Test Equating, Scaling, and Linking


Book Description

By providing an introduction to test equating which both discusses the most frequently used equating methodologies and covering many of the practical issues involved, this volume expands upon the coverage of the first edition by providing a new chapter on test scaling and a second on test linking.




Applying Test Equating Methods


Book Description

This book describes how to use test equating methods in practice. The non-commercial software R is used throughout the book to illustrate how to perform different equating methods when scores data are collected under different data collection designs, such as equivalent groups design, single group design, counterbalanced design and non equivalent groups with anchor test design. The R packages equate, kequate and SNSequate, among others, are used to practically illustrate the different methods, while simulated and real data sets illustrate how the methods are conducted with the program R. The book covers traditional equating methods including, mean and linear equating, frequency estimation equating and chain equating, as well as modern equating methods such as kernel equating, local equating and combinations of these. It also offers chapters on observed and true score item response theory equating and discusses recent developments within the equating field. More specifically it covers the issue of including covariates within the equating process, the use of different kernels and ways of selecting bandwidths in kernel equating, and the Bayesian nonparametric estimation of equating functions. It also illustrates how to evaluate equating in practice using simulation and different equating specific measures such as the standard error of equating, percent relative error, different that matters and others.




The Kernel Method of Test Equating


Book Description

KE is applied to the four major equating designs and to both Chain Equating and Post-Stratification Equating for the Non-Equivalent groups with Anchor Test Design. It will be an important reference for several groups: (a) Statisticians (b) Practitioners and (c) Instructors in psychometric and measurement programs. The authors assume some familiarity with linear and equipercentile test equating, and with matrix algebra.




Test Equating


Book Description

In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques. This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved. The main themes are: - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating. The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented. As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for the first time as part of their graduate study will find this an invaluable text and reference.




Applying Test Equating Methods


Book Description

This book describes how to use test equating methods in practice. The non-commercial software R is used throughout the book to illustrate how to perform different equating methods when scores data are collected under different data collection designs, such as equivalent groups design, single group design, counterbalanced design and non equivalent groups with anchor test design. The R packages equate, kequate and SNSequate, among others, are used to practically illustrate the different methods, while simulated and real data sets illustrate how the methods are conducted with the program R. The book covers traditional equating methods including, mean and linear equating, frequency estimation equating and chain equating, as well as modern equating methods such as kernel equating, local equating and combinations of these. It also offers chapters on observed and true score item response theory equating and discusses recent developments within the equating field. More specifically it covers the issue of including covariates within the equating process, the use of different kernels and ways of selecting bandwidths in kernel equating, and the Bayesian nonparametric estimation of equating functions. It also illustrates how to evaluate equating in practice using simulation and different equating specific measures such as the standard error of equating, percent relative error, different that matters and others.




The Wiley Handbook of Psychometric Testing


Book Description

A must-have resource for researchers, practitioners, and advanced students interested or involved in psychometric testing Over the past hundred years, psychometric testing has proved to be a valuable tool for measuring personality, mental ability, attitudes, and much more. The word ‘psychometrics’ can be translated as ‘mental measurement’; however, the implication that psychometrics as a field is confined to psychology is highly misleading. Scientists and practitioners from virtually every conceivable discipline now use and analyze data collected from questionnaires, scales, and tests developed from psychometric principles, and the field is vibrant with new and useful methods and approaches. This handbook brings together contributions from leading psychometricians in a diverse array of fields around the globe. Each provides accessible and practical information about their specialist area in a three-step format covering historical and standard approaches, innovative issues and techniques, and practical guidance on how to apply the methods discussed. Throughout, real-world examples help to illustrate and clarify key aspects of the topics covered. The aim is to fill a gap for information about psychometric testing that is neither too basic nor too technical and specialized, and will enable researchers, practitioners, and graduate students to expand their knowledge and skills in the area. Provides comprehensive coverage of the field of psychometric testing, from designing a test through writing items to constructing and evaluating scales Takes a practical approach, addressing real issues faced by practitioners and researchers Provides basic and accessible mathematical and statistical foundations of all psychometric techniques discussed Provides example software code to help readers implement the analyses discussed




The Kernel Method of Test Equating


Book Description

KE is applied to the four major equating designs and to both Chain Equating and Post-Stratification Equating for the Non-Equivalent groups with Anchor Test Design. It will be an important reference for several groups: (a) Statisticians (b) Practitioners and (c) Instructors in psychometric and measurement programs. The authors assume some familiarity with linear and equipercentile test equating, and with matrix algebra.




Statistical Models for Test Equating, Scaling, and Linking


Book Description

The goal of this book is to emphasize the formal statistical features of the practice of equating, linking, and scaling. The book encourages the view and discusses the quality of the equating results from the statistical perspective (new models, robustness, fit, testing hypotheses, statistical monitoring) as opposed to placing the focus on the policy and the implications, which although very important, represent a different side of the equating practice. The book contributes to establishing “equating” as a theoretical field, a view that has not been offered often before. The tradition in the practice of equating has been to present the knowledge and skills needed as a craft, which implies that only with years of experience under the guidance of a knowledgeable practitioner could one acquire the required skills. This book challenges this view by indicating how a good equating framework, a sound understanding of the assumptions that underlie the psychometric models, and the use of statistical tests and statistical process control tools can help the practitioner navigate the difficult decisions in choosing the final equating function. This book provides a valuable reference for several groups: (a) statisticians and psychometricians interested in the theory behind equating methods, in the use of model-based statistical methods for data smoothing, and in the evaluation of the equating results in applied work; (b) practitioners who need to equate tests, including those with these responsibilities in testing companies, state testing agencies, and school districts; and (c) instructors in psychometric, measurement, and psychology programs.




Psychometric Methods


Book Description

Grounded in current knowledge and professional practice, this book provides up-to-date coverage of psychometric theory, methods, and interpretation of results. Essential topics include measurement and statistical concepts, scaling models, test design and development, reliability, validity, factor analysis, item response theory, and generalizability theory. Also addressed are norming and test equating, topics not typically covered in traditional psychometrics texts. Examples drawn from a dataset on intelligence testing are used throughout the book, elucidating the assumptions underlying particular methods and providing SPSS (or alternative) syntax for conducting analyses. The companion website presents datasets for all examples as well as PowerPoint slides of figures and key concepts. Pedagogical features include equation boxes with explanations of statistical notation, and end-of-chapter glossaries. The Appendix offers extensions of the topical chapters with example source code from SAS, SPSS, IRTPRO, BILOG-MG, PARSCALE, TESTFACT, and DIMTEST.




Generalized Kernel Equating with Applications in R


Book Description

Generalized Kernel Equating is a comprehensive guide for statisticians, psychometricians, and educational researchers aiming to master test score equating. This book introduces the Generalized Kernel Equating (GKE) framework, providing the necessary tools and methodologies for accurate and fair score comparisons. The book presents test score equating as a statistical problem and covers all commonly used data collection designs. It details the five steps of the GKE framework: presmoothing, estimating score probabilities, continuization, equating transformation, and evaluating the equating transformation. Various presmoothing strategies are explored, including log-linear models, item response theory models, beta4 models, and discrete kernel estimators. The estimation of score probabilities when using IRT models is described and Gaussian kernel continuization is extended to other kernels such as uniform, logistic, epanechnikov and adaptive kernels. Several bandwidth selection methods are described. The kernel equating transformation and variants of it are defined, and both equating-specific and statistical measures for evaluating equating transformations are included. Real data examples, guiding readers through the GKE steps with detailed R code and explanations are provided. Readers are equipped with an advanced knowledge and practical skills for implementing test score equating methods.