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Design of Experiments: An Introduction Based on Linear Models [Minkštas viršelis]

(Iowa State University, Ames, USA)
  • Formatas: Paperback / softback, 376 pages, aukštis x plotis: 234x156 mm, weight: 376 g, 13 Illustrations, black and white
  • Serija: Chapman & Hall/CRC Texts in Statistical Science
  • Išleidimo metai: 31-May-2017
  • Leidėjas: CRC Press
  • ISBN-10: 1138111783
  • ISBN-13: 9781138111783
Kitos knygos pagal šią temą:
Design of Experiments: An Introduction Based on Linear ModelsDidesnis paveikslėlis
  • Formatas: Paperback / softback, 376 pages, aukštis x plotis: 234x156 mm, weight: 376 g, 13 Illustrations, black and white
  • Serija: Chapman & Hall/CRC Texts in Statistical Science
  • Išleidimo metai: 31-May-2017
  • Leidėjas: CRC Press
  • ISBN-10: 1138111783
  • ISBN-13: 9781138111783
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781138111783.html

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.

Recenzijos

A distinctive feature of this excellent book is that it actually focuses on how to design an experiment. In all, an original and very useful book for students and instructors. Stat Papers (2014) 55:12251226

the author has succeeded in striking a balance between the choice of topics and depth in discussion for teaching a course. The book is written with a refreshing style and succeeds in conveying the concepts to a reader. The treatment of the subject matter is thorough and the theory is clearly illustrated along with worked examples. Other books are available on similar topics but this book has the advantage that the chapters start with the classical non-matrix-theory approach to introduce the linear model and then converts it into a matrix theory-based linear model. This helps a reader, particularly a beginner, in clearly understanding the transition from a non-matrix approach to a matrix approach and to apply the results of matrix theory over linear models further. Shalabh, Journal of the Royal Statistical Society, Series A, 2012

Overall, this is a book that is easy to like, with good definitions of designs, few typographical errors, and consistent, straightforward explications of the models I can picture a lot of students using a text aimed at a broad market design course but who need to understand more about what is going on behind the curtain. Morris text also fills that gap very well. Gary W. Oehlert, Biometrics, May 2012

It is truly my pleasure to read this book after reading this book, I benefitted by gaining insights into the modeling aspect of experimental design, and consequentially it helps me appreciate the idea of statistical efficiency behind each design and understand the tools used in data analysis. an excellent reference book that I would recommend to anyone who is serious about learning the nuts and bolts of experimental design and data analysis techniques. Rong Pan, Journal of Quality Technology, Vol. 43, No. 3, July 2011

Preface xvii
1 Introduction 1(12)
1.1 Example: rainfall and grassland
1(1)
1.2 Basic elements of an experiment
2(6)
1.2.1 Treatments and material
3(1)
1.2.2 Control and comparison
4(1)
1.2.3 Responses and measurement processes
5(1)
1.2.4 Replication, blocking, and randomization
6(1)
1.2.5 Validity and optimality
7(1)
1.3 Experiments and experiment-like studies
8(1)
1.4 Models and data analysis
9(1)
1.5 Conclusion
9(1)
1.6 Exercises
10(3)
2 Linear statistical models 13(24)
2.1 Linear vector spaces
13(1)
2.2 Basic linear model
14(1)
2.3 The hat matrix, least-squares estimates, and design information matrix
14(4)
2.3.1 Example
16(2)
2.4 The partitioned linear model
18(1)
2.5 The reduced normal equations
19(4)
2.5.1 Example
21(2)
2.6 Linear and quadratic forms
23(1)
2.7 Estimation and information
24(4)
2.7.1 Pure error and lack of fit
26(2)
2.8 Hypothesis testing and information
28(2)
2.8.1 Example
29(1)
2.9 Blocking and information
30(1)
2.10 Conclusion
31(1)
2.11 Exercises
31(6)
3 Completely randomized designs 37(18)
3.1 Introduction
37(1)
3.1.1 Example: radiation and rats
37(1)
3.2 Models
38(3)
3.2.1 Graphical logic
40(1)
3.3 Matrix formulation
41(3)
3.4 Influence of the design on estimation
44(5)
3.4.1 Allocation
45(3)
3.4.2 Overall experiment size
48(1)
3.5 Influence of design on hypothesis testing
49(1)
3.6 Conclusion
50(1)
3.7 Exercises
50(5)
4 Randomized complete blocks and related designs 55(18)
4.1 Introduction
55(2)
4.1.1 Example: structural reinforcement bars
56(1)
4.2 A model
57(2)
4.2.1 Graphical logic
58(1)
4.3 Matrix formulation
59(2)
4.4 Influence of design on estimation
61(2)
4.4.1 Experiment size
63(1)
4.5 Influence of design on hypothesis testing
63(1)
4.6 Orthogonality and "Condition E"
64(3)
4.7 Conclusion
67(1)
4.8 Exercises
67(6)
5 Latin squares and related designs 73(20)
5.1 Introduction
73(3)
5.1.1 Example: web page links
75(1)
5.2 Replicated Latin squares
76(1)
5.3 A model
77(3)
5.3.1 Graphical logic
79(1)
5.4 Matrix formulation
80(3)
5.5 Influence of design on quality of inference
83(1)
5.6 More general constructions: Graeco-Latin squares
84(3)
5.7 Conclusion
87(1)
5.8 Exercises
87(6)
6 Some data analysis for CRDs and orthogonally blocked designs 93(16)
6.1 Introduction
93(1)
6.2 Diagnostics
93(4)
6.2.1 Residuals
93(2)
6.2.2 Modified Levene test
95(1)
6.2.3 General test for lack of fit
96(1)
6.2.4 Tukey one-degree-of-freedom test
97(1)
6.3 Power transformations
97(3)
6.4 Basic inference
100(1)
6.5 Multiple comparisons
100(5)
6.5.1 Tukey intervals
101(1)
6.5.2 Dunnett intervals
102(1)
6.5.3 Simulation-based intervals for specific problems
102(1)
6.5.4 Scheffe intervals
103(1)
6.5.5 Numerical example
104(1)
6.6 Conclusion
105(1)
6.7 Exercises
106(3)
7 Balanced incomplete block designs 109(20)
7.1 Introduction
109(3)
7.1.1 Example: drugs and blood pressure
110(1)
7.1.2 Existence and construction of BIBDs
111(1)
7.2 A model
112(2)
7.2.1 Graphical logic
112(1)
7.2.2 Example: dishwashing detergents
113(1)
7.3 Matrix formulation
114(5)
7.3.1 Basic analysis: an example
118(1)
7.4 Influence of design on quality of inference
119(2)
7.5 More general constructions
121(3)
7.5.1 Extended complete block designs
121(1)
7.5.2 Partially balanced incomplete block designs
122(2)
7.6 Conclusion
124(1)
7.7 Exercises
124(5)
8 Random block effects 129(14)
8.1 Introduction
129(1)
8.2 Inter- and intra-block analysis
129(3)
8.3 Complete block designs (CBDs) and augmented CBDs
132(2)
8.4 Balanced incomplete block designs (BIBDs)
134(1)
8.5 Combined estimator
135(2)
8.5.1 Example: dishwashing detergents reprise
136(1)
8.6 Why can information be "recovered"?
137(1)
8.7 CBD reprise
138(1)
8.8 Conclusion
139(1)
8.9 Exercises
139(4)
9 Factorial treatment structure 143(24)
9.1 Introduction
143(1)
9.1.1 Example: strength of concrete
144(1)
9.2 An overparameterized model
144(8)
9.2.1 Graphical logic
147(1)
9.2.2 Matrix development for the overparameterized model
148(4)
9.3 An equivalent full-rank model
152(3)
9.3.1 Matrix development for the full-rank model
154(1)
9.4 Estimation
155(2)
9.5 Partitioning of variability and hypothesis testing
157(2)
9.6 Factorial experiments as CRDs, CBDs, LSDs, and BIBDs
159(1)
9.7 Model reduction
160(2)
9.8 Conclusion
162(1)
9.9 Exercises
163(4)
10 Split-plot designs 167(20)
10.1 Introduction
167(2)
10.1.1 Example: strength of fabrics
168(1)
10.1.2 Example: English tutoring
169(1)
10.2 SPD(R,B)
169(6)
10.2.1 A model
170(1)
10.2.2 Analysis
171(4)
10.3 SPD(B,B)
175(3)
10.3.1 A model
176(1)
10.3.2 Analysis
177(1)
10.4 More than two experimental factors
178(1)
10.5 More than two strata of experimental units
178(2)
10.6 Conclusion
180(2)
10.7 Exercises
182(5)
11 Two-level factorial experiments: basics 187(20)
11.1 Introduction
187(1)
11.2 Example: bacteria and nuclease
187(1)
11.3 Two-level factorial structure
188(5)
11.4 Estimation of treatment contrasts
193(3)
11.4.1 Full model
193(1)
11.4.2 Reduced model
193(2)
11.4.3 Examples
195(1)
11.5 Testing factorial effects
196(4)
11.5.1 Individual model terms, experiments with replication
196(1)
11.5.2 Multiple model terms, experiments with replication
197(1)
11.5.3 Experiments without replication
197(3)
11.6 Additional guidelines for model editing
200(1)
11.7 Conclusion
201(1)
11.8 Exercises
201(6)
12 Two-level factorial experiments: blocking 207(20)
12.1 Introduction
207(1)
12.1.1 Models
207(1)
12.1.2 Notation
208(1)
12.2 Complete blocks
208(2)
12.2.1 Example: gophers and burrow plugs
210(1)
12.3 Balanced incomplete block designs (BIBDs)
210(1)
12.4 Regular blocks of size 2f-1
211(5)
12.4.1 Random blocks
214(1)
12.4.2 Partial confounding
215(1)
12.5 Regular blocks of size 2f-2
216(3)
12.6 Regular blocks: general case
219(3)
12.7 Conclusion
222(1)
12.8 Exercises
223(4)
13 Two-level factorial experiments: fractional factorials 227(20)
13.1 Introduction
227(1)
13.2 Regular fractional factorial designs
227(3)
13.3 Analysis
230(1)
13.4 Example: bacteria and bacteriocin
231(1)
13.5 Comparison of fractions
231(3)
13.5.1 Resolution
231(2)
13.5.2 Comparing fractions of equal resolution: aberration
233(1)
13.6 Blocking regular fractional factorial designs
234(1)
13.7 Augmenting regular fractional factorial designs
235(5)
13.7.1 Combining fractions
235(2)
13.7.2 Fold-over designs
237(2)
13.7.3 Blocking combined fractions
239(1)
13.8 Irregular fractional factorial designs
240(2)
13.9 Conclusion
242(1)
13.10 Exercises
243(4)
14 Factorial group screening experiments 247(14)
14.1 Introduction
247(1)
14.2 Example: semiconductors and simulation
248(2)
14.3 Factorial structure of group screening designs
250(3)
14.4 Group screening design considerations
253(3)
14.4.1 Effect cancelling
253(1)
14.4.2 Screening failure
253(1)
14.4.3 Aliasing
254(1)
14.4.4 Screening efficiency
255(1)
14.5 Case study
256(1)
14.6 Conclusion
257(1)
14.7 Exercises
258(3)
15 Regression experiments: first-order polynomial models 261(20)
15.1 Introduction
261(2)
15.1.1 Example: bacteria and elastase
262(1)
15.2 Polynomial models
263(1)
15.3 Designs for first-order models
264(2)
15.3.1 Two-level designs
264(1)
15.3.2 Simplex designs
265(1)
15.4 Blocking experiments for first-order models
266(3)
15.5 Split-plot regression experiments
269(2)
15.5.1 Example: bacteria and elastase reprise
269(2)
15.6 Diagnostics
271(1)
15.6.1 Use of a center point
271(5)
15.6.2 General test for lack-of-fit
272(4)
15.7 Conclusion
276(1)
15.8 Exercises
276(5)
16 Regression experiments: second-order polynomial models 281(18)
16.1 Introduction
281(1)
16.1.1 Example: nasal sprays
281(1)
16.2 Quadratic polynomial models
282(2)
16.3 Designs for second-order models
284(5)
16.3.1 Complete three-level factorial designs
284(2)
16.3.2 Central composite designs
286(1)
16.3.3 Box-Behnken designs
287(1)
16.3.4 Augmented pairs designs
288(1)
16.4 Design scaling and information
289(2)
16.5 Orthogonal blocking
291(1)
16.6 Split-plot designs
292(1)
16.6.1 Example
292(1)
16.7 Bias due to omitted model terms
293(3)
16.8 Conclusion
296(1)
16.9 Exercises
296(3)
17 Introduction to optimal design 299(14)
17.1 Introduction
299(1)
17.2 Optimal design fundamentals
299(2)
17.3 Optimality criteria
301(8)
17.3.1 A-optimality
301(2)
17.3.2 D-optimality
303(1)
17.3.3 Other criteria
304(1)
17.3.4 Examples
304(5)
17.4 Algorithms
309(1)
17.5 Conclusion
310(1)
17.6 Exercises
311(2)
Appendix A: Calculations using R 313(8)
Appendix B: Solution notes for selected exercises 321(20)
References 341(6)
Index 347
Max D. Morris is a professor in the Department of Statistics and the Department of Industrial and Manufacturing Systems Engineering at Iowa State University. A fellow of the American Statistical Association, Dr. Morris is a recipient of the National Institute of Statistical Sciences Sacks Award for Cross-Disciplinary Research and the American Society for Quality Wilcoxon Prize.