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
Written in an accessible, student-friendly style, this book is suitable for a general audience and particularly for those professionals seeking to improve and apply their understanding of experimental design.
Table of Contents:
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
Control 26
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
ANOVA 119
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
ANOVA 130
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
ANOVA 214
Discussion 215
Follow?]on experiments 216
Exercise 216
Extensions 217
Split?]Unit Designs 218
Example: Corrosion Resistance 220
Analysis 1: Plot the data 222
ANOVA 225
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
Index 245
About the Author :
Robert G. Easterling. Dr. Easterling is retired from Sandia National Laboratories where he was a statistical consultant, manager, and senior scientist. He is a Fellow of the American Statistical Association, a former Editor of Technometrics, and a recipient of the American Society for Quality’s Brumbaugh Award. He holds a Ph.D. in statistics from Oklahoma State University.
Review :
“This is an interesting and very useful book that explains the basic concepts and fundamentals of statistical experimental design and analysis to its readers in an easy-to-understand and accessible style”……” Rather than presenting the statistical design of experiments as a cut-and-dried subject, the author spices up this book with a sense of humour and fun”…..” Students, professionals, and researchers will find it interesting. It is a welcome addition to the statistics market” D. V. Chopra, MathSciNet, Aug 2017
“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)
