Author: M. C. Chakrabarti

Publisher: N.A

ISBN: N.A

Category: Experimental design

Page: 120

View: 1640

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: Jürgen Pilz

Publisher: John Wiley & Sons Inc

ISBN: N.A

Category: Mathematics

Page: 296

View: 9815

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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A Linear Models Approach

Author: John H. Skillings,Donald Weber

Publisher: CRC Press

ISBN: 9780849396717

Category: Mathematics

Page: 696

View: 7576

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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Author: Jagdish Narain Srivastava

Publisher: North-Holland

ISBN: N.A

Category: Science

Page: 699

View: 8408

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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Introduction to Experimental Design

Author: Klaus Hinkelmann,Oscar Kempthorne

Publisher: John Wiley & Sons

ISBN: 9780470191743

Category: Mathematics

Page: 640

View: 3646

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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An Introduction Based on Linear Models

Author: Max Morris

Publisher: CRC Press

ISBN: 1439894906

Category: Mathematics

Page: 376

View: 9658

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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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: 8302

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: 0470530685

Category: Mathematics

Page: 600

View: 9969

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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Author: Andrej Pázman

Publisher: Springer

ISBN: N.A

Category: Computers

Page: 228

View: 2883

Introductory remarks about the experiment and its disign. The regression model and methods of estimation. The ordering of designs and the properties of variaces of estimates. Optimality critaria in the regression model. Iterative computation of optimum desings Design of experiments in particular cases. The functional model and measurements of physical fields.
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A No-Name Approach

Author: Thomas Lorenzen,Virgil Anderson

Publisher: CRC Press

ISBN: 9780824790776

Category: Mathematics

Page: 432

View: 9955

Presents a novel approach to the statistical design of experiments, offering a simple way to specify and evaluate all possible designs without restrictions to classes of named designs. The work also presents a scientific design method from the recognition stage to implementation and summarization.
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Bayesian Experimental Design, Best Linear Unbiased Prediction, Bootstrap Error-Adjusted Single-Sample Technique, C+-Probability,

Author: Source Wikipedia

Publisher: University-Press.org

ISBN: 9781230639079

Category:

Page: 94

View: 7808

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 34. Chapters: Bayesian experimental design, Best linear unbiased prediction, Bootstrap error-adjusted single-sample technique, C+-probability, Causal inference, Comparing means, Descriptive research, Design of experiments, Dual-flashlight plot, Factorial experiment, Fold change, Fractional factorial design, Kolmogorov-Smirnov test, Mixed model, Multivariate analysis, Newey-West estimator, Optimal design, Pocock boundary, Principal stratification, Regression analysis, Response surface methodology, Smoothing spline, Structural equation modeling, Structured data analysis (statistics), Student's t-test, Taguchi methods, Volcano plot (statistics). Excerpt: In the design of experiments, optimal designs are a class of experimental designs that are optimal with respect to some statistical criterion. In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum-variance. A non-optimal design requires a greater number of experimental runs to estimate the parameters with the same precision as an optimal design. In practical terms, optimal experiments can reduce the costs of experimentation. The optimality of a design depends on the statistical model and is assessed with respect to a statistical criterion, which is related to the variance-matrix of the estimator. Specifying an appropriate model and specifying a suitable criterion function both require understanding of statistical theory and practical knowledge with designing experiments. Optimal designs are also called optimum designs. Optimal designs offer three advantages over suboptimal experimental designs: Experimental designs are evaluated using statistical criteria. It is known that the least squares estimator minimizes the variance of mean-unbiased estimators (under the conditions of the...
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A Case Study Approach

Author: Peter Goos,Bradley Jones

Publisher: John Wiley & Sons

ISBN: 1119976162

Category: Science

Page: 304

View: 7412

"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: Friedrich Pukelsheim

Publisher: SIAM

ISBN: 0898716047

Category: Mathematics

Page: 454

View: 3270

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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Statistical Principles for Practical Applications

Author: R. Mead

Publisher: Cambridge University Press

ISBN: 9780521287623

Category: Mathematics

Page: 620

View: 6562

In all the experimental sciences, good design of experiments is crucial to the success of research. Well-planned experiments can provide a great deal of information efficiently and can be used to test several hypotheses simultaneously. This book is about the statistical principles of good experimental design and is intended for all applied statisticians and practising scientists engaged in the design, implementation and analysis of experiments. Professor Mead has written the book with the emphasis on the logical principles of statistical design and employs a minimum of mathematics. Throughout he assumes that the large-scale analysis of data will be performed by computers and he is thus able to devote more attention to discussions of how all of the available information can be used to extract the clearest answers to many questions. The principles are illustrated with a wide range of examples drawn from medicine, agriculture, industry and other disciplines. Numerous exercises are given to help the reader practise techniques and to appreciate the difference that good design of experiments can make to a scientific project.
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Author: Douglas C. Montgomery

Publisher: John Wiley & Sons

ISBN: 0470128666

Category: Technology & Engineering

Page: 680

View: 1478

This bestselling professional reference has helped over 100,000 engineers and scientists with the success of their experiments. The new edition includes more software examples taken from the three most dominant programs in the field: Minitab, JMP, and SAS. Additional material has also been added in several chapters, including new developments in robust design and factorial designs. New examples and exercises are also presented to illustrate the use of designed experiments in service and transactional organizations. Engineers will be able to apply this information to improve the quality and efficiency of working systems.
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Author: Paul G. Mathews

Publisher: ASQ Quality Press

ISBN: 0873896378

Category: Computers

Page: 499

View: 845

Most of the classic DOE books were written before DOE software was generally available, so the technical level that they assumed was that of the engineer or scientist who had to write his or her own analysis software. In this practical introduction to DOE, guided by the capabilities of the common software packages, Paul Mathews presents the basic types and methods of designed experiments appropriate for engineers, scientists, quality engineers, and Six Sigma Black Belts and Master Black Belts. Although instructions in the use of MINITAB are detailed enough to provide effective guidance to a new MINITAB user, the book is still general enough to be very helpful to users of other DOE software packages. Every chapter contains many examples with detailed solutions including extensive output from MINITAB. Preview a sample chapter from this book along with the full table of contents by clicking here.You will need Adobe Acrobat to view this pdf file.
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Author: Lloyd Condra

Publisher: CRC Press

ISBN: 9780824705275

Category: Technology & Engineering

Page: 416

View: 9565

A guide to implementing and operating a practical reliability program using carefully designed experiments to provide information quickly, efficiently and cost effectively. It emphasizes real world solutions to daily problems. The second edition contains a special expanded section demonstrating how to combine accelerated testing with design of experiments for immediate improvement.
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