Chalmers recently published a critique of the use of ordinal a[alpha] proposed in Zumbo et al. as a measure of test reliability in certain research settings. In this response, we take up the task of refuting Chalmers' critique. We identify three broad misconceptions that characterize Chalmers' criticisms: (1) confusing assumptions with…

On the occasion of Psychometrika's fiftieth anniversary, the past twenty-five years' developments in mental test theory are reviewed. Psychometrika articles treating topics in test theory are listed in a bibliography. (Author/LMO)

Deciding whether sets of test data are consistent with any of a large class of item response models is considered. The assumption of local independence is weakened to a new condition, local nonnegative dependence (LND). Necessary and sufficient conditions are derived for a LND item response model. (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…

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)

New ability estimators have been proposed by Wainer and Wright (1980) and Mislevy and Bock (1981) that are resistant against guessing and careless behaviors exhibited by some examinees. This paper presents another class of ability estimators that are resistant to departures from the underlying assumptions concerning guessing and carelessness. In…

An important determinant of equating process efficiency is the correlation between the anchor test and components of each form. Use of some monotonic function of this correlation as a measure of equating efficiency is suggested. A model relating anchor test length and test reliability to this measure of efficiency is presented. (Author/DWH)

This paper traces the course of the consequences of viewing test responses as simply providing dichotomous data concerning ordinal relations. It begins by proposing that the score matrix is best considered to be items-plus-persons by items-plus-persons, and recording the wrongs as well as the rights. (Author/CTM)

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…

Significant to a latent trait or item response theory analysis of a mental test is the determination of exactly what is being quantified. The following are practical problems to be considered in the formulation of a good theory: (1) deciding whether two tests measure the same trait or traits; (2) analyzing the relative contributions of a pair of…

Statistical significance and "abnormality" have been used as criteria for the evaluation of intra-individual subtest score differences. Shortcomings of these criteria are identified, and improved estimates of the true score differences are suggested. The applicability of the abnormality criterion to these improved estimates is reviewed.…

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…

To assess the effects of correlated abilities on test characteristics, and to explore the effects of correlated abilities on the use of a multidimensional item response theory model which does not explicitly account for such a correlation, two tests were constructed. One had two relatively unidimensional subsets of items, the other had all…

This paper deals with test fairness regarding a test consisting of two parts: (1) a "common" section, taken by all students; and (2) a "variable" section, in which some students may answer a different set of questions from other students. For example, a test taken by several thousand students each year contains a common multiple-choice portion and…

The use of Bayesian decision theory to solve problems in test-based decision making is discussed. Four basic decision problems are distinguished: (1) selection; (2) mastery; (3) placement; and (4) classification, the situation where each treatment has its own criterion. Each type of decision can be identified as a specific configuration of one or…