Statistics for Experimenters - George E P Box

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Résumé :

Preface to the Second Edition xv

Chapter 1 Catalyzing the Generation of Knowledge 1

1.1. The Learning Process 1

1.2. Important Considerations 5

1.3. The Experimenter's Problem and Statistical Methods 6

1.4. A Typical Investigation 9

1.5. How to Use Statistical Techniques 13

References and Further Reading 14

Chapter 2 Basics (Probability, Parameters, and Statistics) 17

2.1. Experimental Error 17

2.2. Distributions 18

2.3. Statistics and Parameters 23

2.4. Measures of Location and Spread 24

2.5. The Normal Distribution 27

2.6. Normal Probability Plots 33

2.7. Randomness and Random Variables 34

2.8. Covariance and Correlation as Measures of Linear Dependence 37

2.9. Student's t Distribution 39

2.10. Estimates of Parameters 43

2.11. Random Sampling from a Normal Population 44

2.12. The Chi-Square and F Distributions 46

2.13. The Binomial Distribution 48

2.14. The Poisson Distribution 54

Appendix 2A. Mean and Variance of Linear Combinations of Observations 57

References and Further Reading 60

Chapter 3 Comparing Two Entities: Reference Distributions, Tests, and Confidence Intervals 67

3.1. Relevant Reference Sets and Distributions 67

3.2. Randomized Paired Comparison Design: Boys' Shoes Example 81

3.3. Blocking and Randomization 92

3.4. Reprise: Comparison, Replication, Randomization, and Blocking in Simple Experiments 94

3.5. More on Significance Tests 94

3.6. Inferences About Data that are Discrete: Binomial Distribution 105

3.7. Inferences about Frequencies (Counts Per Unit): The Poisson Distribution 110

3.8. Contingency Tables and Tests of Association 112

Appendix 3A. Comparison of the Robustness of Tests to Compare Two Entities 117

Appendix 3B. Calculation of reference distribution from past data 120

References and Further Reading 123

Chapter 4 Comparing a Number of Entities, Randomized Blocks, and Latin Squares 133

4.1. Comparing k Treatments in a Fully Randomized Design 133

4.2. Randomized Block Designs 145

4.3. A Preliminary Note on Split-Plot Experiments and their Relationship to Randomized Blocks 156

4.4. More than one blocking component: Latin Squares 157

4.5. Balanced Incomplete Block Designs 162

Appendix 4A. The Rationale for the Graphical Anova 166

Appendix 4B. Some Useful Latin Square, Graeco-Latin Square, and Hyper-Graeco-Latin Square Designs 167

References and Further Reading 168

Chapter 5 Factorial Designs at Two Levels 173

5.1. Introduction 173

5.2. Example 1: The Effects of Three Factors (Variables) on Clarity of Film 174

5.3. Example 2: The Effects of Three Factors on Three Physical Properties of a Polymer Solution 175

5.4. A 2³ Factorial Design: Pilot Plant Investigation 177

5.5. Calculation of Main Effects 178

5.6. Interaction Effects 181

5.7. Genuine Replicate Runs 183

5.8. Interpretation of Results 185

5.9. The Table of Contrasts 186

5.10. Misuse of the ANOVA for 2^k Factorial Experiments 188

5.11. Eyeing the Data 190

5.12. Dealing with More Than One Response: A Pet Food Experiment 193

5.13. A 2⁴ Factorial Design: Process Development Study 199

5.14. Analysis Using Normal and Lenth Plots 203

5.15. Other Models for Factorial Data 208

5.16. Blocking the 2^k Factorial Designs 211

5.17. Learning by Doing 215

5.18. Summary 219

Appendix 5A. Blocking Larger Factorial Design...

Biographie:
GEORGE E. P. BOX, PhD, DSc, is Ronald Aylmer Fisher Professor Emeritus of Statistics and Industrial Engineering at the University of Wisconsin-Madison. He is a Fellow of the Royal Society, an Honorary Fellow and Shewhart and Deming Medalist of the American Society for Quality and was awarded the Guy Medal in Gold of the Royal Statistical Society. He is also the recipient of the Samuel S. Wilks Memorial Medal of the American Statistical Association.

J. STUART HUNTER, PhD, DSc, is Professor Emeritus of Civil Engineering at Princeton University. Dr. Hunter is a member of the National Academy of Engineering and has served as consultant to many industries and government agencies. He has been a staff member of the National Academy of Sciences, Committee on National Statistics...

Sommaire:
A Classic adapted to modern times

Rewritten and updated, this new edition of Statistics for Experimenters adopts the same approaches as the landmark First Edition by teaching with examples, readily understood graphics, and the appropriate use of computers. Catalyzing innovation, problem solving, and discovery, the Second Edition provides experimenters with the scientific and statistical tools needed to maximize the knowledge gained from research data, illustrating how these tools may best be utilized during all stages of the investigative process. The authors' practical approach starts with a problem that needs to be solved and then examines the appropriate statistical methods of design and analysis.

Providing even greater accessibility for its users, the Second Edition is thoroughly revised and updated to reflect the changes in techniques and technologies since the publication of the classic First Edition.

Among the new topics included are:

• Graphical Analysis of Variance
• Computer Analysis of Complex Designs
• Simplification by transformation
• Hands-on experimentation using Response Service Methods
• Further development of robust product and process design using split plot arrangements and minimization of error transmission
• Introduction to Process Control, Forecasting and Time Series
• Illustrations demonstrating how multi-response problems can be solved using the concepts of active and inert factor spaces and canonical spaces
• Bayesian approaches to model selection and sequential experimentation

An appendix featuring Quaquaversal quotes from a variety of sources including noted statisticians and scientists to famous philosophers is provided to illustrate key concepts and enliven the learning process.

All the computations in the Second Edition can be done utilizing the statistical language R. Functions for displaying ANOVA and lamba plots, Bayesian screening, and model building are all included and R packages are available online. All theses topics can also be applied utilizing easy-to-use commercial software packages.

Complete with applications covering the physical, engineering, biological, and social sciences, Statistics for Experimenters is designed for individuals who must use statistical approaches to conduct an experiment, but do not necessarily have formal training in statistics. Experimenters need only a basic understanding of mathematics to master all the statistical methods presented. This text is an essential reference for all researchers and is a highly recommended course book for undergraduate and graduate students.