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.

Preface to the Second Edition.

Chapter 1. Catalizing the Generation of Knowledge.

1.1. The Learning Process.

1.2. Important Considerations.

1.3. The Experimenter’s Problem and Statistical Methods.

1.4. A Typical Investigation.

1.5. How to Use Statistical Techniques.

References and Further Reading.

Chapter 2. Basics: Probability, Parameters and Statistics.

2.1. Experimental Error.

2.2. Distributions.

2.3. Statistics and Parameters.

2.4. Measures of Location and Spread.

2.5. The Normal Distribution.

2.6. Normal Probability Plots.

2.7. Randomness and Random Variables.

2.8. Covariance and Correlation as Measures of Linear Dependence.

2.9. Student’s t Distribution.

2.10. Estimates of Parameters.

2.11. Random Sampling from a Normal Population.

2.12. The Chi-Square and F Distributions.

2.13. The Binomial Distribution.

2.14. The Poisson Distribution.

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

References and Further Reading.

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

3.1. Relevant Reference Sets and Distributions.

3.2. Randomized Paired Comparison Design: Boys’ Shoes Example.

3.3. Blocking and Randomization.

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

3.5. More on Significance Tests.

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

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

3.8. Contingency Tables and Tests of Association.

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

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

References and Further Reading.

Chapter 4. Comparing a Number of Entities: Randomized Blocks and Latin Squares.

4.1. Comparing k Treatments in a Fully Randomized Design.

4.2. Randomized Block Designs.

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

4.4. More than one blocking component: Latin Squares.

4.5. Balanced Incomplete Block Designs.

Appendix 4A. The Rationale for the Graphical ANOVA.

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

References and Further Reading.

Chapter 5. Factorial Designs at Two Levels: Advantages of Experimental Design.

5.1. Introduction.

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

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

5.4. A 23 Factorial Design: Pilot Plant Investigation.

5.5. Calculation of Main Effects.

5.6. Interaction Effects.

5.7. Genuine Replicate Runs.

5.8. Interpretation of Results.

5.9. The Table of Contrasts.

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

5.11. Eyeing the Data.

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

5.13. A 24 Factorial Design: Process Development Study.

5.14. Analysis Using Normal and Lenth Plots.

5.15. Other Models for Factorial Data.

5.16. Blocking the 2k Factorial Designs.

5.17. Learning by Doing.

5.18. Summary.

Appendix 5A. Blocking Larger Factorial Designs.

Appendix 5B. Partial Confounding.

References and Further Reading.

Chapter 6. Fraction Factorial Designs: Economy in Experimentation.

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

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

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

6.4. The Anatomy of the Half Fraction.

6.5. The 27−4III Design: A Bicycle Example.

6.6. Eight-Run Designs.

6.7. Using Table 6.6: An Illustration.

6.8. Sign Switching, Foldover, and Sequential Assembly.

6.9. An Investigation Using Multiple-Column Foldover.

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

6.11. Sixteen-Run Designs.

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

6.13. The 28−4 IV Nodal Sixteenth Fraction of a 28 Factorial.

6.14. The 215−11 III Nodal Design: The Sixty-Fourth Fraction of the 215 Factorial.

6.15. Constructing Other Two-Level Fractions.

6.16. Elimination of Block Effects.

References and Further Reading.

Chapter 7. Other Fractionals, Analysis and Choosing Follow-up Runs.

7.1. Plackett and Burman Designs.

7.2. Choosing Follow-Up Runs.

7.3. Justifications for the Use of Fractionals.

Appendix 7A. Technical Details.

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

Appendix 7C. Hall’s Orthogonal Designs.

References and Further Reading.

Chapter 8. Factorial Designs and Data Transformation.

8.1. A Two-Way (Factorial) Design.

8.2. Simplification and Increased Sensitivity from Transformation.

Appendix 8A. Rationale for Data Transformation.

Appendix 8B. Bartlett’s χ2ν for Testing Inhomogeneity of Variance.

References and Further Reading.

Chapter 9. Multiple Sources of Variation: Split Plot Designs, Variance Components and Error Transmission.

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

9.2. Split-Plot Designs.

9.3. Estimating Variance Components.

9.4. Transmission of Error.

References and Further Reading.

Chapter 10. Least Squares and Why You Need to Design Experiments.

10.1. Estimation With Least Squares.

10.2. The Versatility of Least Squares.

10.3. The Origins of Experimental Design.

10.4. Nonlinear Models.

Appendix 10A. Vector Representation of Statistical Concepts.

Appendix 10B. Matrix Version of Least Squares.

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

Appendix 10D. Unweighted and Weighted Least Squares.

References and Further Reading.

Chapter 11. Modelling Relationships, Sequential Assembly: Basics for Response Surface Methods.

11.1. Some Empirical Models.

11.2. Some Experimental Designs and the Design Information Function.

11.3. Is the Surface Sufficiently Well Estimated?

11.4. Sequential Design Strategy.

11.5. Canonical Analysis.

11.6. Box–Behnken Designs.

References and Further Reading.

Chapter 12. Some Applications of Response Surface Methods.

12.1. Iterative Experimentation To Improve a Product Design.

12.2. Simplification of a Response Function by Data Transformation.

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

12.4. Exploring Canonical Factor Spaces.

12.5. From Empiricism to Mechanism.

12.6. Uses of RSM.

Appendix 12A. Average Variance of ˆy.

Appendix 12B.

References and Further Reading.

Chapter 13. Designing Robust Products: An Introduction.

13.1. Environmental Robustness.

13.2. Robustness To Component Variation.

Appendix 13A. A Mathematical Formulation for Environmental Robustness.

Appendix 13B. Choice of Criteria.

References and Further Reading.

Chapter 14. Process Control, Forecasting and Times Series: An Introduction.

14.1. Process Monitoring.

14.2. The Exponentially Weighted Moving Average.

14.3. The CuSum Chart.

14.4. Process Adjustment.

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

14.6. Using a Model to Make a Forecast.

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

References and Further Reading.

Chapter 15. Evolutionary Process Operation.

15.1. More than One Factor.

15.2. Multiple Responses.

15.3. The Evolutionary Process Operation Committee.

References and Further Reading.

Appendix Tables.

Author Index.

Subject Index.

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; statistician in residence at the University of Wisconsin; and is the founding editor of Technometrics.

The late WILLIAM G. HUNTER, PhD, was Professor of Statistics and Engineering at the University of Wisconsin–Madison.