# e-book Test Equating: Methods and Practices

The first edition of this book was entitled Test Equating: Theory and Methods and was published in This second edition includes coverage of test scaling and linking, and the sections on equating have been updated and expanded. It is intended as an instructional text for advanced graduate students or new professionals, and as a reference for experienced professionals. I read this book as a professional statistician whose introduction to test equating, scaling, and linking occurs here. Test equating methods are used to equate scores from multiple test forms, different versions of a test designed to be the same in content, though the different forms may introduce differences in difficulty.

Test scaling is the process of developing common scales to which scores on tests are related. Test linking relates scores from tests which may differ in both content and difficulty. While equating, scaling, and linking are often used together and there is some overlap among them, there is also enough distinguishing each from the others to justify treatment as separate topics. Here are simple examples of each. I teach an introductory statistics course, and the students periodically take examinations.

Suppose these tests consist of multiple choice ques- tions. I might produce and administer multiple forms of the same exam. Suppose the different forms were constructed by drawing from a test bank of questions.

## Test equating sleep scales: applying the Leunbach’s model

To be fair to the students, I might adjust for possible differences in difficulty by equating the scores on the different forms before relating them to the percentage of total scale. Now suppose a transfer student had previously taken an introductory statistics course with similar, but not exactly the same, content. Applications on a larger scale over longer time periods can be much more complicated than this, of course, and the book proceeds through methods for dealing with these com- plexities.

Chapter 1 contains a general introduction, defining equating, scaling and linking.

## Test Equating, Scaling, and Linking : Methods and Practices

Desirable properties of successful equating are discussed. One is the sensible group invari- ance property, which requires the equating relationship between test forms to be the same regardless of which group of examinees is used for the equating. These properties create a philosophical framework in which equating is conducted, reminiscent of philosophical founda- tions of statistical inference such as the sufficiency and likelihood principles.

Random equating error, where groups of examinees are regarded as random samples from populations of all such examinees, is known to statisticians as the random error induced by random sampling. Chapters 2 through 5 introduce the equating methods mean equating, linear equating and equipercentile equating.

Test Equating Scaling and Linking Methods and Practices Statistics for Social and Behavioral Science

These respectively involve equating the means, z-scores, and cumulative distributions of the test scores. Chapters 2 and 3 assume a random groups de- sign, where each examinee group takes one form of the exam and the subjects are randomly assigned to one of the groups, as in a completely randomized design.

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• Test Equating, Scaling, and Linking?

Living Standards Analytics Dominique Haughton. Multidimensional Item Response Theory M. Statistical Confidentiality George T. Back cover copy 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.

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.

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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.

Table of contents Introduction and Concepts. Review Text "The new edition of Test Equating, Scaling, and Linking: Methods and Practices is a welcome update to a book which has become a classic in equating and linking.