This booklet is a conceptual introduction to item response theory (IRT), which many large-scale testing programs use for constructing and scoring their tests. Although IRT is essentially mathematical, the approach here is nonmathematical, in order to serve as an introduction on the topic for people who want to understand why IRT is used and what…

The current project, Exploring Math Education Relations by Analyzing Large Data Sets (EMERALDS) II, is an attempt to identify specific Common Core State Standards procedural, conceptual, and problem-solving competencies in earlier grades that best predict success in algebraic areas in later grades. The data for this study include two cohorts of…

This booklet grew out of a half-day class on equating that author Samuel Livingston teaches for new statistical staff at Educational Testing Service (ETS). The class is a nonmathematical introduction to the topic, emphasizing conceptual understanding and practical applications. The class consists of illustrated lectures, interspersed with…

Estimation of item response model parameters and ability distribution parameters has been, and will remain, an important topic in the educational testing field. Much research has been dedicated to addressing this task. Some studies have focused on item parameter estimation when the latent ability was assumed to follow a normal distribution,…

The nature of the matching criterion (usually the total score) in the study of differential item functioning (DIF) has been shown to impact the accuracy of different DIF detection procedures. One of the topics related to the nature of the matching criterion is whether the studied item should be included. Although many studies exist that suggest…

Providing information to test takers and test score users about the abilities of test takers at different score levels has been a persistent problem in educational and psychological measurement (Carroll, 1993). Scale anchoring (Beaton & Allen, 1992), a technique that describes what students at different points on a score scale know and can do,…

There has been an increased interest in developing computer-adaptive testing (CAT) and multistage assessments for K-12 accountability assessments. The move to adaptive testing has been met with some resistance by those in the field of special education who express concern about routing of students with divergent profiles (e.g., some students with…

The nonequivalent groups with anchor test (NEAT) design involves missing data that are missing by design. Three popular equating methods that can be used with a NEAT design are the poststratification equating method, the chain equipercentile equating method, and the item-response-theory observed-score-equating method. These three methods each…

This paper examines item response theory (IRT) scale transformations and IRT scale linking methods used in the Non-Equivalent Groups with Anchor Test (NEAT) design to equate two tests, X and Y. It proposes a unifying approach to the commonly used IRT linking methods: mean-mean, mean-var linking, concurrent calibration, Stocking and Lord and…

Item parameter estimates vary for a variety of reasons, including estimation error, characteristics of the examinee samples, and context effects (e.g., item location effects, section location effects, etc.). Although we expect variation based on theory, there is reason to believe that observed variation in item parameter estimates exceeds what…