This study develops a theoretical model for the costs of an exam as a function of its duration. Two kind of costs are distinguished: (1) the costs of measurement errors and (2) the costs of the measurement. Both costs are expressed in time of the student. Based on a classical test theory model, enriched with assumptions on the context, the costs…

The study aims to examine whether differential item function is displayed in three different test forms that have item orders of random and sequential versions (easy-to-hard and hard-to-easy), based on Classical Test Theory (CTT) and Item Response Theory (IRT) methods and bearing item difficulty levels in mind. In the correlational research, the…

Research on the graphical facilitation of probabilistic reasoning has been characterised by the effort expended to identify valid assessment tools. The authors developed an assessment instrument to compare reasoning performances when problems were presented in verbal-numerical and graphical-pictorial formats. A sample of undergraduate psychology…

The grades K-2 Florida Center for Reading Research (FCRR) Reading Assessment (FRA) consists of computer-adaptive alphabetic and oral language screening tasks that provide a Probability of Literacy Success (PLS) linked to grade-level performance (i.e., the 40th percentile) on the word reading (in kindergarten) or reading comprehension (in grades…

This mixed, causal-comparative study was an investigation of culture infusion methods and AYP of two different public schools in Chicago, a school that infuses African culture and a school that does not. The purpose of the study was to identify if there was a significant causative relationship between culture infusion methods and Adequate Yearly…

In this commentary, the author points out few issues, one being that there are models mislabeled as diagnostic, which deal with linear decompositions of item difficulties rather than estimating multidimensional skill variables. The author discusses the issue that there are many new names for essentially well-known models for multiple simultaneous…

Letter-name identification has been widely used as part of early screening to identify children who might be at risk for future word reading difficulty. The goal of the present study was to examine whether a reduced set of letters could have similar diagnostic accuracy rather than a full set (i.e., 26 letters) when used as a screen. First, we…

Diagnostic assessment is currently an active research area in educational measurement. Literature related to diagnostic modeling has been in existence for several decades, but a great deal of research has been conducted within the last decade or so, especially within the last five years. The author summarizes the key components in the application…

Several current international comparative large-scale assessments of educational achievement (ICLSA) make use of "Rasch models", to address functions essential for valid cross-cultural comparisons. From a historical perspective, ICLSA and Georg Rasch's "models for measurement" emerged at about the same time, half a century ago. However, the…

Presents a model of tests and measurement that identifies test scores with Hilbert space vectors and true and error components of scores with linear operators. This geometric point of view brings to light relations among elementary concepts in test theory, including reliability, validity, and parallel tests. (Author/SLD)

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…

This article addresses issues in model building and statistical inference in the context of student modeling. The use of probability-based reasoning to explicate hypothesized and empirical relationships and to structure inference in the context of proportional reasoning tasks is discussed. Ideas are illustrated with an example concerning…

In an invitational address to the Victorian Institute of Educational Research, the author discussed Bayesian theory and its relationship to the design and construction of tailored or adaptive tests. Bayesian thinking involves recognizing the role of prior probabilities and using these probabilities in combination with new data to arrive at future…