Ebook: Design and Analysis of Experiments

Our initial motivation for writing this book was the observation from various students that the subject of design and analysis of experiments can seem like “a bunch of miscellaneous topics. ”Webelievethattheidenti?cationoftheobjectivesoftheexperimentandthepractical considerations governing the design form the heart of the subject matter and serve as the link between the various analytical techniques. We also believe that learning about design and analysis of experiments is best achieved by the planning, running, and analyzing of a simple experiment. With these considerations in mind, we have included throughout the book the details of the planning stage of several experiments that were run in the course of teaching our classes. The experiments were run by students in statistics and the applied sciences and are suf?ciently simple that it is possible to discuss the planning of the entire experiment in a few pages, and the procedures can be reproduced by readers of the book. In each of these experiments, we had access to the investigators’ actual report, including the dif?culties they came across and how they decided on the treatment factors, the needed number of observations, and the layout of the design. In the later chapters, we have included details of a number of published experiments. The outlines of many other student and published experiments appear as exercises at the ends of the chapters. Complementing the practical aspects of the design are the statistical aspects of the anal ysis. We have developed the theory of estimable functions and analysis of variance with somecare,butatalowmathematicallevel.

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The design and analysis of experiments is an essential part of investigation and discovery in science, of process and product improvement in manufacturing, and of comparison of competing protocols or treatments in the applied sciences. This book offers a step by step guide to the experimental planning process and the ensuing analysis of normally distributed data. Design and Analysis of Experiments emphasizes the practical considerations governing the design of an experiment based on the objectives of the study and a solid statistical foundation for the analysis. Almost all data sets in the book have been obtained from real experiments, either run by students in statistics and the applied sciences, or published in the scientific literature. Details of the planning stage of numerous different experiments are discussed. The statistical analysis of experimental data is based on estimable functions and is developed with some care. Design and Analysis of Experiments starts with basic principles and techniques of experimental design and analysis of experiments. It provides a checklist for the planning of experiments, and explains the estimation of treatment contrasts and analysis of variance. These basics are then applied in a wide variety of settings. Designs covered include completely randomized designs, complete and incomplete block designs, row-column designs, single replicate designs with confounding, fractional factorial designs, response surface designs, and designs involving nested factors and factors with random effects, including split-plot designs. The book is accessible to all readers who have a good basic knowledge of expected values, confidence intervals and hypothesis tests. It is ideal for use in the classroom at both the senior undergraduate and the graduate level. A guide to the use of the SAS System computer

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The design and analysis of experiments is an essential part of investigation and discovery in science, of process and product improvement in manufacturing, and of comparison of competing protocols or treatments in the applied sciences. This book offers a step by step guide to the experimental planning process and the ensuing analysis of normally distributed data. Design and Analysis of Experiments emphasizes the practical considerations governing the design of an experiment based on the objectives of the study and a solid statistical foundation for the analysis. Almost all data sets in the book have been obtained from real experiments, either run by students in statistics and the applied sciences, or published in the scientific literature. Details of the planning stage of numerous different experiments are discussed. The statistical analysis of experimental data is based on estimable functions and is developed with some care. Design and Analysis of Experiments starts with basic principles and techniques of experimental design and analysis of experiments. It provides a checklist for the planning of experiments, and explains the estimation of treatment contrasts and analysis of variance. These basics are then applied in a wide variety of settings. Designs covered include completely randomized designs, complete and incomplete block designs, row-column designs, single replicate designs with confounding, fractional factorial designs, response surface designs, and designs involving nested factors and factors with random effects, including split-plot designs. The book is accessible to all readers who have a good basic knowledge of expected values, confidence intervals and hypothesis tests. It is ideal for use in the classroom at both the senior undergraduate and the graduate level. A guide to the use of the SAS System computer
Content:
Front Matter....Pages i-xix
Principles and Techniques....Pages 1-6
Planning Experiments....Pages 7-32
Designs with One Source of Variation....Pages 33-65
Inferences for Contrasts and Treatment Means....Pages 67-101
Checking Model Assumptions....Pages 103-134
6 Experiments with Two Crossed Treatment Factors....Pages 135-191
Several Crossed Treatment Factors....Pages 193-242
Polynomial Regression....Pages 243-276
Analysis of Covariance....Pages 277-294
Complete Block Designs....Pages 295-337
Incomplete Block Designs....Pages 339-385
Designs with Two Blocking Factors....Pages 387-420
Confounded Two-Level Factorial Experiments....Pages 421-460
Confounding in General Factorial Experiments....Pages 461-481
Fractional Factorial Experiments....Pages 483-545
Response Surface Methodology....Pages 547-592
Random Effects and Variance Components....Pages 593-643
Nested Models....Pages 645-673
Split-Plot Designs....Pages 675-694
Back Matter....Pages 695-743

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The design and analysis of experiments is an essential part of investigation and discovery in science, of process and product improvement in manufacturing, and of comparison of competing protocols or treatments in the applied sciences. This book offers a step by step guide to the experimental planning process and the ensuing analysis of normally distributed data. Design and Analysis of Experiments emphasizes the practical considerations governing the design of an experiment based on the objectives of the study and a solid statistical foundation for the analysis. Almost all data sets in the book have been obtained from real experiments, either run by students in statistics and the applied sciences, or published in the scientific literature. Details of the planning stage of numerous different experiments are discussed. The statistical analysis of experimental data is based on estimable functions and is developed with some care. Design and Analysis of Experiments starts with basic principles and techniques of experimental design and analysis of experiments. It provides a checklist for the planning of experiments, and explains the estimation of treatment contrasts and analysis of variance. These basics are then applied in a wide variety of settings. Designs covered include completely randomized designs, complete and incomplete block designs, row-column designs, single replicate designs with confounding, fractional factorial designs, response surface designs, and designs involving nested factors and factors with random effects, including split-plot designs. The book is accessible to all readers who have a good basic knowledge of expected values, confidence intervals and hypothesis tests. It is ideal for use in the classroom at both the senior undergraduate and the graduate level. A guide to the use of the SAS System computer
Content:
Front Matter....Pages i-xix
Principles and Techniques....Pages 1-6
Planning Experiments....Pages 7-32
Designs with One Source of Variation....Pages 33-65
Inferences for Contrasts and Treatment Means....Pages 67-101
Checking Model Assumptions....Pages 103-134
6 Experiments with Two Crossed Treatment Factors....Pages 135-191
Several Crossed Treatment Factors....Pages 193-242
Polynomial Regression....Pages 243-276
Analysis of Covariance....Pages 277-294
Complete Block Designs....Pages 295-337
Incomplete Block Designs....Pages 339-385
Designs with Two Blocking Factors....Pages 387-420
Confounded Two-Level Factorial Experiments....Pages 421-460
Confounding in General Factorial Experiments....Pages 461-481
Fractional Factorial Experiments....Pages 483-545
Response Surface Methodology....Pages 547-592
Random Effects and Variance Components....Pages 593-643
Nested Models....Pages 645-673
Split-Plot Designs....Pages 675-694
Back Matter....Pages 695-743
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