The Theory of the Design of Experiments

Author: D.R. Cox
Publisher: CRC Press
ISBN: 1420035835
Format: PDF, ePub
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Why study the theory of experiment design? Although it can be useful to know about special designs for specific purposes, experience suggests that a particular design can rarely be used directly. It needs adaptation to accommodate the circumstances of the experiment. Successful designs depend upon adapting general theoretical principles to the special constraints of individual applications. Written for a general audience of researchers across the range of experimental disciplines, The Theory of the Design of Experiments presents the major topics associated with experiment design, focusing on the key concepts and the statistical structure of those concepts. The authors keep the level of mathematics elementary, for the most part, and downplay methods of data analysis. Their emphasis is firmly on design, but appendices offer self-contained reviews of algebra and some standard methods of analysis. From their development in association with agricultural field trials, through their adaptation to the physical sciences, industry, and medicine, the statistical aspects of the design of experiments have become well refined. In statistics courses of study, however, the design of experiments very often receives much less emphasis than methods of analysis. The Theory of the Design of Experiments fills this potential gap in the education of practicing statisticians, statistics students, and researchers in all fields.

Theory of Factorial Design

Author: Ching-Shui Cheng
Publisher: CRC Press
ISBN: 1466505583
Format: PDF
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Bringing together both new and old results, Theory of Factorial Design: Single- and Multi-Stratum Experiments provides a rigorous, systematic, and up-to-date treatment of the theoretical aspects of factorial design. To prepare readers for a general theory, the author first presents a unified treatment of several simple designs, including completely randomized designs, block designs, and row-column designs. As such, the book is accessible to readers with minimal exposure to experimental design. With exercises and numerous examples, it is suitable as a reference for researchers and as a textbook for advanced graduate students. In addition to traditional topics and a thorough discussion of the popular minimum aberration criterion, the book covers many topics and new results not found in existing books. These include results on the structures of two-level resolution IV designs, methods for constructing such designs beyond the familiar foldover method, the extension of minimum aberration to nonregular designs, the equivalence of generalized minimum aberration and minimum moment aberration, a Bayesian approach, and some results on nonregular designs. The book also presents a theory that provides a unifying framework for the design and analysis of factorial experiments with multiple strata (error terms) arising from complicated structures of the experimental units. This theory can be systematically applied to various structures of experimental units instead of treating each on a case-by-case basis.

Statistics in the 21st Century

Author: Martin A. Tanner
Publisher: CRC Press
ISBN: 1420035398
Format: PDF, Kindle
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Exactly what is the state of the art in statistics as we move forward into the 21st century? What promises, what trends does its future hold? Through the reflections of 70 of the world's leading statistical methodologists, researchers, theorists, and practitioners, Statistics in the 21st Century answers those questions. Originally published in the Journal of the American Statistical Association, this collection of vignettes examines our statistical past, comments on our present, and speculates on our future. Although the coverage is broad and the topics diverse, it reveals the essential intellectual unity of the field as we see the same themes recurring in different contexts. We see how the development of statistics has been driven by the unprecedented and still growing range of applications, by the explosion in computer technology, and by the new types of data that continue to emerge and advance the discipline. Organized around major areas of application and leading up to vignettes on theory and methods, Statistics in the 21st Century forms a landmark record of the progress and perceived future of the discipline. No student, researcher, or practitioner of statistics should miss this extraordinary opportunity to view the past, present, and future world of statistics through the eyes of its foremost thinkers.

Number Theoretic Methods in Statistics

Author: Kai-Tai Fang
Publisher: CRC Press
ISBN: 9780412465208
Format: PDF
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This book is a survey of recent work on the application of number theory in statistics. The essence of number-theoretic methods is to find a set of points that are universally scattered over an s-dimensional unit cube. In certain circumstances this set can be used instead of random numbers in the Monte Carlo method. The idea can also be applied to other problems such as in experimental design. This book will illustrate the idea of number-theoretic methods and their application in statistics. The emphasis is on applying the methods to practical problems so only part-proofs of theorems are given.

Robust Nonparametric Statistical Methods Second Edition

Author: Thomas P. Hettmansperger
Publisher: CRC Press
ISBN: 1439809097
Format: PDF, ePub
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Presenting an extensive set of tools and methods for data analysis, Robust Nonparametric Statistical Methods, Second Edition covers univariate tests and estimates with extensions to linear models, multivariate models, times series models, experimental designs, and mixed models. It follows the approach of the first edition by developing rank-based methods from the unifying theme of geometry. This edition, however, includes more models and methods and significantly extends the possible analyses based on ranks. New to the Second Edition A new section on rank procedures for nonlinear models A new chapter on models with dependent error structure, covering rank methods for mixed models, general estimating equations, and time series New material on the development of computationally efficient affine invariant/equivariant sign methods based on transform-retransform techniques in multivariate models Taking a comprehensive, unified approach to statistical analysis, the book continues to describe one- and two-sample problems, the basic development of rank methods in the linear model, and fixed effects experimental designs. It also explores models with dependent error structure and multivariate models. The authors illustrate the implementation of the methods using many real-world examples and R. More information about the data sets and R packages can be found at www.crcpress.com

Algebraic Statistics

Author: Giovanni Pistone
Publisher: CRC Press
ISBN: 1420035762
Format: PDF, ePub, Mobi
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Written by pioneers in this exciting new field, Algebraic Statistics introduces the application of polynomial algebra to experimental design, discrete probability, and statistics. It begins with an introduction to Gröbner bases and a thorough description of their applications to experimental design. A special chapter covers the binary case with new application to coherent systems in reliability and two level factorial designs. The work paves the way, in the last two chapters, for the application of computer algebra to discrete probability and statistical modelling through the important concept of an algebraic statistical model. As the first book on the subject, Algebraic Statistics presents many opportunities for spin-off research and applications and should become a landmark work welcomed by both the statistical community and its relatives in mathematics and computer science.

Design of Comparative Experiments

Author: R. A. Bailey
Publisher: Cambridge University Press
ISBN: 1139469916
Format: PDF
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This book should be on the shelf of every practising statistician who designs experiments. Good design considers units and treatments first, and then allocates treatments to units. It does not choose from a menu of named designs. This approach requires a notation for units that does not depend on the treatments applied. Most structure on the set of observational units, or on the set of treatments, can be defined by factors. This book develops a coherent framework for thinking about factors and their relationships, including the use of Hasse diagrams. These are used to elucidate structure, calculate degrees of freedom and allocate treatment subspaces to appropriate strata. Based on a one-term course the author has taught since 1989, the book is ideal for advanced undergraduate and beginning graduate courses. Examples, exercises and discussion questions are drawn from a wide range of real applications: from drug development, to agriculture, to manufacturing.

Missing Data Analysis in Practice

Author: Trivellore Raghunathan
Publisher: CRC Press
ISBN: 1482211939
Format: PDF, Kindle
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Missing Data Analysis in Practice provides practical methods for analyzing missing data along with the heuristic reasoning for understanding the theoretical underpinnings. Drawing on his 25 years of experience researching, teaching, and consulting in quantitative areas, the author presents both frequentist and Bayesian perspectives. He describes easy-to-implement approaches, the underlying assumptions, and practical means for assessing these assumptions. Actual and simulated data sets illustrate important concepts, with the data sets and codes available online. The book underscores the development of missing data methods and their adaptation to practical problems. It mainly focuses on the traditional missing data problem. The author also shows how to use the missing data framework in many other statistical problems, such as measurement error, finite population inference, disclosure limitation, combing information from multiple data sources, and causal inference.

Statistical Evidence

Author: Richard Royall
Publisher: Routledge
ISBN: 1351414550
Format: PDF, ePub, Mobi
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Interpreting statistical data as evidence, Statistical Evidence: A Likelihood Paradigm focuses on the law of likelihood, fundamental to solving many of the problems associated with interpreting data in this way. Statistics has long neglected this principle, resulting in a seriously defective methodology. This book redresses the balance, explaining why science has clung to a defective methodology despite its well-known defects. After examining the strengths and weaknesses of the work of Neyman and Pearson and the Fisher paradigm, the author proposes an alternative paradigm which provides, in the law of likelihood, the explicit concept of evidence missing from the other paradigms. At the same time, this new paradigm retains the elements of objective measurement and control of the frequency of misleading results, features which made the old paradigms so important to science. The likelihood paradigm leads to statistical methods that have a compelling rationale and an elegant simplicity, no longer forcing the reader to choose between frequentist and Bayesian statistics.

ROC Curves for Continuous Data

Author: Wojtek J. Krzanowski
Publisher: CRC Press
ISBN: 9781439800225
Format: PDF, ePub, Docs
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Since ROC curves have become ubiquitous in many application areas, the various advances have been scattered across disparate articles and texts. ROC Curves for Continuous Data is the first book solely devoted to the subject, bringing together all the relevant material to provide a clear understanding of how to analyze ROC curves. The fundamental theory of ROC curves The book first discusses the relationship between the ROC curve and numerous performance measures and then extends the theory into practice by describing how ROC curves are estimated. Further building on the theory, the authors present statistical tests for ROC curves and their summary statistics. They consider the impact of covariates on ROC curves, examine the important special problem of comparing two ROC curves, and cover Bayesian methods for ROC analysis. Special topics The text then moves on to extensions of the basic analysis to cope with more complex situations, such as the combination of multiple ROC curves and problems induced by the presence of more than two classes. Focusing on design and interpretation issues, it covers missing data, verification bias, sample size determination, the design of ROC studies, and the choice of optimum threshold from the ROC curve. The final chapter explores applications that not only illustrate some of the techniques but also demonstrate the very wide applicability of these techniques across different disciplines. With nearly 5,000 articles published to date relating to ROC analysis, the explosive interest in ROC curves and their analysis will continue in the foreseeable future. Embracing this growth of interest, this timely book will undoubtedly guide present and future users of ROC analysis.