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Fundamentals of Statistical Experimental Design and Analysis


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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 SandiaNational Laboratories where he was a statistical consultant,manager, and senior scientist. He is a Fellow of the AmericanStatistical Association, a former Editor of Technometrics,and a recipient of the American Society for Quality sBrumbaugh Award. He holds a Ph.D. in statistics from Oklahoma StateUniversity.


"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)

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