In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of…

The Non-Equivalent groups with Anchor Test (NEAT) design involves "missing data" that are "missing by design." Three nonlinear observed score equating methods used with a NEAT design are the "frequency estimation equipercentile equating" (FEEE), the "chain equipercentile equating" (CEE), and the "item-response-theory observed-score-equating" (IRT…

After many equatings have been conducted in a testing program, equating errors can accumulate to a degree that is not negligible compared to the standard error of measurement. In this paper, the author investigates the asymptotic accumulative standard error of equating (ASEE) for linear equating methods, including chained linear, Tucker, and…

Rasch models are characterised by sufficient statistics for all parameters. In the Rasch unidimensional model for two ordered categories, the parameterisation of the person and item is symmetrical and it is readily established that the total scores of a person and item are sufficient statistics for their respective parameters. In contrast, in the…

Different data imputation techniques that are useful for equipercentile equating are discussed, and empirical data are used to evaluate the accuracy of these techniques as compared with chained equipercentile equating. The kernel estimator, the EM algorithm, the EB model, and the iterative moment estimator are considered. (SLD)

Tau-equivalence means that two tests produce equal true scores for individuals but that the distribution of errors for the tests could be different. This paper examines the effect of performing equipercentile equating techniques on tau-equivalent tests. (JKS)

Estimation techniques for generating the covariance matrix for two new tests and an existing test without the necessity of any examinee having to take two complete tests is presented. An application of these techniques to linear, observed-score, test equating is presented. (Author/JKS)

An asymptotic expression for the reliability of a linearly equated test is developed using normal theory. Reliability is expressed as the product of test reliability before equating and an adjustment term that is a function of the sample sizes used to estimate the linear equating transformation. The approach is illustrated. (SLD)

Derives a set of linear conditions of item-response functions that guarantees identical observed-score distributions on two test forms. The conditions can be added as constraints to a linear programming model for test assembly. An example illustrates the use of the model for an item pool from the Law School Admissions Test (LSAT). (SLD)

A cubic spline method for smoothing equipercentile equating relationships under the common item nonequivalent populations design is described. Statistical techniques based on bootstrap estimation are presented for choosing an equating method/degree of smoothing. Smoothing decreases the estimate of random error but results in an increase in…