Author

# William G. Hunter

Bio: William G. Hunter is an academic researcher from University of Wisconsin-Madison. The author has contributed to research in topic(s): Model building & Design of experiments. The author has an hindex of 31, co-authored 61 publication(s) receiving 15065 citation(s).

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01 Jan 1978

TL;DR: This paper used external reference distribution to compare two means and compared more than two treatment means, and compared the effects of different means and treatments in the United States of America, using the Declaration of Independence as an example.

Abstract: Science and Statistics. COMPARING TWO TREATMENTS. Use of External Reference Distribution to Compare Two Means. Random Sampling and the Declaration of Independence. Randomization and Blocking with Paired Comparisons. Significance Tests and Confidence Intervals for Means, Variances, Proportions and Frequences. COMPARING MORE THAN TWO TREATMENTS. Experiments to Compare k Treatment Means. Randomized Block and Two--Way Factorial Designs. Designs with More Than One Blocking Variable. MEASURING THE EFFECTS OF VARIABLES. Empirical Modeling. Factorial Designs at Two Levels. More Applications of Factorial Designs. Fractional Factorial Designs at Two Levels. More Applications of Fractional Factorial Designs. BUILDING MODELS AND USING THEM. Simple Modeling with Least Squares (Regression Analysis). Response Surface Methods. Mechanistic Model Building. Study of Variation. Modeling Dependence: Times Series. Appendix Tables. Index.

4,118 citations

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2,727 citations

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2,627 citations

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01 Jan 2005

TL;DR: In this paper, the authors describe the learning process of statistical methods for the generation of knowledge and their application to the problem of statistical analysis of real-world data, and present several examples.

Abstract: 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 chi2nu 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 y. 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.

1,710 citations

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TL;DR: In this article, the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution, and algorithms are presented for constructing these minimum aberration designs.

Abstract: For studying k variables in N runs, all 2 k–p designs of maximum resolution are not equally good. In this paper the concept of aberration is proposed as a way of selecting the best designs from those with maximum resolution. Algorithms are presented for constructing these minimum aberration designs.

415 citations

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21 Mar 2002

TL;DR: An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data is as discussed by the authors, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced.

Abstract: An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature The book is supported by a website that provides all data sets, questions for each chapter and links to software

9,098 citations

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Hewlett-Packard

^{1}TL;DR: This book offers a complete blueprint for structuring projects to achieve rapid completion with high engineering productivity during the research and development phase to ensure that high quality products can be made quickly and at the lowest possible cost.

Abstract: From the Publisher:
Phadke was trained in robust design techniques by Genichi Taguchi, the mastermind behind Japanese quality manufacturing technologies and the father of Japanese quality control. Taguchi's approach is currently under consideration to be adopted as a student protocol with the US govrnment. The foreword is written by Taguchi. This book offers a complete blueprint for structuring projects to achieve rapid completion with high engineering productivity during the research and development phase to ensure that high quality products can be made quickly and at the lowest possible cost. Some topics covered are: orthogonol arrays, how to construct orthogonal arrays, computer-aided robutst design techniques, dynamic systems design methods, and more.

3,862 citations

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TL;DR: In this paper, the complex mechanisms of Fenton and Fenton-like reactions and the important factors influencing these reactions, from both a fundamental and practical perspective, in applications to water and soil treatment, are discussed.

Abstract: Fenton chemistry encompasses reactions of hydrogen peroxide in the presence of iron to generate highly reactive species such as the hydroxyl radical and possibly others. In this review, the complex mechanisms of Fenton and Fenton-like reactions and the important factors influencing these reactions, from both a fundamental and practical perspective, in applications to water and soil treatment, are discussed. The review covers modified versions including the photoassisted Fenton reaction, use of chelated iron, electro-Fenton reactions, and Fenton reactions using heterogeneous catalysts. Sections are devoted to nonclassical pathways, by-products, kinetics and process modeling, experimental design methodology, soil and aquifer treatment, use of Fenton in combination with other advanced oxidation processes or biodegradation, economic comparison with other advanced oxidation processes, and case studies.

2,745 citations

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TL;DR: In this paper, alternative formulations of Levene's test statistic for equality of variances are found to be robust under nonnormality, using more robust estimators of central location in place of the mean.

Abstract: Alternative formulations of Levene's test statistic for equality of variances are found to be robust under nonnormality. These statistics use more robust estimators of central location in place of the mean. They are compared with the unmodified Levene's statistic, a jackknife procedure, and a χ2 test suggested by Layard which are all found to be less robust under nonnormality.

2,385 citations

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01 Apr 2004

TL;DR: In this paper, the authors present a method for sensitivity analysis of a fish population model using Monte Carlo filtering and variance-based methods, which is based on the Bayesian uncertainty estimation.

Abstract: PREFACE. 1. A WORKED EXAMPLE. 1.1 A simple model. 1.2 Modulus version of the simple model. 1.3 Six--factor version of the simple model. 1.4 The simple model 'by groups'. 1.5 The (less) simple correlated--input model. 1.6 Conclusions. 2. GLOBAL SENSITIVITY ANALYSIS FOR IMPORTANCE ASSESSMENT. 2.1 Examples at a glance. 2.2 What is sensitivity analysis? 2.3 Properties of an ideal sensitivity analysis method. 2.4 Defensible settings for sensitivity analysis. 2.5 Caveats. 3. TEST CASES. 3.1 The jumping man. Applying variance--based methods. 3.2 Handling the risk of a financial portfolio: the problem of hedging. Applying Monte Carlo filtering and variance--based methods. 3.3 A model of fish population dynamics. Applying the method of Morris. 3.4 The Level E model. Radionuclide migration in the geosphere. Applying variance--based methods and Monte Carlo filtering. 3.5 Two spheres. Applying variance based methods in estimation/calibration problems. 3.6 A chemical experiment. Applying variance based methods in estimation/calibration problems. 3.7 An analytical example. Applying the method of Morris. 4. THE SCREENING EXERCISE. 4.1 Introduction. 4.2 The method of Morris. 4.3 Implementing the method. 4.4 Putting the method to work: an analytical example. 4.5 Putting the method to work: sensitivity analysis of a fish population model. 4.6 Conclusions. 5. METHODS BASED ON DECOMPOSING THE VARIANCE OF THE OUTPUT. 5.1 The settings. 5.2 Factors Prioritisation Setting. 5.3 First--order effects and interactions. 5.4 Application of Si to Setting 'Factors Prioritisation'. 5.5 More on variance decompositions. 5.6 Factors Fixing (FF) Setting. 5.7 Variance Cutting (VC) Setting. 5.8 Properties of the variance based methods. 5.9 How to compute the sensitivity indices: the case of orthogonal input. 5.9.1 A digression on the Fourier Amplitude Sensitivity Test (FAST). 5.10 How to compute the sensitivity indices: the case of non--orthogonal input. 5.11 Putting the method to work: the Level E model. 5.11.1 Case of orthogonal input factors. 5.11.2 Case of correlated input factors. 5.12 Putting the method to work: the bungee jumping model. 5.13 Caveats. 6. SENSITIVITY ANALYSIS IN DIAGNOSTIC MODELLING: MONTE CARLO FILTERING AND REGIONALISED SENSITIVITY ANALYSIS, BAYESIAN UNCERTAINTY ESTIMATION AND GLOBAL SENSITIVITY ANALYSIS. 6.1 Model calibration and Factors Mapping Setting. 6.2 Monte Carlo filtering and regionalised sensitivity analysis. 6.2.1 Caveats. 6.3 Putting MC filtering and RSA to work: the problem of hedging a financial portfolio. 6.4 Putting MC filtering and RSA to work: the Level E test case. 6.5 Bayesian uncertainty estimation and global sensitivity analysis. 6.5.1 Bayesian uncertainty estimation. 6.5.2 The GLUE case. 6.5.3 Using global sensitivity analysis in the Bayesian uncertainty estimation. 6.5.4 Implementation of the method. 6.6 Putting Bayesian analysis and global SA to work: two spheres. 6.7 Putting Bayesian analysis and global SA to work: a chemical experiment. 6.7.1 Bayesian uncertainty analysis (GLUE case). 6.7.2 Global sensitivity analysis. 6.7.3 Correlation analysis. 6.7.4 Further analysis by varying temperature in the data set: fewer interactions in the model. 6.8 Caveats. 7. HOW TO USE SIMLAB. 7.1 Introduction. 7.2 How to obtain and install SIMLAB. 7.3 SIMLAB main panel. 7.4 Sample generation. 7.4.1 FAST. 7.4.2 Fixed sampling. 7.4.3 Latin hypercube sampling (LHS). 7.4.4 The method of Morris. 7.4.5 Quasi--Random LpTau. 7.4.6 Random. 7.4.7 Replicated Latin Hypercube (r--LHS). 7.4.8 The method of Sobol'. 7.4.9 How to induce dependencies in the input factors. 7.5 How to execute models. 7.6 Sensitivity analysis. 8. FAMOUS QUOTES: SENSITIVITY ANALYSIS IN THE SCIENTIFIC DISCOURSE. REFERENCES. INDEX.

2,296 citations