Robert L. Brennan

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

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

In 1972 a monograph by Cronbach, Gleser, Nanda, and Rajaratnam was published entitled The Dependability of Behavioral Measurements. That book incorporated, systematized, and extended their previous research into what came to be called generalizability theory, which liberalizes classical test theory, in part through the application of analysis of variance proce­ dures that focus on variance components. Generalizability theory is perhaps the most broadly defined measurement model currently in existence, and the Cronbach et al. (1972) treatment of the theory represents a major con­ tribution to psychometrics. However, as Cronbach et al. (1972, p. 3) state, their book is "complexly organized and by no means simple to follow" and, of course, it is nearly 30 years old. In 1983, ACT, Inc. published my monograph entitled Elements of Gen­ eralizability Theory, with a slightly revised version appearing in 1992. That treatment is considerably less comprehensive than Cronbach et al. (1972) but still detailed enough to convey much ofthe richness of the theory and to facilitate its application. However, the 1983/1992 monograph is essen­ tially two decades old, it does not cover multivariate generalizability theory in depth, and it does not incorporate recent developments in statistics that bear upon the estimation of variance components. Also, of course, there have been numerous developments in generalizability theory in the last 20 years.

In 1972 a monograph by Cronbach, Gleser, Nanda, and Rajaratnam was published entitled The Dependability of Behavioral Measurements. That book incorporated, systematized, and extended their previous research into what came to be called generalizability theory, which liberalizes classical test theory, in part through the application of analysis of variance proce­ dures that focus on variance components. Generalizability theory is perhaps the most broadly defined measurement model currently in existence, and the Cronbach et al. (1972) treatment of the theory represents a major con­ tribution to psychometrics. However, as Cronbach et al. (1972, p. 3) state, their book is "complexly organized and by no means simple to follow" and, of course, it is nearly 30 years old. In 1983, ACT, Inc. published my monograph entitled Elements of Gen­ eralizability Theory, with a slightly revised version appearing in 1992. That treatment is considerably less comprehensive than Cronbach et al. (1972) but still detailed enough to convey much ofthe richness of the theory and to facilitate its application. However, the 1983/1992 monograph is essen­ tially two decades old, it does not cover multivariate generalizability theory in depth, and it does not incorporate recent developments in statistics that bear upon the estimation of variance components. Also, of course, there have been numerous developments in generalizability theory in the last 20 years.