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)

From a decision theoretic viewpoint, a general coefficient (delta) for tests is derived. The coefficient is applied to three kinds of decision situations. The first situation involves a true score estimated by a function of the observed score of a subject on a test (point estimation). Using the squared error loss function and Kelley's formula for…

Classical test theory is based on the concept of a true score for each examinee, defined as the expected or average score across an infinite number of repeated parallel tests. In most cases, there is only a score from a single administration of the test in question. The difference between this single observed score and the underlying true score is…

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)

Basic issues in criterion-referenced measurement are addressed. In section II, issues involved in determining what a person does and can do are considered. A preliminary analysis of "can" is given which shows that there are several important senses of "can". In section III, results of an analysis of "ability" 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…