A Comparison Of Four Linear Equating Methods For The Common Item Nonequivalent Groups Design Using Simulation Methods

Test Equating, Scaling, and Linking

This book provides an introduction to test equating, scaling and linking, including those concepts and practical issues that are critical for developers and all other testing professionals. In addition to statistical procedures, successful equating, scaling and linking involves many aspects of testing, including procedures to develop tests, to administer and score tests and to interpret scores earned on tests. Test equating methods are used with many standardized tests in education and psychology to ensure that scores from multiple test forms can be used interchangeably. Test scaling is the process of developing score scales that are used when scores on standardized tests are reported. In test linking, scores from two or more tests are related to one another. Linking has received much recent attention, due largely to investigations of linking similarly named tests from different test publishers or tests constructed for different purposes. In recent years, researchers from the education, psychology and statistics communities have contributed to the rapidly growing statistical and psychometric methodologies used in test equating, scaling and linking. In addition to the literature covered in previous editions, this new edition presents coverage of significant recent research. In order to assist researchers, advanced graduate students and testing professionals, examples are used frequently and conceptual issues are stressed. New material includes model determination in log-linear smoothing, in-depth presentation of chained linear and equipercentile equating, equating criteria, test scoring and a new section on scores for mixed-format tests. In the third edition, each chapter contains a reference list, rather than having a single reference list at the end of the volume The themes of the third edition include: * the purposes of equating, scaling and linking and their practical context * data collection designs * statistical methodology * designing reasonable and useful equating, scaling, and linking studies * importance of test development and quality control processes to equating * equating error, and the underlying statistical assumptions for equating

A Comparison of Four Linear Equating Methods for the Common-item Nonequivalent Groups Design Using Simulation Methods

A Comparison of Four Linear Equating Methods for the Common-Item Nonequivalent Groups Design Using Simulation Methods. ACT Research Report Series, 2013 (2)

This paper investigates four methods of linear equating under the common item nonequivalent groups design. Three of the methods are well known: Tucker, Angoff-Levine, and Congeneric-Levine. A fourth method is presented as a variant of the Congeneric-Levine method. Using simulation data generated from the three-parameter logistic IRT model we compare the accuracy of the four methods under a variety of conditions involving group differences between the old and new groups. The sampling properties of the methods' parameter estimates are also investigated. The results indicate that the Tucker method is less accurate than the other three methods when group differences exist, especially when sample size is large (800). However, the Tucker method's gamma has the smallest sampling error, especially when sample size is small. Appended are: (1) Tables A1-A8; and (2) Figures B-1 through B-7.