Advanced Distance Sampling: Estimating Abundance of Biological Populations

drawing from a test bank of questions. Then the test forms are the same in content, but may differ in difficulty, because they do not contain exactly the same questions. 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. To relate this student’s performance in this other course, the student’s exam scores would have to be linked to the exam scores of students in my course before being related to the percentage of total scale. 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 complexities. Chapter 1 contains a general introduction, defining equating, scaling, and linking. Desirable properties of successful equating are discussed. One is the sensible group invariance 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 that is reminiscent of the philosophical foundations of statistical inference, such as the sufficiency and likelihood principles. Also discussed are equating designs—new applications of sampling/experimental design that determine the administration of test forms. 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 2–5 introduce the equating methods mean equating, linear equating, and equipercentile equating. These, respectively, involve equating the means, z scores, and cumulative distributions of the test scores. Chapters 2 and 3 assume a random groups design, 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. Chapters 4 and 5 treat equating under a different design: the nonequivalent groups design. The equating methods work in a way familiar to statisticians, often involving parametric models that require certain statistical assumptions. These models are applied by substituting sample estimates for the model parameters and subsequently checking the veracity of the statistical assumptions. Also discussed are ways to reduce the error of estimated equating relationships, such as smoothing methods that involve log-linear models and cubic splines in equipercentile equating. Chapter 6 moves to item response theory (IRT) equating methods, which model the distribution of examinee responses as a function of the native ability of the examinee: equating is done by assuming that individuals with the same native ability take the different test forms. Problems suited for numerical methods arise; the authors discuss the application of Newton–Raphson and numerical integration. Chapter 7 deals with estimating standard errors of equating. The authors discuss bootstrapping and the delta method. The standard errors are used to compare precision in estimating equation relationships for different designs and methods, and to determine sample size. Chapter 8 discusses practical issues in equating: test development, test standardization and quality control, equating design and implementation, choosing from among the statistical equating procedures, and comparability issues in special circumstances of test administration. Chapter 9 treats score scales for tests. As the authors state on page 329, “Scaling is the process of associating numbers or other ordered indicators with the performance of examinees. ” A great deal is covered here, including vertical scaling and developmental score scales. Chapter 10 introduces the reader to linking. Topics covered include linking categorization schemes and criteria, as well as types of linking and the Mislevy/Linn taxonomy of score linking methods. The authors discuss the group invariance property and statistical methods for checking group invariance. Chapter 11 concludes with a discussion of current and future challenges in equating, scaling, and linking. The two appendixes contain answers to exercises and details on computer programs that perform some of the methods covered in the text. These programs are freely available via the Internet. To a statistician reader, the book is an applied statistics text, where the application is novel. Many familiar statistical techniques appear here with a new emphasis. As mentioned, the book covers density estimation and smoothing with the log-linear method and cublic splines, experimental designs, regression, bootstrapping, and analytic techniques such as the delta method. Another method that the authors briefly mention and that apparently is gaining ground is kernel smoothing in equating. The methods are based on and evaluated according to statistical criteria, sometimes presented with technical details and sometimes not. There are informative examples throughout and practical issues in application are discussed. This book provides a good combination of comprehensiveness and rigor while preserving a clear presentation. References are copious and the index is adequate. With the increasing emphasis on assessment and accountability in education, it would benefit those in academia to have some knowledge of the issues, and their complexities, in assessment. This text provides a reasonable introduction to these topics and suggests there are contributions to be made by statisticians in this area. Statisticians who collaborate or may collaborate with those in the measurement community, or who perhaps seek to develop a new specialty, would be well served by this book.