theories can be further condensed. (Author/RC)

An alternative to the uniform probability distribution model for ordinal data is considered. Implications for statistics and for test theory are discussed. (JKS)

Since the primary purpose of classical testing is to rank order examinees consistently, the absolute value of the true score has been relatively unimportant. However, the major purpose of criterion referenced testing is to estimate the true capabilities of examinees to perform specific tasks. Hence, the problems of true score determination assume…

Because it is a true score model employing item parameters which are independent of the examined sample, item characteristic curve theory (ICC) offers several advantages over classical measurement theory. In this paper an approach to biased item identification using ICC theory is described and applied. The ICC theory approach is attractive in that…

A probabilistic hypothesis testing procedure to assess the fit of hypothesized hierarchical structures for test item data is discussed. Statistical procedures are presented which are useful for evaluating the fit of data of a certain class of probabilistic models. These models apply to sets of dichotomous (O,1) responses for which there are…

Two fundamental problems in mental test theory are to estimate true score and to estimate the amount of error when testing an examinee. In this report, three probability models which characterize a single test item in terms of a population of examinees are described. How these models may be modified to characterize a single examinee in terms of an…

The previous theoretical development of the Poisson process as a strong model for the true-score theory of mental tests is discussed, and additional theoretical properties of the model from the standpoint of individual examinees are developed. The paper introduces the Erlang process as a family of test theory models and shows in the context of…

The Answer-Until-Correct (AUC) procedure has been proposed in order to increase the reliability of multiple-choice items. A model for examinees' behavior when they must respond to each item until they answer it correctly is presented. An expression for the reliability of AUC items, as a function of the characteristics of the item and the scoring…