A Linear Models Approach

Author: John H. Skillings,Donald Weber

Publisher: CRC Press

ISBN: 9780849396717

Category: Mathematics

Page: 696

View: 8786

Most texts on experimental design fall into one of two distinct categories. There are theoretical works with few applications and minimal discussion on design, and there are methods books with limited or no discussion of the underlying theory. Furthermore, most of these tend to either treat the analysis of each design separately with little attempt to unify procedures, or they will integrate the analysis for the designs into one general technique. A First Course in the Design of Experiments: A Linear Models Approach stands apart. It presents theory and methods, emphasizes both the design selection for an experiment and the analysis of data, and integrates the analysis for the various designs with the general theory for linear models. The authors begin with a general introduction then lead students through the theoretical results, the various design models, and the analytical concepts that will enable them to analyze virtually any design. Rife with examples and exercises, the text also encourages using computers to analyze data. The authors use the SAS software package throughout the book, but also demonstrate how any regression program can be used for analysis. With its balanced presentation of theory, methods, and applications and its highly readable style, A First Course in the Design of Experiments proves ideal as a text for a beginning graduate or upper-level undergraduate course in the design and analysis of experiments.
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An Introduction Based on Linear Models

Author: Max Morris

Publisher: CRC Press

ISBN: 1439894906

Category: Mathematics

Page: 376

View: 4011

Offering deep insight into the connections between design choice and the resulting statistical analysis, Design of Experiments: An Introduction Based on Linear Models explores how experiments are designed using the language of linear statistical models. The book presents an organized framework for understanding the statistical aspects of experimental design as a whole within the structure provided by general linear models, rather than as a collection of seemingly unrelated solutions to unique problems. The core material can be found in the first thirteen chapters. These chapters cover a review of linear statistical models, completely randomized designs, randomized complete blocks designs, Latin squares, analysis of data from orthogonally blocked designs, balanced incomplete block designs, random block effects, split-plot designs, and two-level factorial experiments. The remainder of the text discusses factorial group screening experiments, regression model design, and an introduction to optimal design. To emphasize the practical value of design, most chapters contain a short example of a real-world experiment. Details of the calculations performed using R, along with an overview of the R commands, are provided in an appendix. This text enables students to fully appreciate the fundamental concepts and techniques of experimental design as well as the real-world value of design. It gives them a profound understanding of how design selection affects the information obtained in an experiment.
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Author: Jürgen Pilz

Publisher: John Wiley & Sons Inc

ISBN: N.A

Category: Mathematics

Page: 296

View: 1631

Presents a clear treatment of the design and analysis of linear regression experiments in the presence of prior knowledge about the model parameters. Develops a unified approach to estimation and design; provides a Bayesian alternative to the least squares estimator; and indicates methods for the construction of optimal designs for the Bayes estimator. Material is also applicable to some well-known estimators using prior knowledge that is not available in the form of a prior distribution for the model parameters; such as mixed linear, minimax linear and ridge-type estimators.
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Author: M. C. Chakrabarti

Publisher: N.A

ISBN: N.A

Category: Experimental design

Page: 120

View: 2132

Theory of linear estimation; General structure of analysis of designs;Standard designs; Applications of galois fields and finite geometry in the constrution of designs; Some selected topics in design of experiments.
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Author: Friedrich Pukelsheim

Publisher: SIAM

ISBN: 0898716047

Category: Mathematics

Page: 454

View: 7955

Optimal Design of Experiments offers a rare blend of linear algebra, convex analysis, and statistics. The optimal design for statistical experiments is first formulated as a concave matrix optimization problem. Using tools from convex analysis, the problem is solved generally for a wide class of optimality criteria such as D-, A-, or E-optimality. The book then offers a complementary approach that calls for the study of the symmetry properties of the design problem, exploiting such notions as matrix majorization and the Kiefer matrix ordering. The results are illustrated with optimal designs for polynomial fit models, Bayes designs, balanced incomplete block designs, exchangeable designs on the cube, rotatable designs on the sphere, and many other examples.
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Author: Angela Dean,Daniel Voss,Danel Draguljic

Publisher: Springer

ISBN: 3319522507

Category: Mathematics

Page: 842

View: 6756

This book offers a step-by-step guide to the experimental planning process and the ensuing analysis of normally distributed data, emphasizing the practical considerations governing the design of an experiment. Data sets are taken from real experiments and sample SAS programs are included with each chapter. Experimental design is an essential part of investigation and discovery in science; this book will serve as a modern and comprehensive reference to the subject.
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Author: Ravindra B. Bapat

Publisher: Springer Science & Business Media

ISBN: 1447127382

Category: Mathematics

Page: 167

View: 3482

Linear Algebra and Linear Models comprises a concise and rigorous introduction to linear algebra required for statistics followed by the basic aspects of the theory of linear estimation and hypothesis testing. The emphasis is on the approach using generalized inverses. Topics such as the multivariate normal distribution and distribution of quadratic forms are included. For this third edition, the material has been reorganised to develop the linear algebra in the first six chapters, to serve as a first course on linear algebra that is especially suitable for students of statistics or for those looking for a matrix theoretic approach to the subject. Other key features include: coverage of topics such as rank additivity, inequalities for eigenvalues and singular values; a new chapter on linear mixed models; over seventy additional problems on rank: the matrix rank is an important and rich topic with connections to many aspects of linear algebra such as generalized inverses, idempotent matrices and partitioned matrices. This text is aimed primarily at advanced undergraduate and first-year graduate students taking courses in linear algebra, linear models, multivariate analysis and design of experiments. A wealth of exercises, complete with hints and solutions, help to consolidate understanding. Researchers in mathematics and statistics will also find the book a useful source of results and problems.
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International Series of Monographs in Applied Statistics and Biometry

Author: S. N. Roy,R. Gnanadesikan,J. N. Srivastava

Publisher: Elsevier

ISBN: 148315789X

Category: Reference

Page: 314

View: 5667

Analysis and Design of Certain Quantitative Multiresponse Experiments highlights (i) the need for multivariate analysis of variance (MANOVA); (ii) the need for multivariate design for multiresponse experiments; and (iii) the actual procedures and interpretation that have been used for this purpose by the authors. The development in this monograph is such that the theory and methods of uniresponse analysis and design stay very close to classical ANOVA. The book first discusses the multivariate aspect of linear models for location type of parameters, but under a univariate design, i.e. one in which each experimental unit is measured or studied with respect to all the responses. Separate chapters cover point estimation of location parameters; testing of linear hypotheses; properties of test procedures; and confidence bounds on a set of parametric functions. Subsequent chapters discuss a graphical internal comparison method for analyzing certain kinds of multiresponse experimental data; two classes of multiresponse designs, i.e. designated hierarchical and p-block designs; and the construction of various kinds of multiresponse designs.
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Author: Klaus Hinkelmann,Oscar Kempthorne

Publisher: John Wiley & Sons

ISBN: 9780470191743

Category: Mathematics

Page: 640

View: 5191

This user-friendly new edition reflects a modern and accessible approach to experimental design and analysis Design and Analysis of Experiments, Volume 1, Second Edition provides a general introduction to the philosophy, theory, and practice of designing scientific comparative experiments and also details the intricacies that are often encountered throughout the design and analysis processes. With the addition of extensive numerical examples and expanded treatment of key concepts, this book further addresses the needs of practitioners and successfully provides a solid understanding of the relationship between the quality of experimental design and the validity of conclusions. This Second Edition continues to provide the theoretical basis of the principles of experimental design in conjunction with the statistical framework within which to apply the fundamental concepts. The difference between experimental studies and observational studies is addressed, along with a discussion of the various components of experimental design: the error-control design, the treatment design, and the observation design. A series of error-control designs are presented based on fundamental design principles, such as randomization, local control (blocking), the Latin square principle, the split-unit principle, and the notion of factorial treatment structure. This book also emphasizes the practical aspects of designing and analyzing experiments and features: Increased coverage of the practical aspects of designing and analyzing experiments, complete with the steps needed to plan and construct an experiment A case study that explores the various types of interaction between both treatment and blocking factors, and numerical and graphical techniques are provided to analyze and interpret these interactions Discussion of the important distinctions between two types of blocking factors and their role in the process of drawing statistical inferences from an experiment A new chapter devoted entirely to repeated measures, highlighting its relationship to split-plot and split-block designs Numerical examples using SAS® to illustrate the analyses of data from various designs and to construct factorial designs that relate the results to the theoretical derivations Design and Analysis of Experiments, Volume 1, Second Edition is an ideal textbook for first-year graduate courses in experimental design and also serves as a practical, hands-on reference for statisticians and researchers across a wide array of subject areas, including biological sciences, engineering, medicine, pharmacology, psychology, and business.
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A Case Study Approach

Author: Peter Goos,Bradley Jones

Publisher: John Wiley & Sons

ISBN: 1119976162

Category: Science

Page: 304

View: 693

"This is an engaging and informative book on the modern practice of experimental design. The authors' writing style is entertaining, the consulting dialogs are extremely enjoyable, and the technical material is presented brilliantly but not overwhelmingly. The book is a joy to read. Everyone who practices or teaches DOE should read this book." - Douglas C. Montgomery, Regents Professor, Department of Industrial Engineering, Arizona State University "It's been said: 'Design for the experiment, don't experiment for the design.' This book ably demonstrates this notion by showing how tailor-made, optimal designs can be effectively employed to meet a client's actual needs. It should be required reading for anyone interested in using the design of experiments in industrial settings." —Christopher J. Nachtsheim, Frank A Donaldson Chair in Operations Management, Carlson School of Management, University of Minnesota This book demonstrates the utility of the computer-aided optimal design approach using real industrial examples. These examples address questions such as the following: How can I do screening inexpensively if I have dozens of factors to investigate? What can I do if I have day-to-day variability and I can only perform 3 runs a day? How can I do RSM cost effectively if I have categorical factors? How can I design and analyze experiments when there is a factor that can only be changed a few times over the study? How can I include both ingredients in a mixture and processing factors in the same study? How can I design an experiment if there are many factor combinations that are impossible to run? How can I make sure that a time trend due to warming up of equipment does not affect the conclusions from a study? How can I take into account batch information in when designing experiments involving multiple batches? How can I add runs to a botched experiment to resolve ambiguities? While answering these questions the book also shows how to evaluate and compare designs. This allows researchers to make sensible trade-offs between the cost of experimentation and the amount of information they obtain.
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Author: Gerry P. Quinn,Michael J. Keough

Publisher: Cambridge University Press

ISBN: 1139432893

Category: Nature

Page: N.A

View: 1422

An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data. The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models. Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models. Multivariate techniques, including classification and ordination, are then introduced. Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results. The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature. The book is supported by a website that provides all data sets, questions for each chapter and links to software.
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Author: Klaus Hinkelmann,Oscar Kempthorne

Publisher: John Wiley & Sons

ISBN: 0470530685

Category: Mathematics

Page: 600

View: 3986

This book discusses special modifications and extensions of designs that arise in certain fields of application such as genetics, bioinformatics, agriculture, medicine, manufacturing, marketing, etc. Well-known and highly-regarded contributors have written individual chapters that have been extensively reviewed by the Editor to ensure that each individual contribution relates to material found in Volumes 1 and 2 of this book series. The chapters in Volume 3 have an introductory/historical component and proceed to a more advanced technical level to discuss the latest results and future developm.
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A Realistic Approach

Author: Virgil L. Anderson,Robert A. McLean

Publisher: CRC Press

ISBN: 9780824761318

Category: Mathematics

Page: 440

View: 7695

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Author: Angela Dean,Max Morris,John Stufken,Derek Bingham

Publisher: CRC Press

ISBN: 146650434X

Category: Mathematics

Page: 960

View: 1097

Handbook of Design and Analysis of Experiments provides a detailed overview of the tools required for the optimal design of experiments and their analyses. The handbook gives a unified treatment of a wide range of topics, covering the latest developments. This carefully edited collection of 25 chapters in seven sections synthesizes the state of the art in the theory and applications of designed experiments and their analyses. Written by leading researchers in the field, the chapters offer a balanced blend of methodology and applications. The first section presents a historical look at experimental design and the fundamental theory of parameter estimation in linear models. The second section deals with settings such as response surfaces and block designs in which the response is modeled by a linear model, the third section covers designs with multiple factors (both treatment and blocking factors), and the fourth section presents optimal designs for generalized linear models, other nonlinear models, and spatial models. The fifth section addresses issues involved in designing various computer experiments. The sixth section explores "cross-cutting" issues relevant to all experimental designs, including robustness and algorithms. The final section illustrates the application of experimental design in recently developed areas. This comprehensive handbook equips new researchers with a broad understanding of the field’s numerous techniques and applications. The book is also a valuable reference for more experienced research statisticians working in engineering and manufacturing, the basic sciences, and any discipline that depends on controlled experimental investigation.
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Author: Douglas C. Montgomery

Publisher: John Wiley & Sons

ISBN: 1119113474

Category: Experimental design

Page: 630

View: 9701

TRY (FREE for 14 days), OR RENT this title: www.wileystudentchoice.com Design and Analysis of Experiments, 9th Edition continues to help senior and graduate students in engineering, business, and statistics-as well as working practitioners-to design and analyze experiments for improving the quality, efficiency and performance of working systems. This bestselling text maintains its comprehensive coverage by including: new examples, exercises, and problems (including in the areas of biochemistry and biotechnology); new topics and problems in the area of response surface; new topics in nested and split-plot design; and the residual maximum likelihood method is now emphasized throughout the book.
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Sample Size Determination and Block Designs

Author: Dieter Rasch,Günter Herrendörfer

Publisher: Springer Science & Business Media

ISBN: 9789027716842

Category: Computers

Page: 200

View: 4806

A heuristic introduction to experimental design; Optimum statistical experimental design as a branch of mathematical statistics; Definitios of the most important experimental designs; Properties and the construction of block designs; The nummber of nonisomorphic elementary bib in restricted; The analysis of block designs; The choice of optimal experimental designs; Appendix.
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Author: Jagdish Narain Srivastava

Publisher: North-Holland

ISBN: N.A

Category: Science

Page: 699

View: 6160

Designs and estimators for variance components; Combined intra-and inter-block estimation of treatment effects in incomplete block designs; Updating methods for linear models for the addition or deletion of observations; Approaches in sequential design of experiments; Two recent areas of sample survey research; Fitting and looking at linear and log linear fits; Tests of model specification based on residuals; Minimal unbiased designs for linear parametric functions; Optimal experimental designs for discriminating two rival regression models; Multivariate statistical inference under marginal structure; The availability of tables useful in analyzing linear models; Data monitoring criteria for linear models; Computing optimum designs for covariance models;Repeated measurement designs I; Design of genetical experiments; Recent developments in randomized response designs; Robustness and designs.
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