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…

The testlet comprises a set of items based on a common stimulus. When the testlet is used in the tests, there may violate the local independence assumption, and in this case, it would not be appropriate to use traditional item response theory models in the tests in which the testlet is included. When the testlet is discussed, one of the most…

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…

This simulation study examines the characteristics of the Explanatory Item Response Model (EIRM) when estimating treatment effects when compared to classical test theory (CTT) sum and mean scores and item response theory (IRT)-based theta scores. Results show that the EIRM and IRT theta scores provide generally equivalent bias and false positive…

In this ITEMS module, we provide a two-part introduction to the topic of reliability from the perspective of "classical test theory" (CTT). In the first part, which is directed primarily at beginning learners, we review and build on the content presented in the original didactic ITEMS article by Traub and Rowley (1991). Specifically, we…

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…

For proper assessment selection understanding the statistical similarities amongst assessments that measure the same, or very similar, topics is imperative. This study seeks to extend the comparative analysis between the brief electricity and magnetism assessment (BEMA) and the conceptual survey of electricity and magnetism (CSEM) presented by…

Spearman's correction for attenuation (measurement error) corrects a correlation coefficient for measurement errors in either-or-both of two variables, and follows from the assumptions of classical test theory. Spearman's equation removes all measurement error from a correlation coefficient which translates into "increasing the reliability of…

Current procedures for equating number-correct scores using traditional item response theory (IRT) methods assume local independence. However, when tests are constructed using testlets, one concern is the violation of the local item independence assumption. The testlet response theory (TRT) model is one way to accommodate local item dependence.…

There are well-defined theoretical differences between the classical test theory (CTT) and item response theory (IRT) frameworks. It is understood that in the CTT framework, person and item statistics are test- and sample-dependent. This is not the perception with IRT. For this reason, the IRT framework is considered to be theoretically superior…

Item response theory (IRT) has so many advantages than its precedent Classical Test Theory (CTT) such as non-changing item parameters, ability parameter estimations free from the items. However, in order to get these advantages, some assumptions should be met and they are; unidimensionality, normality and local independence. However, it is not…

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…

The frequently neglected and often misunderstood relationship between classical test theory and item response theory is discussed for the unidimensional case with binary measures and no guessing. It is pointed out that popular item response models can be directly obtained from classical test theory-based models by accounting for the discrete…

Scientific models and modeling play an important role in science, and students' understanding of scientific models is essential for their understanding of scientific concepts. The measurement instrument of "Students' Understanding of Models in Science" (SUMS), developed by Treagust, Chittleborough & Mamiala ("International…

Cultural consensus theory (CCT) is a data aggregation technique with many applications in the social and behavioral sciences. We describe the intuition and theory behind a set of CCT models for continuous type data using maximum likelihood inference methodology. We describe how bias parameters can be incorporated into these models. We introduce…