Muutke küpsiste eelistusi

Optimal Experimental Design with R [Pehme köide]

2.50/5 (2 hinnangut Goodreads-ist)
, , ,
  • Formaat: Paperback / softback, 345 pages, kõrgus x laius: 234x156 mm, kaal: 453 g
  • Ilmumisaeg: 05-Sep-2019
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 0367382768
  • ISBN-13: 9780367382766
Teised raamatud teemal:
Optimal Experimental Design with RSuurem pilt
  • Formaat: Paperback / softback, 345 pages, kõrgus x laius: 234x156 mm, kaal: 453 g
  • Ilmumisaeg: 05-Sep-2019
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 0367382768
  • ISBN-13: 9780367382766
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780367382766.html
Märksõnad:
Experimental design is often overlooked in the literature of applied and mathematical statistics: statistics is taught and understood as merely a collection of methods for analyzing data. Consequently, experimenters seldom think about optimal design, including prerequisites such as the necessary sample size needed for a precise answer for an experimental question.





Providing a concise introduction to experimental design theory, Optimal Experimental Design with R:



















Introduces the philosophy of experimental design Provides an easy process for constructing experimental designs and calculating necessary sample size using R programs Teaches by example using a custom made R program package: OPDOE











Consisting of detailed, data-rich examples, this book introduces experimenters to the philosophy of experimentation, experimental design, and data collection. It gives researchers and statisticians guidance in the construction of optimum experimental designs using R programs, including sample size calculations, hypothesis testing, and confidence estimation. A final chapter of in-depth theoretical details is included for interested mathematical statisticians.
List of Figures xi
List of Tables xiii
Preface xvii
Acknowledgments xix
1 Introduction 1(12)
1.1 Experimentation and empirical research
1(3)
1.2 Designing experiments
4(2)
1.3 Some basic definitions
6(2)
1.4 Block designs
8(3)
1.5 About the R-programs
11(2)
I Determining the Minimal Size of an Experiment for Given Precision 13(158)
2 Sample Size Determination in Completely Randomised Designs
17(38)
2.1 Introduction
17(3)
2.1.1 Sample size to be determined
17(2)
2.1.2 What to do when the size of an experiment is given in advance
19(1)
2.2 Confidence estimation
20(13)
2.2.1 Confidence intervals for expectations
20(10)
2.2.1.1 One-sample case, σ2 known
20(2)
2.2.1.2 One-sample case, σ2 unknown
22(3)
2.2.1.3 Confidence intervals for the expectation of the normal distribution in the presence of a noise factor
25(2)
2.2.1.4 One-sample case, σ2 unknown, paired observations
27(1)
2.2.1.5 Two-sample case, σ2 unknown, independent samples-equal variances
28(1)
2.2.1.6 Two-sample case, σ2 unknown, independent samples -unequal variances
29(1)
2.2.2 Confidence intervals for probabilities
30(2)
2.2.3 Confidence interval for the variance of the normal distribution
32(1)
2.3 Selection procedures
33(2)
2.4 Testing hypotheses
35(16)
2.4.1 Testing hypotheses about means of normal distributions
36(11)
2.4.1.1 One-sample problem, univariate
36(2)
2.4.1.2 One-sample problem, bivariate
38(3)
2.4.1.3 Two-sample problem, equal variances
41(2)
2.4.1.4 Two-sample problem, unequal variances
43(1)
2.4.1.5 Comparing more than two means, equal variances
44(3)
2.4.2 Testing hypotheses about probabilities
47(3)
2.4.2.1 One-sample problem
47(1)
2.4.2.2 Two-sample problem
48(2)
2.4.3 Comparing two variances
50(1)
2.5 Summary of sample size formulae
51(4)
3 Size of Experiments in Analysis of Variance Models
55(72)
3.1 Introduction
55(4)
3.2 One-way layout
59(6)
3.3 Two-way layout
65(14)
3.3.1 Two-way analysis of variance-cross-classification
66(8)
3.3.1.1 Two-way analysis of variance-cross-classification-Model I
68(4)
3.3.1.2 Two-way analysis of variance-cross-classification-mixed model
72(2)
3.3.2 Nested-classification A > B
74(5)
3.3.2.1 Two-way analysis of variance-nested classification-Model I
74(2)
3.3.2.2 Two-way analysis of variance-nested classification-mixed model, A fixed and B random
76(2)
3.3.2.3 Two-way analysis of variance-nested classification-mixed model, B fixed and A random
78(1)
3.4 Three-way layout
79(48)
3.4.1 Three-way analysis of variance-cross-classification A x B x C
80(10)
3.4.1.1 Three-way analysis of variance-classification A x B x C-Model I
81(4)
3.4.1.2 Three-way analysis of variance-cross classification A x B x C-Model III
85(1)
3.4.1.3 Three-way analysis of variance-cross classification A x B x C-Model IV
86(4)
3.4.2 Three-way analysis of variance-nested classification A > B > C
90(12)
3.4.2.1 Three-way analysis of variance-nested classification-Model I
91(2)
3.4.2.2 Three-way analysis of variance-nested classification-Model III
93(2)
3.4.2.3 Three-way analysis of variance-nested classification-Model IV
95(3)
3.4.2.4 Three-way analysis of variance-nested classification-Model V
98(1)
3.4.2.5 Three-way analysis of variance-nested classification-Model VI
99(1)
3.4.2.6 Three-way analysis of variance-nested classification-Model VII
100(1)
3.4.2.7 Three-way analysis of variance-nested classification-Model VIII
101(1)
3.4.3 Three-way analysis of variance-mixed classification (A x B) > C
102(9)
3.4.3.1 Three-way analysis of variance-mixed classification (A x B) > C-Model I
104(2)
3.4.3.2 Three-way analysis of variance-mixed classification (A x B) > C-Model III
106(1)
3.4.3.3 Three-way analysis of variance-mixed classification (A x B) > C-Model IV
107(1)
3.4.3.4 Three-way analysis of variance-mixed classification (A x B) > C-Model V
108(2)
3.4.3.5 Three-way analysis of variance-mixed classification (A x B) > C-Model VI
110(1)
3.4.4 Three-way analysis of variance-mixed classification (A > B) x C
111(17)
3.4.4.1 Three-way analysis of variance-mixed classification (A > B) x C-Model I
112(4)
3.4.4.2 Three-way analysis of variance-mixed classification (A > B) x C-Model III
116(2)
3.4.4.3 Three-way analysis of variance-mixed classification (A > B) x C-Model IV
118(1)
3.4.4.4 Three-way analysis of variance-mixed classification (A > B) x C-Model V
119(2)
3.4.4.5 Three-way analysis of variance-mixed classification (A > B) x C-Model VI
121(2)
3.4.4.6 Three-way analysis of variance-mixed classification (A > B) x C-Model VII
123(1)
3.4.4.7 Three-way analysis of variance-mixed classification (A > B) x C-Model VIII
124(3)
4 Sample Size Determination in Model II of Regression Analysis
127(12)
4.1 Introduction
127(1)
4.2 Confidence intervals
128(5)
4.2.1 Confidence intervals for the slope
129(1)
4.2.2 A confidence interval for the correlation coefficient
130(1)
4.2.3 Confidence intervals for partial correlation coefficients
131(1)
4.2.4 A confidence interval for E(y/x) = β0 + β1x
131(2)
4.3 Hypothesis testing
133(3)
4.3.1 Comparing the correlation coefficient with a constant
133(1)
4.3.2 Comparing two correlation coefficients
134(1)
4.3.3 Comparing the slope with a constant
135(1)
4.3.4 Test of parallelism of two regression lines
135(1)
4.4 Selection procedures
136(3)
5 Sequential Designs
139(32)
5.1 Introduction
139(3)
5.2 Wald's sequential likelihood ratio test (SLRT) for one-parametric exponential families
142(7)
5.3 Test about means for unknown variances
149(10)
5.3.1 The sequential t-test
149(2)
5.3.2 Approximation of the likelihood function for the construction of an approximate t-test
151(3)
5.3.3 Approximate tests for binary data
154(2)
5.3.4 Approximate tests for the two-sample problem
156(3)
5.4 Triangular designs
159(7)
5.4.1 Basic principles
159(1)
5.4.2 Testing hypotheses about means of normal distributions
160(3)
5.4.2.1 One-sample problem
160(1)
5.4.2.2 Two-sample problem
161(2)
5.4.3 Testing hypotheses about probabilities
163(22)
5.4.3.1 One-sample problem
163(2)
5.4.3.2 Two-sample problem
165(1)
5.5 A sequential selection procedure
166(5)
II Construction of Optimal Designs 171(88)
6 Constructing Balanced Incomplete Block Designs
175(36)
6.1 Introduction
175(2)
6.2 Basic definitions
177(8)
6.3 Construction of BIBD
185(26)
6.3.1 Specific methods
185(24)
6.3.2 General method
209(2)
7 Constructing Fractional Factorial Designs
211(24)
7.1 Introduction and basic notations
211(3)
7.2 Factorial designs-basic definitions
214(7)
7.3 Fractional factorial designs with two levels of each factor (2p-k-designs)
221(7)
7.4 Fractional factorial designs with three levels of each factor (3p-m-designs)
228(7)
8 Exact Optimal Designs and Sample Sizes in Model I of Regression Analysis
235(24)
8.1 Introduction
235(10)
8.1.1 The multiple linear regression Model I
236(2)
8.1.2 Simple polynomial regression
238(1)
8.1.3 Intrinsically non-linear regression
239(6)
8.2 Exact Φ-optimal designs
245(10)
8.2.1 Simple linear regression
246(2)
8.2.2 Polynomial regression
248(1)
8.2.3 Intrinsically non-linear regression
249(6)
8.2.4 Replication-free designs
255(1)
8.3 Determining the size of an experiment
255(8)
8.3.1 Simple linear regression
255(4)
III Special Designs 259(30)
9 Second Order Designs
263(16)
9.1 Central composite designs
264(4)
9.2 Doehlert designs
268(2)
9.3 D-optimum and G-optimum second order designs
270(1)
9.4 Comparing the determinant criterion for some examples
271(8)
9.4.1 Two factors
271(3)
9.4.2 Three factors
274(5)
10 Mixture Designs
279(10)
10.1 Introduction
279(4)
10.2 The simplex lattice designs
283(1)
10.3 Simplex centroid designs
284(1)
10.4 Extreme vertice designs
284(1)
10.5 Augmented designs
285(1)
10.6 Constructing optimal mixture designs with R
285(1)
10.7 An example
286(3)
A Theoretical Background 289(18)
A.1 Non-central distributions
289(1)
A.2 Groups, fields and finite geometries
290(5)
A.3 Difference sets
295(5)
A.4 Hadamard matrices
300(3)
A.5 Existence and non-existence of non-trivial BIBD
303(2)
A.6 Conference matrices
305(2)
References 307(12)
Index 319
Dieter Rasch: Currently Senior Consultant at the Centre of Experimental Design: University of Natural Resources and Life Sciences, Vienna, Dr. Rasch is an Elected Member of the International Statistical Institute (ISI), a Fellow of the IMS, and author/co-author of 46 books and more than 260 scientific papers.





From 1958- 1990, Dr. Rasch was Head of the Deparment (and Institute) of Biometry at the Research Centre Dummerstorf-Rostock, Germany. Afterwards, Dr. Rasch was professor of Mathematical Statistics at the University of Wageningen, The Netherlands from 1991 to 2000. Since 2000, he has served as a guest professor at the Math. Inst. of the University of Klagenfurt, the University Vienna, and at the Institute of Applied Statistics and Computing, University of Natural Resources and Life Sciences (2007 to 2010).





Albrecht Gebhardt: Assistant professor at the Institute of Statistics, University of Klagenfurt since 2004.





Jürgen Pilz: Professor and Chair of Applied Statistics at the University of Klagenfurt (UniKlu), Austria since 1994, and the head of the Department of Statistics at UniKlu since 2007. He has held many guest professorships, including at Purdue University, USA, Charles University, Prague,Czech Republic, the University of Augsburg, Germany, and the University of British Columbia, Vancouver, Canada. He is an Elected Member of the Int. Statist. Institute (ISI), a Fellow of the IMS, and author/co-author of six books and more than 100 scientific papers.

Rob Verdooren: A Consultant Statistician at Danone Research, Centre for Spceialised Nutrition, Wageningen, the Netherlands. He is retired Associate Professor in Experimental Design and Analysis at the Agricultural Uniiversity Wageningen, the Netherlands. Besides Experimental Design, his interests lies in Biostatistics and the design and analysis of breeding trials of Oil Palms in Indonesia.