A model is proposed for the description of ordinal test scores based on the definition of true score as expected rank; its deviations are compared with results from classical test theory. An unbiased estimator of population true score from sample data is calculated. Score variance and population reliability are examined. (Author/BJG)

This paper is aimed at demonstrating that Charles Spearman postulated neither a platonic true-error distinction nor a requirement for constant true scores under repeated measurement. (Author/RC)

Classical test theory findings can be derived from the concepts of conditional expectation, conditional independence, and related notions. It is shown that these concepts provide precisely the formalism needed to obtain the classical results with minimal assumptions and with greatest economy in the methods of proof. (RC)

The use of Cohen's kappa index as a measure of the reliability of multiple classifications is developed. Special cases of the index as well as the effects of test length on the index are also explored. (JKS)

A model for the setting of mastery cut scores is presented. The model, based on the beta-binomial test distribution, allows for hand calculation of cut scores. The model provides a simple way to explore the consequences of selecting a particular cut score. (Author/JKS)

The relatively hard problem of transforming a given set of curves to curves with the same shape can sometimes be reduced to the easier problem of rendering curves parallel. In this paper a group is associated with the given curves, and it is shown that the reduction from the hard problem to the easy problem is valid whenever the group is…

Empirical Bayes point estimates of true score may be obtained if the distribution of observed score for a fixed examinee is approximated in one of several ways by a well-known compound binomial model. The Bayes estimates of true score may be expressed in terms of the observed score distribution and the distribution of a hypothetical binomial test.…

Four criterion-referenced reliability coefficicents were compared to the Kuder-Richardson estimates and to each other. The Kuder-Richardson formulas 20 and 21, the Livingston, the Subkoviak and two Huynh coefficients were computed for a random sample of 33 criterion-referenced tests. The Subkoviak coefficient yielded the highest mean value;…

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)

The reliabilities of various observational measures were determined, and the influence of both the number and the length of the observation periods on reliability was examined, both separately and jointly. A single simplifying assumption leads to a variant of the Spearman-Brown formula, which may have wider application. (Author/CTM)

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

Several important implications in latent trait theory, with implications for individualized or tailored testing, are pointed out. A way of using the information function in tailored testing in connection with the standard error estimation of the ability level using maximum likelihood estimation is suggested. (Author/JKS)

The reliability of a criterion referenced test was defined as a measure of the degree to which the test discriminates between an individual's level of performance and a predetermined criterion level. The variances of observed and true scores were defined as the squared deviation of the score from the criterion. Based on these definitions and the…

The literature on criterion referenced testing is full of discussions concerning whether classical measurement techniques are appropriate, whether variance is necessary, whether new indices of reliability are needed, and the like. What appears to be lacking, however, is a clear and simple discussion of why the problems occur. This paper suggests…

The results of five studies into the characteristics of wrong answers as a class of divergent behavior are presented. The evidence from these studies, when taken in combination, suggests that the tendency of researchers to ignore wrong answers has been a fundamental procedural error of broad scope and serious consequences. Instead of the straight…