The current literature on test equating generally defines it as the process necessary to obtain score comparability between different test forms. The definition is in contrast with Lord's foundational paper which viewed equating as the process required to obtain comparability of measurement scale between forms. The distinction between the notions…

The Wisconsin Card Sorting Test (WCST) assesses executive and frontal lobe function and can be administered manually or by computer. Despite the widespread application of the 2 versions, the psychometric equivalence of their scores has rarely been evaluated and only a limited set of criteria has been considered. The present experimental study (N =…

In this study we examined variations of the nonequivalent groups equating design for tests containing both multiple-choice (MC) and constructed-response (CR) items to determine which design was most effective in producing equivalent scores across the two tests to be equated. Using data from a large-scale exam, this study investigated the use of…

This exploratory study was built on research spanning three decades. Petersen, Marco, and Stewart (1982) conducted a major empirical investigation of the efficacy of different equating methods. The studies reported in Dorans (1990) examined how different equating methods performed across samples selected in different ways. Recent population…

The correlation between a short-form (SF) test and its full-scale (FS) counterpart is a mainstay in the evaluation of SF validity. However, in correcting for overlapping error variance in this measure, investigators have overattenuated the validity coefficient through an intuitive misapplication of P. Levy's (1967) formula. The authors of the…

Dorans and Holland (2000) and von Davier, Holland, and Thayer (2003) introduced measures of the degree to which an observed-score equating function is sensitive to the population on which it is computed. This article extends the findings of Dorans and Holland and of von Davier et al. to item response theory (IRT) true-score equating methods that…

This paper discusses loglinear models for assessing differential item functioning (DIF). Loglinear and logit models that have been suggested for studying DIF are reviewed, and loglinear formulations of the logit models are given. A polynomial loglinear model for assessing DIF is introduced. Two examples using the polynomial loglinear model for…

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)

Determining whether score distributions differ on two or more test forms administered to samples of examinees from a single population is explored using three statistical tests using loglinear models. Examples are presented of applying tests of distribution differences to decide if equating is needed for alternative forms of a test. (SLD)

A quadratic curve test equating method for equating different test forms under a random-groups data collection design is proposed that equates the first three central moments of the test forms. When applied to real test data, the method performs as well as other equating methods. Procedures from implementing the test are described. (SLD)

The feasibility of using linear and equipercentile equating methods (W. H. Angoff, 1984) to equate forms of the Test of Written English (TWE) by using the Test of English as a Foreign Language (TOEFL) as an anchor was explored. These two equating methods assume that either the TOEFL test and TWE test measure the same skills or that the examinee…

A procedure for checking the score equivalence of nearly identical editions of a test is described. The procedure employs the standard error of equating (SEE) and utilizes graphical representation of score conversion deviation from the identity function in standard error units. Two illustrations of the procedure involving Scholastic Aptitude Test…

Equating a test form to itself through a chain of equatings, commonly referred to as circular equating, has been widely used as a criterion to evaluate the adequacy of equating. This paper uses both analytical methods and simulation methods to show that this criterion is in general invalid in serving this purpose. For the random groups design done…

Recent years have seen growing use of tests with mixed item formats, e.g., partly containing dichotomously scored items and partly consisting of polytomously scored items. A matching two test characteristic curves method (CCM) for placing these mixed format items on the same metric is described and evaluated in this paper under a common-item…

For a growing number of test translations, there is a need for equating that provides scores that can be used interchangeably for both source- and target-language forms, but basic equating requirements cannot usually be met in the cross-lingual case. The situation is more problematic in verbal tests, where translation has more impact on item…