Fundamentals of Statistical Experimental Design and Analysis

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.

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