A conceptualization of multiple-choice exams in terms of signal detection theory (SDT) leads to simple measures of item difficulty and item discrimination that are closely related to, but also distinct from, those used in classical item analysis (CIA). The theory defines a "true split," depending on whether or not examinees know an item,…

This article explores the amount of equating error at a passing score when equating scores from exams with small samples sizes. This article focuses on equating using classical test theory methods of Tucker linear, Levine linear, frequency estimation, and chained equipercentile equating. Both simulation and real data studies were used in the…

The van Hiele theory and van Hiele Geometry Test have been extensively used in mathematics assessments across countries. The purpose of this study is to use classical test theory (CTT) and cognitive diagnostic modeling (CDM) frameworks to examine psychometric properties of the van Hiele Geometry Test and to compare how various classification…

Brennan noted that users of test scores often want (indeed, demand) that subscores be reported, along with total test scores, for diagnostic purposes. Haberman suggested a method based on classical test theory (CTT) to determine if subscores have added value over the total score. One way to interpret the method is that a subscore has added value…

This article is a response to the commentaries on the position paper on observed-score equating by van der Linden (this issue). The response focuses on the more general issues in these commentaries, such as the nature of the observed scores that are equated, the importance of test-theory assumptions in equating, the necessity to use multiple…

While agreeing with van der Linden (this issue) that test equating needs better theoretical underpinnings, my comments criticize several aspects of his article. His examples are, for the most part, worthless; he does not use well-established terminology correctly; his view of 100 years of attempts to give a theoretical basis for equating is…

In spite of all of the technical progress in observed-score equating, several of the more conceptual aspects of the process still are not well understood. As a result, the equating literature struggles with rather complex criteria of equating, lack of a test-theoretic foundation, confusing terminology, and ad hoc analyses. A return to Lord's…

Recently, there has been an increasing level of interest in subscores for their potential diagnostic value. Haberman suggested a method based on classical test theory to determine whether subscores have added value over total scores. In this article I first provide a rich collection of results regarding when subscores were found to have added…

Two different traditions of response-time (RT) modeling are reviewed: the tradition of distinct models for RTs and responses, and the tradition of model integration in which RTs are incorporated in response models or the other way around. Several conceptual issues underlying both traditions are made explicit and analyzed for their consequences. We…

A potential undesirable effect of multistage testing is differential speededness, which happens if some of the test takers run out of time because they receive subtests with items that are more time intensive than others. This article shows how a probabilistic response-time model can be used for estimating differences in time intensities and speed…

Methods for evaluating the consistency of responses to test items were compared. When a researcher is unwilling to make the assumptions of classical test theory, has only a small number of items, or is in a tailored testing context, Cliff's dominance indices may be useful. (Author/CTM)

The standardization method for assessing unexpected differential item performance or differential item functioning is introduced. Findings of five studies are summarized, in which the statistical method of standardization is used to look for unexpected differences in item performance across different subpopulations of the Scholastic Aptitude Test.…

A decision-theoretic approach to the question of reliability in categorically scored examinations is explored. The concepts of true scores and errors are discussed as they deviate from conventional psychometric definitions and measurement error in categorical scores is cast in terms of misclassifications. A reliability measure based on…

For measuring the face validity of a test, Nevo suggested that test takers and nonprofessional users rate items on a five point scale. This article questions the ability of those raters and the credibility of the aggregated judgment as evidence of the validity of the test. (JAZ)

Because test scores are ordinal not cordinal attributes, the average test score often is a misleading way to summarize the scores of a group of individuals. Similarly, correlation coefficients may be misleading summary measures of association between test scores. Proper, readily interpretable, summary statistics are developed from a theory of…