Design and Analysis of Experiments

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Springer Science & Business Media, Dec 21, 2000 - Mathematics - 742 pages
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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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Contents

Principles and Techniques
1
Planning Experiments
7
Designs with One Source of Variation
33
Inferences for Contrasts and Treatment Means
67
Checking Model Assumptions
103
Experiments with Two Crossed Treatment Factors
135
4 2 Estimation of σ2 for the TwoWay Complete Model 6 4 3 Multiple Comparisons for the Complete Model 6 4 4 Analysis of Variance for the Com...
147
Several Crossed Treatment Factors
193
Designs with Two Blocking Factors
387
103
403
Confounded TwoLevel Factorial Experiments
421
Response Surface Methodology
547
Exercises
586
Random Effects and Variance Components
593
Nested Models
645
SplitPlot Designs
675

Polynomial Regression
243
Analysis of Covariance
277
Exercises
292
Incomplete Block Designs
339

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