The Theory of the Design of Experiments

Author: D.R. Cox
Publisher: CRC Press
ISBN: 1420035835
Format: PDF, ePub, Mobi
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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, ePub, Mobi
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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.

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.

Statistics in the 21st Century

Author: Martin A. Tanner
Publisher: CRC Press
ISBN: 1420035398
Format: PDF
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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.

Algebraic Statistics

Author: Giovanni Pistone
Publisher: CRC Press
ISBN: 1420035762
Format: PDF, ePub, Docs
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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.

Components of Variance

Author: D.R. Cox
Publisher: CRC Press
ISBN: 1482285940
Format: PDF, ePub, Mobi
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Identifying the sources and measuring the impact of haphazard variations are important in any number of research applications, from clinical trials and genetics to industrial design and psychometric testing. Only in very simple situations can such variations be represented effectively by independent, identically distributed random variables or by random sampling from a hypothetical infinite population. Components of Variance illuminates the complexities of the subject, setting forth its principles with focus on both the development of models for detailed analyses and the statistical techniques themselves. The authors first consider balanced and unbalanced situations, then move to the treatment of non-normal data, beginning with the Poisson and binomial models and followed by extensions to survival data and more general situations. In the final chapter, they discuss ways of extending and assessing various models, including the study of exceedances, the use of nonlinear representations, the study of transformations of the response variable, and the detailed examination of the distributional form of the underlying random variables. Careful signposting and numerous examples from genetic data analysis, clinical trial design, longitudinal data analysis, industrial design, and meta-analysis make this book accessible - and valuable - not only to statisticians but to all applied research scientists who use statistical methods.

Robust Nonparametric Statistical Methods Second Edition

Author: Thomas P. Hettmansperger
Publisher: CRC Press
ISBN: 1439809097
Format: PDF
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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

Design of Comparative Experiments

Author: R. A. Bailey
Publisher: Cambridge University Press
ISBN: 1139469916
Format: PDF, Docs
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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, Docs
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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.

Randomised Response Adaptive Designs in Clinical Trials

Author: Anthony C Atkinson
Publisher: CRC Press
ISBN: 1584886935
Format: PDF, Mobi
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Randomised Response-Adaptive Designs in Clinical Trials presents methods for the randomised allocation of treatments to patients in sequential clinical trials. Emphasizing the practical application of clinical trial designs, the book is designed for medical and applied statisticians, clinicians, and statisticians in training. After introducing clinical trials in drug development, the authors assess a simple adaptive design for binary responses without covariates. They discuss randomisation and covariate balance in normally distributed responses and cover many important response-adaptive designs for binary responses. The book then develops response-adaptive designs for continuous and longitudinal responses, optimum designs with covariates, and response-adaptive designs with covariates. It also covers response-adaptive designs that are derived by optimising an objective function subject to constraints on the variance of estimated parametric functions. The concluding chapter explores future directions in the development of adaptive designs.