The R software provides packages and functions that provide data analysis in classical true score, generalizability theory, item response theory, and Rasch measurement theories. A brief list of notable articles in each measurement theory and the first measurement journals is followed by a list of R psychometric software packages. Each psychometric…

This article provides a brief description of a Windows application called IRTEQ. IRTEQ employs an intuitive, user-friendly graphic user interface that can rescale one test form to another by using various item response theory (IRT) scaling methods. It supports various IRT models for test forms. It can also equate test scores on the scale of one…

This paper provides formulas for expected true-score measures and reliability of binary items as a function of their Rasch difficulty parameters when the trait distribution is normal or logistic. With the proposed formula, one can evaluate the theoretical values of classical reliability indexes for norm-referenced and criterion-referenced…

Proposes formulas for expected true-score measures and reliability of binary items as a function of their Rasch difficulty when the trait (ability) distribution is normal or logistic. Provides an illustrative example for using the proposed formulas. (SLD)

This paper provides analytic evaluations of expected (marginal) true-score measures for binary items given their item response theory (IRT) calibration. Under the assumption of normal trait distributions, marginalized true scores, error variance, true score variance, and reliability for norm-referenced and criterion-references interpretations are…

Exact formulas for classical error variance are provided for Rasch measurement with logistic distributions. An approximation formula with the normal ability distribution is also provided. With the proposed formulas, the additive contribution of individual items to the population error variance can be determined without knowledge of the other test…

The performance of three equating methods--the presmoothed equipercentile method, the item response theory (IRT) true score method, and the IRT observed score method--were examined based on three equating criteria: the same distributions property, the first-order equity property, and the second-order equity property. The magnitude of the…