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.
Table of 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
