A general framework of latent trait item response models for continuous responses is given. In contrast to classical test theory (CTT) models, which traditionally distinguish between true scores and error scores, the responses are clearly linked to latent traits. It is shown that CTT models can be derived as special cases, but the model class is…

Diagnostic tests are typically administered in a multiple-choice (MC) format due to their advantages of objectivity and time efficiency. The MC-deterministic input, noisy "and" gate (DINA) family of models, a representative class of cognitive diagnostic models for MC items, efficiently and parsimoniously estimates the mastery profiles of…

It is a much-lamented fact that research with the potential to inform or influence education policy instead remains policy inert. There are many reasons for this frustrating state of affairs, including a lack of strategic thinking on the part of researchers on how to successfully accomplish outreach--as opposed to communication with peers…

Nondichotomous response models have been of greater interest in recent years due to the increasing use of different scoring methods and various performance measures. As an important alternative to dichotomous scoring, the use of continuous response formats has been found in the literature. To assess finer-grained skills or attributes and to…

This article promotes the use of modern test theory in testing situations where sum scores for binary responses are now used. It directly compares the efficiencies and biases of classical and modern test analyses and finds an improvement in the root mean squared error of ability estimates of about 5% for two designed multiple-choice tests and…

A method for medical screening is adapted to differential item functioning (DIF). Its essential elements are explicit declarations of the level of DIF that is acceptable and of the loss function that quantifies the consequences of the two kinds of inappropriate classification of an item. Instead of a single level and a single function, sets of…

Many well-known equations in classical test theory are mathematical identities in populations of individuals but not in random samples from those populations. First, test scores are subject to the same sampling error that is familiar in statistical estimation and hypothesis testing. Second, the assumptions made in derivation of formulas in test…

Provides a general mathematical framework is provided that can be specialized to four different reliability coefficients. Consideration of this general framework makes it easier to convey to students the individual character of the formulations of reliability and the extent of their underlying similarity. (SLD)

A statistical test for detecting answer copying on multiple-choice items is presented. The test is based on the exact null distribution of the number of random matches between two test takers under the assumption that the response process follows a known response model. The null distribution can easily be generalized to the family of distributions…

Equating a new standard test to an old reference test is considered when samples for equating are not randomly selected from the target population of test takers, identifying two problems from equating from biased samples. An empirical example with data from the Armed Services Vocational Aptitude Battery illustrates the approach. (SLD)