fundamentals of statistical experimental design and analysis

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Fundamentals of Statistical Experimental Design and Analysis 1st Edition

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Professionals in all areas – business; government; the physical, life, and social sciences; engineering; medicine, etc. – benefit from using statistical experimental design to better understand their worlds and then use that understanding to improve the products, processes, and programs they are responsible for. This book aims to provide the practitioners of tomorrow with a memorable, easy to read, engaging guide to statistics and experimental design. This book uses examples, drawn from a variety of established texts, and embeds them in a business or scientific context, seasoned with a dash of humor, to emphasize the issues and ideas that led to the experiment and the what-do-we-do-next? steps after the experiment. Graphical data displays are emphasized as means of discovery and communication and formulas are minimized, with a focus on interpreting the results that software produce. The role of subject-matter knowledge, and passion, is also illustrated. The examples do not require specialized knowledge, and the lessons they contain are transferrable to other contexts.   Fundamentals of Statistical Experimental Design and Analysis introduces the basic elements of an experimental design, and the basic concepts underlying statistical analyses. Subsequent chapters address the following families of experimental designs:

• Completely Randomized designs, with single or multiple treatment factors, quantitative or qualitative
• Randomized Block designs
• Latin Square designs
• Split-Unit designs
• Repeated Measures designs
• Robust designs
• Optimal designs
• ISBN-10 1118954637
• ISBN-13 978-1118954638
• Edition 1st
• Publisher Wiley
• Publication date September 8, 2015
• Language English
• Dimensions 7.7 x 0.72 x 10 inches
• Print length 272 pages
• See all details

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Editorial Reviews

“Easterling sets out to provide a textbook for an undergraduate course in applied experimental design for a mixed group of students. He succeeds admirably. Although many excellent texts on experimental design exist for statistics students, most are too technical for mixed disciplines. This book covers only basic designs but with extensive discussion of matters other textbooks elide or ignore. Examples from respected textbooks are elaborated to show the reasoning underpinning experimentation and the need to combine statistical and subject-area knowledge … this is a book that can be enjoyed by students being taught how and why to work with a statistician, and by statisticians who want to work more productively in teams with other disciplines.” Significance, 14:6 (2017)

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Professionals in all areas – business; government; the physical, life, and social sciences; engineering; medicine, etc. – benefit from using statistical experimental design to better understand their worlds and then use that understanding to improve the products, processes, and programs they are responsible for. This book aims to provide the practitioners of tomorrow with a memorable, easy to read, engaging guide to statistics and experimental design. This book uses examples, drawn from a variety of established texts, and embeds them in a business or scientific context, seasoned with a dash of humor, to emphasize the issues and ideas that led to the experiment and the what-do-we-do-next? steps after the experiment. Graphical data displays are emphasized as means of discovery and communication and formulas are minimized, with a focus on interpreting the results that software produce. The role of subject-matter knowledge, and passion, is also illustrated. The examples do not require specialized knowledge, and the lessons they contain are transferrable to other contexts. Fundamentals of Statistical Experimental Design and Analysis introduces the basic elements of an experimental design, and the basic concepts underlying statistical analyses. Subsequent chapters address the following families of experimental designs:

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• Publisher ‏ : ‎ Wiley; 1st edition (September 8, 2015)
• Language ‏ : ‎ English
• Hardcover ‏ : ‎ 272 pages
• ISBN-10 ‏ : ‎ 1118954637
• ISBN-13 ‏ : ‎ 978-1118954638
• Item Weight ‏ : ‎ 1.65 pounds
• Dimensions ‏ : ‎ 7.7 x 0.72 x 10 inches
• #2,379 in Statistics (Books)
• #5,494 in Probability & Statistics (Books)
• #18,900 in Core

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SIMILAR ITEMS (based on metadata)

Fundamentals of Statistical Experimental Design and Analysis

Robert G. Easterling

Cedar Crest, New Mexico, USA

This edition first published 2015 © 2015 John Wiley & Sons, Ltd

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For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com.

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All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher.

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Library of Congress Cataloging-in-Publication Data

Easterling, Robert G.  Fundamentals of statistical experimental design and analysis / Robert G. Easterling, Cedar Crest, New Mexico, USA.   pages cm  Includes bibliographical references and index.

ISBN 978-1-118-95463-8 (cloth) 1. Mathematical statistics–Study and teaching. 2. Mathematical statistics–Anecdotes. 3. Experimental design. I. Title. QA276.18.E27 2015 519.5′7–dc23

    2015015481

A catalogue record for this book is available from the British Library.

Dedications

Experimental Design Mentors, Oklahoma State University David Weeks Bob Morrison

Statistical Consulting Mentor, Sandia National Laboratories Dick Prairie

I have a dream: that professionals in all areas—business; government; the physical, life, and social sciences; engineering; medicine; and others—will increasingly use statistical experimental design to better understand their worlds and to use that understanding to improve the products, processes, and programs they are responsible for. To this end, these professionals need to be inspired and taught, early, to conduct well-conceived and well-executed experiments and then properly extract, communicate, and act on information generated by the experiment. This learning can and should happen at the undergraduate level—in a way that carries over into a student’s eventual career. This text is aimed at fulfilling that goal.

Many excellent statistical texts on experimental design and analysis have been written by statisticians, primarily for students in statistics. These texts are generally more technical and more comprehensive than is appropriate for a mixed-discipline undergraduate audience and a one-semester course, the audience and scope this text addresses. Such texts tend to focus heavily on statistical analysis, for a catalog of designs. In practice, however, finding and implementing an experimental design capable of answering questions of importance are often where the battle is won. The data from a well-designed experiment may almost analyze themselves—often graphically. Rising generations of statisticians and the professionals with whom they will collaborate need more training on the design process than may be provided in graduate-level statistical texts.

Additionally, there are many experimental design texts, typically used in research methods courses in individual disciplines, that focus on one area of application. This book is aimed at a more heterogeneous collection of students who may not yet have chosen a particular career path. The examples have been chosen to be understandable without any specialized knowledge, while the basic ideas are transferable to particular situations and applications a student will subsequently encounter.

Successful experiments require subject-matter knowledge and passion and the statistical tools to translate that knowledge and passion into useful information. Archie Bunker, in the TV series, All in the Family , once told his son-in-law (approximately and with typical inadvertent profundity), “Don’t give me no sta s tistics (sic), Meathead. I want facts!” Statistical texts naturally focus on “ sta s tistics ”: here’s how to calculate a regression line, a confidence interval, an analysis of variance table, etc. For the professional in fields other than statistics, those methods are only a means to an end: revealing and understanding new facts pertinent to his or her area of interest. This text strives to make the connection between facts and statistics . Students should see from the beginning the connection between the statistics and the wider business or scientific context served by those statistics.

To achieve this goal, I tell stories about experiments, and bring in appropriate analyses, graphical and mathematical, as needed to move the stories along. I try to describe the situation that led to the experiment, what was learned, and what might happen after the experiment: “Fire the quality manager! Give the worthy statistician a bonus!” Experimental results need to be communicated in clear and convincing ways, so I emphasize graphical displays more than is often done in experimental design texts.

My stories are built around examples in statistical texts on experimental design, especially examples found in the classic text, Statistics for Experimenters , by Box, Hunter, and Hunter (1978, 2005). This “BHH” text has been on my desk since the first edition came out. I have taught several university classes based on it and have incorporated some of its material into my introductory statistics classes. Most of the examples are simple at first glance, but I have found it useful to (shamelessly) expand the stories in ways that address more of the design issues and more of the what-do-we-do-next issues. I try to make the stories provocative and entertaining because real-life experimentation is provocative and entertaining. I want the issues and concepts to be discussable by an interdisciplinary group of students and the lessons to be transferable to a student’s particular interests, with enough staying power to affect the student’s subsequent career. An underlying theme is that it is subject-matter enthusiasms that give rise to experiments, shape their design, and guide actions based on the findings. Statistical experimental design and data analysis methods facilitate and enhance the whole process. In short, statistics is a team sport. This text tries to demonstrate that.

In 1974, I taught at the University of Wisconsin and had the opportunity to attend the renowned Monday night “beer seminars” in the basement of the late Professor George Box’s home. He would invite researchers in to discuss their work, and the evening would turn into a grand consulting session among George, the researcher, and the students and faculty in attendance. The late Bill Hunter, also a professor in the Statistics Department and an innovative teacher of experimental design, was often a participant. I learned a lot in those sessions and hope that the atmosphere of those Monday night consulting sessions is reflected in the stories I have created here. The other H in BHH is J. Stuart Hunter, also an innovator in the teaching of experimental design; his presentations and articles have influenced me greatly, and his support for this book is especially valued. He puts humor into statistics that nobody would believe exists. I attended several Gordon Research Conferences at which B, H, and H all generated a lot of fun. Statistics can be fun. I have fun being a statistician and I have tried to spice this book with a sense of fun. (Please note that this book’s title begins with fun.)

In this book, mathematical detail takes a backseat to the stories and the pictures. Experimental design is not just for the mathematically inclined. I rely on software to do the analyses, and I focus on the story, not formulas. Once you understand the structure of a basic analysis of variance, I believe you can rely on software (and maybe a friendly, local statistician) to calculate an ANOVA table of the sort considered in this text. Thus, I do not give formulas for sums of squares for every design considered. Ample references are just a quick Google or Wikipedia search away for the mathematically intrigued students or instructors so inclined. I give formulas for standard errors and confidence intervals where needed. I would be pleased if class discussions and questions, and alternate stories, led to displays and analyses not covered in my stories.

To offset my expanded stories, I limit the scope of this text’s topics to what I think is appropriate for an introductory course. I indicate and reference possible extensions beyond the text’s coverage. Individual instructors can tailor their excursions into such areas in ways that fit their students. This text can best be used by instructors with experience in designing experiments, analyzing the resulting data, and working with collaborators or clients to develop next steps. They can usefully supplement my stories with theirs.

Chapter-end assignments emphasize the experimental design process, not computational exercises. I want students to pursue their passions and design experiments that could illuminate issues of interest to them. I want them to think about the displays and analyses they would use more than I want them to practice turning the crank on somebody else’s data. Ideally, I would like for these exercises to be worked by two- or three-person teams, as in the real-world environment a student will encounter after college. (My ideal class makeup would be half statistics-leaning majors and half majors from a variety of other fields, and I would pair a stat major with a nonstat major to do assignments and projects.)

Existing texts contain an ample supply of analysis exercises that an instructor can choose from and assign, if desired. Some are listed at the end of this Preface. Individual instructors may or should have their own favorite texts and exercises. I would suggest only that each selected analysis exercise should be augmented by Analysis 1: Plot the data . These exercise resources are also useful windows on aspects of experimental design and analysis beyond the scope of this book that a student might want to pursue later in his studies or her career.

Software packages such as Minitab® also provide exercises. Teaching analysis methods in conjunction with software is also left to the individual instructor and campus resources. I use Minitab in most of my graphical displays and quantitative analyses, just because it suits my needs. Microsoft Excel® can also be used for many of the analyses and displays in this book. JMP® software covers basic analyses and provides more advanced capabilities that could be used and taught. Individual instructors should choose the software appropriate for their classrooms and campuses.

Projects provide another opportunity to experience and develop the ability to conceive, design, conduct, analyze, and communicate the results of experiments that students care about. I still recall my long-ago experiment to evaluate the effect of salt and sugar on water’s time to boil (not that boiling water was a youthful passion of mine, but getting an assignment done on time was). A four-burner kitchen stove was integral to the design. I cannot tell you the effects of salt and sugar on time to boil, but I was able to reject with certainty the hypothesis that “a watched pot never boils.” Again, I would encourage these projects to be done by small teams, rather than individually. Supplementary online material for the widely used text by Montgomery (2013) contains a large number of examples of student projects. I encourage students to seek inspiration from such examples. Much real-world research is motivated by a desire to extend or improve upon prior work in a particular field, so if students want to find better ways to design and test paper airplanes, more power to them. I also recommend oral and written reports by students to develop the communication skills that are so important in their subsequent careers. This is time well spent.

In-class experiments are another valuable learning tool. George Box, Bill Hunter, Stuart Hunter, and the Wisconsin program are innovators in this area. The second edition of BHH (Box, Hunter, and Hunter 2005) contains a case study of their popular paper-helicopter design problem. In my classes, I simplify the problem to a two- or three-factor design space to simplify the task and shorten the time required by this exercise.

This text provides in Chapter 3 enough of basic statistical concepts (estimation, significance tests, and confidence intervals), within the context of designed experiments, that a previous course in statistics should not be required. Again, I think that once concepts are understood, a student or working professional can understand and appreciate the application of those concepts to other situations. My hope is that this text will make it more likely that universities will offer an undergraduate (and beginning graduate)-level course in experimental design. This could be taught as a stand-alone course, or, as was the case when I taught at the University of Auckland, one course could have two parallel tracks: experimental design and survey sampling, taught by different instructors. This text should also be useful for short courses in business, industry, and government.

I am convinced that personal and organizational progress, and even national and global progress, depends on how well we, the people, individually and collectively, deal with data. The statistical design of experiments and analysis of the resulting data can greatly enhance our ability to learn from data. In George Box’s engagingly illustrated formulation (Box 2006), scientific progress occurs when intelligent, interested people intervene, experimentally, in processes to bring about potentially interesting events and then use their intelligence and the experimental results to better understand and improve those processes. My sincere hope is that this text will advance that cause.

• Box, G., (2006) Improving Almost Anything: Ideas and Essays , revised ed., John Wiley & Sons, Inc., New York.
• Box, G., Hunter, J., and Hunter, W. (1978, 2005) Statistics for Experimenters , 1st and 2nd eds., John Wiley & Sons, New York.
• Montgomery, D. (2009, 2013) Design and Analysis of Experiments , 7th and 8th eds., John Wiley & Sons, Inc., New York.

Statistical Software

JMP Statistical Discovery Software. jmp.com

Microsoft Excel. microsoftstore.com

Minitab Statistical Software. minitab.com

Sources for Student Exercises (in addition to the above references)

• Cobb, G. (1997) Design and Analysis of Experiments , Springer-Verlag, New York.
• Cochran, W. G., and Cox, G. M. (1957) Experimental Designs , John Wiley & Sons, Inc., New York.
• Ledolter, J., and Swersey, A. J. (2007) Testing 1-2-3: Experimental Design with Applications in Marketing and Service Operations . Stanford University Press, Stanford, CA.
• Morris, M. (2011) Design of Experiments: An Introduction Based on Linear Models , Chapman and Hall/CRC Press, New York.
• NIST/SEMATECH (2012) e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/
• Oehlert, G. W. (2000) A First Course in Design and Analysis of Experiments , Freeman & Company, New York.
• Wu, C.F., and Hamada, M. (2000). Experiments: Planning, Analysis, and Parameter Design Optimization , John Wiley & Sons, Inc., New York.

Acknowledgments

After my retirement from Sandia National Laboratories Vijay Nair, University of Michigan, invited me to teach an introductory course on experimental design at that campus. That experience and subsequent teaching opportunities at the University of Auckland, McMurry University, and the Naval Postgraduate School led to the development of class notes that evolved into this book. My wife, Susie, and I thoroughly enjoyed life as an itinerant Visiting Professor and greatly benefited from the stimulating environments provided by these universities.

I particularly want to thank the following authors for granting me permission to use examples from their texts: George Box and J. Stuart Hunter ( Statistics for Experimenters ); Johannes Ledolter, Arthur Swersey, and Gordon Bell ( Testing 1-2-3 : Experimental Design with Applications in Marketing and Service Operations ); Douglas Montgomery ( Design and Analysis of Experiments ); Chris Triggs (Sample Surveys and Experimental Designs); and George Milliken and Dallas Johnson ( Analysis of Messy Data , vol . I ., Designed Experiments ). Wiley’s reviewers provided insightful and helpful comments on the draft manuscript, and a review of the manuscript from a student’s perspective by Naveen Narisetty, University of Michigan, was especially valuable. Max Morris, Iowa State University, provided a very helpful sounding board throughout. I also am thankful to Prachi Sinha Sahay, Jo Taylor, and Kathryn Sharples of the editorial staff at John Wiley & Sons, and to Umamaheshwari Chelladurai and Prasanna Venkatakrishnan who shepherded this project through to publication.

Robert G. Easterling Cedar Crest, New Mexico

John Wiley & Sons Ltd for permission to use material from the following books:

• Statistics for Experimenters (Box, Hunter, and Hunter, 1978, 2005)
• Design and Analysis of Experiments , 5th ed. (Montgomery 2001)
• Chance Encounters (Wild and Seber, 2000)

Stanford University Press for permission to use material from:

• Testing 1-2-3 (Ledolter and Swersey, 2007)

Chapman and Hall/CRC Press for permission to use material from:

• Analysis of Messy Data Volume I: Designed Experiments , 2nd ed., (Milliken and Johnson, 2009)

Department of Statistics, University of Auckland, for permission to use material from:

• Sample Surveys and Experimental Designs (Scott and Triggs 2003)

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• Preface xiii
• Acknowledgments xix
• Credits xxi
• 1 Introduction 1
• Motivation: Why Experiment? 1
• Steps in an Experimental Program 2
• Planning and analysis 2
• Communication 3
• Subject ]Matter Passion 4
• Case Study 5
• Overview of Text 9
• Assignment 10
• References 10
• 2 Fundamentals of Experimental Design 11
• Introduction 11
• Experimental Structure 13
• Experimental units 13
• Blocks and block structures 15
• Treatments and treatment structures 17
• Response measurement 19
• Principles of Experimental Design 20
• Replication 21
• Randomization 22
• Blocking 24
• Assignment 27
• References 27
• 3 Fundamentals of Statistical Data Analysis 29
• Introduction 29
• Boys Shoes Experiment 30
• Experimental design 30
• Graphical displays 31
• Significance testing 34
• Probability and probability distributions 34
• Sign test 36
• Misinterpretation of P ]values 38
• Randomization test 39
• Normal distribution theory t ]test 40
• Summary and discussion: Significance tests 46
• Economic analysis: The bigger picture 48
• Statistical confidence intervals 50
• Discussion 53
• Why calculate statistical confidence limits? 54
• Sample size determination 54
• Tomato Fertilizer Experiment 56
• Experimental design 56
• Analysis 1: Plot the data 56
• The value of randomization 58
• The importance of ancillary data 59
• A New Tomato Experiment 59
• Analysis 1: Plot the data 59
• Significance tests 62
• Rank sum test 63
• Randomization test 64
• Normal theory t ]test 66
• Confidence intervals 69
• Determining the size of an experiment 71
• Comparing Standard Deviations 77
• Discussion 79
• Appendix 3.A The Binomial Distribution 79
• Appendix 3.B Sampling from a Normal Distribution 81
• Appendix 3.C Statistical Underpinnings 85
• Single sample 86
• Two samples 87
• Assignment 89
• References 89
• 4 Completely Randomized Design 91
• Introduction 91
• Design Issues 92
• CRD: Single Qualitative Factor 92
• Example: Market research 92
• Analysis of Variance 95
• Within ]group variation 96
• Among ]groups variation 97
• The F ]test 98
• Analysis of variance 99
• Discussion 100
• Results 101
• Testing the Assumptions of Equal Variances and Normality 103
• Confidence Intervals 103
• Inference 105
• Statistical Prediction Interval 105
• Example: Tomato Fertilizer Experiment Revisited 106
• Sizing a Completely Randomized Experiment 107
• CRD: Single Quantitative Factor 107
• Example: Growth rate of rats 108
• Graphical display 109
• Curve fit 109
• Analysis of variance 111
• Design Issues 113
• Enhanced Case Study: Power Window Gear Teeth 114
• Graphical display 117
• Discussion 120
• Assignment 120
• References 121
• 5 Completely Randomized Design with Multiple Treatment Factors 123
• Introduction 123
• Design Issues 124
• Example 1 (Two qualitative factors): Poisons and antidotes 124
• Analysis 1: Plot the data 126
• Eyeball analysis 126
• Interaction 128
• Generalizing the ANOVA for a CRD with two factors 131
• Antidote B versus Antidote D 132
• Estimation of effects 133
• Prediction intervals 135
• Probability estimation and tolerance intervals 136
• Further experiments 138
• Example 2 (Two quantitative factors): Ethanol blends and CO emissions 139
• Data displays 142
• Discussion 144
• Regression analysis and ANOVA 145
• Discussion 148
• Response Surface Designs 149
• Extensions: More than two treatment factors 150
• Example 3: Poison/antidote experiment extended 151
• Example 4: Ethanol experiment extended 154
• Special Case: Two ]Level Factorial Experiments 155
• Example 5: Pot production 156
• Analysis 1: Look at the data 158
• Analysis 2: Regression analysis 159
• Analysis 2: Stepwise regression 162
• Analysis 3: Effect sparsity and graphical analysis 162
• Fractional Two ]Level Factorials 167
• Example 6: E ]mail marketing 167
• One ]factor ]at ]a ]time designs 168
• Results: E ]mail experiment 170
• Example 7: Flower pot experiment revisited 171
• Extensions 175
• Assignment 175
• References 175
• 6 Randomized Complete Block Design 177
• Introduction 177
• Design Issues 178
• RBD with replication: Example 1 battery experiment 179
• Analysis 1: Plot the data 180
• Analysis of variance 181
• Reliability analysis 183
• Further analysis 184
• Bringing subject ]matter knowledge to bear 185
• Example 2: More tomato fertilizer experiments 187
• Example 3: More gear teeth experiments 188
• RBD with Single Replication 188
• Example 4: Penicillin production 189
• Components of variation 191
• Sizing a Randomized Block Experiment 194
• True Replication 195
• Example 5: Cookies 195
• Example 6: Battery experiment revisited 196
• Example 7: Boys shoes revisited 197
• Extensions of the RBD 199
• Multifactor treatments and blocks example: Penicillin experiment extended 199
• Example 8: A blocks ]only experiment
• textile production 201
• Analysis 1: Plot the data 201
• Discussion 202
• Balanced Incomplete Block Designs 203
• Example: Boys shoes revisited again 203
• Summary 205
• Assignment 205
• References 205
• 7 Other Experimental Designs 207
• Introduction 207
• Latin Square Design 208
• Example: Gasoline additives and car emissions 208
• Analysis 1: Plot the data 212
• Discussion 215
• Follow ]on experiments 216
• Exercise 216
• Extensions 217
• Split ]Unit Designs 218
• Example: Corrosion Resistance 220
• Analysis 1: Plot the data 222
• Discussion 228
• Repeated Measures Designs 230
• Example: Effects of drugs on heart rate 231
• Analysis 1: Plot the data 232
• Discussion 234
• Extensions 235
• Robust Designs 235
• Introduction 235
• Variance transmission 235
• Mathematical model: Robustness 238
• Concluding comments 239
• Optimal Designs 240
• Introduction 240
• Finding optimal experimental designs 240
• Design augmentation 242
• Assignment 243
• References 243
• (source: Nielsen Book Data)

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Fundamentals of Statistical Experimental Design and Analysis by Robert G. Easterling

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I have a dream: that professionals in all areas—business; government; the physical, life, and social sciences; engineering; medicine; and others—will increasingly use statistical experimental design to better understand their worlds and to use that understanding to improve the products, processes, and programs they are responsible for. To this end, these professionals need to be inspired and taught, early, to conduct well-conceived and well-executed experiments and then properly extract, communicate, and act on information generated by the experiment. This learning can and should happen at the undergraduate level—in a way that carries over into a student’s eventual career. This text is aimed at fulfilling that goal.

Many excellent statistical texts on experimental design and analysis have been written by statisticians, primarily for students in statistics. These texts are generally more technical and more comprehensive than is appropriate for a mixed-discipline undergraduate audience and a one-semester course, the audience and scope this text addresses. Such texts tend to focus heavily on statistical analysis, for a catalog of designs. In practice, however, finding and implementing an experimental design capable of answering questions of importance are often where the battle is won. The data from a well-designed experiment may almost analyze themselves—often graphically. Rising generations of statisticians and the professionals with whom they will collaborate need more ...

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