Generalizability Theory

Generalizability Theory
Author: Robert L. Brennan
Publisher: Springer Science & Business Media
Total Pages: 564
Release: 2001-08-09
Genre: Education
ISBN: 9780387952826

Generalizability theory offers an extensive conceptual framework and a powerful set of statistical procedures for characterizing and quantifying the fallibility of measurements. Robert Brennan, the author, has written the most comprehensive and up-to-date treatment of generalizability theory. The book provides a synthesis of those parts of the statistical literature that are directly applicable to generalizability theory. The principal intended audience is measurement practitioners and graduate students in the behavioral and social sciences, although a few examples and references are provided from other fields. Readers will benefit from some familiarity with classical test theory and analysis of variance, but the treatment of most topics does not presume specific background.

Generalizability Theory

Generalizability Theory
Author: Richard J. Shavelson
Publisher: SAGE
Total Pages: 156
Release: 1991-07-23
Genre: Mathematics
ISBN: 9780803937451

In this volume, Shavelson and Webb offer an intuitive development of generalizability theory and cover a wide variety of topics such as generalizability studies with nested facets and with fixed facets, measurement error and generalizability coefficients, and decision studies with same and with different designs. Detailed illustrations, examples and exercises all serve to clearly describe the logic underlying major concepts in generalizability theory and assist readers in applying these methods when investigating the consistency of their own measurements.

Variance Components

Variance Components
Author: Shayle R. Searle
Publisher: John Wiley & Sons
Total Pages: 537
Release: 2009-09-25
Genre: Mathematics
ISBN: 0470317698

WILEY-INTERSCIENCE PAPERBACK SERIES The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. ". . .Variance Components is an excellent book. It is organized and well written, and provides many references to a variety of topics. I recommend it to anyone with interest in linear models." —Journal of the American Statistical Association "This book provides a broad coverage of methods for estimating variance components which appeal to students and research workers . . . The authors make an outstanding contribution to teaching and research in the field of variance component estimation." —Mathematical Reviews "The authors have done an excellent job in collecting materials on a broad range of topics. Readers will indeed gain from using this book . . . I must say that the authors have done a commendable job in their scholarly presentation." —Technometrics This book focuses on summarizing the variability of statistical data known as the analysis of variance table. Penned in a readable style, it provides an up-to-date treatment of research in the area. The book begins with the history of analysis of variance and continues with discussions of balanced data, analysis of variance for unbalanced data, predictions of random variables, hierarchical models and Bayesian estimation, binary and discrete data, and the dispersion mean model.

Psychometric Methods

Psychometric Methods
Author: Larry R. Price
Publisher: Guilford Publications
Total Pages: 569
Release: 2016-12-12
Genre: Social Science
ISBN: 146252477X

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.

Handbook of Applied Multivariate Statistics and Mathematical Modeling

Handbook of Applied Multivariate Statistics and Mathematical Modeling
Author: Howard E.A. Tinsley
Publisher: Academic Press
Total Pages: 751
Release: 2000-05-22
Genre: Mathematics
ISBN: 0080533566

Multivariate statistics and mathematical models provide flexible and powerful tools essential in most disciplines. Nevertheless, many practicing researchers lack an adequate knowledge of these techniques, or did once know the techniques, but have not been able to keep abreast of new developments. The Handbook of Applied Multivariate Statistics and Mathematical Modeling explains the appropriate uses of multivariate procedures and mathematical modeling techniques, and prescribe practices that enable applied researchers to use these procedures effectively without needing to concern themselves with the mathematical basis. The Handbook emphasizes using models and statistics as tools. The objective of the book is to inform readers about which tool to use to accomplish which task. Each chapter begins with a discussion of what kinds of questions a particular technique can and cannot answer. As multivariate statistics and modeling techniques are useful across disciplines, these examples include issues of concern in biological and social sciences as well as the humanities.

Elements of Finite Model Theory

Elements of Finite Model Theory
Author: Leonid Libkin
Publisher: Springer Science & Business Media
Total Pages: 320
Release: 2013-03-09
Genre: Mathematics
ISBN: 3662070030

Emphasizes the computer science aspects of the subject. Details applications in databases, complexity theory, and formal languages, as well as other branches of computer science.

The Finite Element Method: Theory, Implementation, and Applications

The Finite Element Method: Theory, Implementation, and Applications
Author: Mats G. Larson
Publisher: Springer Science & Business Media
Total Pages: 403
Release: 2013-01-13
Genre: Computers
ISBN: 3642332870

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​

Applying Generalizability Theory using EduG

Applying Generalizability Theory using EduG
Author: Jean Cardinet
Publisher: Taylor & Francis
Total Pages: 235
Release: 2011-03-04
Genre: Psychology
ISBN: 1135240337

Intended to help improve measurement and data collection methods in the behavioral, social, and medical sciences, this book demonstrates an expanded and accessible use of Generalizability Theory (G theory). G theory conceptually models the way in which the reliability of measurement is ascertained. Sources of score variation are identified as potential contributors to measurement error and taken into account accordingly. The authors demonstrate the powerful potential of G theory by showing how to improve the quality of any kind of measurement, regardless of the discipline. Readers will appreciate the conversational style used to present a comprehensive review of G theory and its application using the freeware EduG. To maximize understanding the authors illustrate all fundamental principles with concrete examples from different fields and contexts. Annotated applications lead students through the main concepts of G theory, while illustrating both the use of EduG and interpretation of its output. Formulas are avoided wherever possible. Exercises with data sets available on the Psychology Press website allow readers to carry out their own analyses to reinforce understanding. Brief overviews of analysis of variance, estimation, and the statistical error model are provided for review. The procedures involved in carrying out a generalizability study using EduG follow, as well as guidance in the interpretation of results. Real-world applications of G theory to the assessment of depression, managerial ability, attitudes, and writing and mathematical skills are then presented. Next, annotated exercises provide an opportunity for readers to use EduG and interpret its results. The book concludes with a review of the development of G theory and possible new directions of application. Finally, for those with a strong statistical background, the appendixes provide the formulas used by EduG. Ideal as a supplement for courses on measurement theory and/or generalizability theory taught in departments of psychology, education, medicine, and the social sciences, this text will also appeal to researchers from a variety of fields interested in learning how to apply G theory to their studies.