実験計画者のための統計学(第2版)<br>Statistics for Experimenters : Design, Innovation, and discovery (Wiley Series in Probability and Statistics) (2ND)

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実験計画者のための統計学(第2版)
Statistics for Experimenters : Design, Innovation, and discovery (Wiley Series in Probability and Statistics) (2ND)

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  • 製本 Hardcover:ハードカバー版/ページ数 633 p.
  • 言語 ENG
  • 商品コード 9780471718130
  • DDC分類 519.5

基本説明

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.

Full Description

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.

Contents

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 2k 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 2k Factorial Designs 211

5.17. Learning by Doing 215

5.18. Summary 219

Appendix 5A. Blocking Larger Factorial Designs 219

Appendix 5B. Partial Confounding 221

References and Further Reading 222

Chapter 6 Fractional Factorial Designs 235

6.1. Effects of Five Factors on Six Properties of Films in Eight Runs 235

6.2. Stability of New Product, Four Factors in Eight Runs, a 24-1 Design 236

6.3. A Half-Fraction Example: The Modification of a Bearing 239

6.4. The Anatomy of the Half Fraction 240

6.5. The 2III 7-4 Design: A Bicycle Example 244

6.6. Eight-Run Designs 246

6.7. Using Table 6.6: An Illustration 247

6.8. Sign Switching, Foldover, and Sequential Assembly 249

6.9. An Investigation Using Multiple-Column Foldover 252

6.10. Increasing Design Resolution from III to IV by Foldover 257

6.11. Sixteen-Run Designs 258

6.12. The 25-1 Nodal Half Replicate of the 25 Factorial: Reactor Example 259

6.13. The 2IV 8-4 Nodal Sixteenth Fraction of a 28 Factorial 263

6.14. The 2 III 15-11 Nodal Design: the Sixty-fourth Fraction of the 215 Factorial 266

6.15. Constructing Other Two-Level Fractions 269

6.16. Elimination of Block Effects 271

References and Further Reading 273

Chapter 7 Additional Fractionals and Analysis 281

7.1. Plackett and Burman Designs 281

7.2. Choosing Follow-Up Runs 294

7.3. Justifications for the Use of Fractionals 303

Appendix 7A. Technical Details 305

Appendix 7B. An Approximate Partial Analysis for PB Designs 308

Appendix 7C. Hall's Orthogonal Designs 310

References and Further Reading 313

Chapter 8 Factorial Designs and Data Transformation 317

8.1. A Two-Way (Factorial) Design 317

8.2. Simplification and Increased Sensitivity from Transformation 320

Appendix 8A. Rationale for Data Transformation 329

Appendix 8B. Bartlett's χν2 for Testing Inhomogeneity of Variance 329

References and Further Reading 329

Chapter 9 Multiple Sources of Variation 335

9.1. Split-Plot Designs, Variance Components, and Error Transmission 335

9.2. Split-Plot Designs 335

9.3. Estimating Variance Components 345

9.4. Transmission of Error 353

References and Further Reading 359

Chapter 10 Least Squares and Why We Need Designed Experiments 363

10.1. Estimation With Least Squares 364

10.2. The Versatility of Least Squares 378

10.3. The Origins of Experimental Design 397

10.4. Nonlinear Models 407

Appendix 10A. Vector Representation of Statistical Concepts 410

Appendix 10B. Matrix Version of Least Squares 416

Appendix 10C. Analysis of Factorials, Botched and Otherwise 418

Appendix 10D. Unweighted and Weighted Least Squares 420

References and Further Reading 424

Chapter 11 Modeling, Geometry, and Experimental Design 437

11.1. Some Empirical Models 441

11.2. Some Experimental Designs and the Design Information Function 447

11.3. Is the Surface Sufficiently Well Estimated? 453

11.4. Sequential Design Strategy 454

11.5. Canonical Analysis 461

11.6. Box-Behnken Designs 475

References and Further Reading 483

Chapter 12 Some Applications of Response Surface Methods 489

12.1. Iterative Experimentation To Improve a Product Design 489

12.2. Simplification of a Response Function by Data Transformation 503

12.3. Detecting and Exploiting Active and Inactive Factor Spaces for Multiple-Response Data 509

12.4. Exploring Canonical Factor Spaces 513

12.5. From Empiricism to Mechanism 518

12.6. Uses of RSM 526

Appendix 12A. Average Variance of ŷ 526

Appendix 12B. 528

References and Further Reading 530

Chapter 13 Designing Robust Products and Processes: An Introduction 539

13.1. Environmental Robustness 539

13.2. Robustness To Component Variation 549

Appendix 13A. A Mathematical Formulation for Environmental Robustness 556

Appendix 13B. Choice of Criteria 558

References and Further Reading 559

Chapter 14 Process Control, Forecasting, and Time Series: An Introduction 565

14.1. Process Monitoring 565

14.2. The Exponentially Weighted Moving Average 569

14.3. The CuSum Chart 574

14.4. Process Adjustment 576

14.5. A Brief Look At Some Time Series Models and Applications 585

14.6. Using a Model to Make a Forecast 588

14.7. Intervention Analysis: A Los Angeles Air Pollution Example 593

References and Further Reading 595

Chapter 15 Evolutionary Process Operation 599

15.1. More than One Factor 602

15.2. Multiple Responses 606

15.3. The Evolutionary Process Operation Committee 607

References and Further Reading 608

Appendix Tables 611

Author Index 625

Subject Index 629

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