Design and Analysis of Experiments
Springer Science & Business Media, Dec 21, 2000 - Mathematics - 742 pages
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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Principles and Techniques
Designs with One Source of Variation
Inferences for Contrasts and Treatment Means
Checking Model Assumptions
Experiments with Two Crossed Treatment Factors
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...
Several Crossed Treatment Factors
Designs with Two Blocking Factors
Confounded TwoLevel Factorial Experiments
Response Surface Methodology
Random Effects and Variance Components
Other editions - View all
aliased analysis of variance average balanced incomplete block blocking factor brand calculated central composite design coded column blocks completely randomized design confidence intervals confidence level confounded contrast coefficients contrast estimates corresponding covariate degrees of freedom Degrees of Sum equal error variables Example experimental units factor levels factorial experiment Freedom Squares Square incomplete block design interaction contrast interaction plot lack of fit Latin square least squares estimates main effects mean response multiple comparisons negligible noise factors null hypothesis number of observations obtained one-way analysis orthogonal output p-value pairwise comparisons parameters PROC GLM quadratic randomized complete block regression model response variable row blocks sample sizes SAS program SAS System Section shown in Table significance level Source of Degrees sstot Sum of Mean sum of squares treatment combinations treatment contrasts treatment effects treatment factor treatment labels TRTMT Type variance model variance table Variation Freedom Squares zero