Cognitive diagnostic models (CDMs) have great promise for providing diagnostic information to aid learning and instruction, and a large number of CDMs have been proposed. However, the assumptions and performances of different CDMs and their applications in regard to reading comprehension tests are not fully understood. In the present study, we…

English language proficiency assessments (ELPA) are used in the United States to measure annually the English language progress and proficiency of English-language learners (ELLs), a subgroup of language minority students who receive language acquisition support mandated and largely funded by Title III (NCLB, 2001). ELPA proficient and…

This paper presents the author's response to Xiaoming Xi's article titled "How do we go about investigating test fairness?" In this response, the author focuses on test fairness and Toulmin's model of argument structure, Xi's proposal, and the challenges the proposal brings. Xi proposes an approach to investigating test fairness to guide…

This article investigates how measurement models and statistical procedures can be applied to estimate the accuracy of proficiency classification in language testing. The paper starts with a concise introduction of four measurement models: the classical test theory (CTT) model, the dichotomous item response theory (IRT) model, the testlet response…