实验设计和分析 英文版PDF电子书下载

1．Principles and Techniques 1

1.1．Design:Basic Principles and Techniques 1

1.1.1．The Art of Experimentation 1

1.1.2．Replication 2

1.1.3．Blocking 3

1.1.4．Randomization 3

1.2．Analysis:Basic Principles and Techniques 5

2．Planning Experiments 7

2.1．Introduction 7

2.2．A Checklist for Planning Experiments 7

2.3．A Real Experiment—Cotton-Spinning Experiment 14

2.4．Some Standard Experimental Designs 17

2.4.1．Completely Randomized Designs 18

2.4.2．Block Designs 18

2.4.3．Designs with Two or More Blocking Factors 19

2.4.4．Split-Plot Designs 21

2.5．More Real Experiments 22

2.5.1．Soap Experiment 22

2.5.2．Battery Experiment 26

2.5.3．Cake-Baking Experiment 29

Exercises 31

3．Designs with One Source of Variation 33

3.1．Introduction 33

3.2．Randomization 34

3.3．Model for a Completely Randomized Design 35

3.4．Estimation of Parameters 37

3.4.1．Estimable Functions of Parameters 37

3.4.2．Notation 37

3.4.3．Obtaining Least Squares Estimates 38

3.4.4．Properties of Least Squares Estimators 40

3.4.5．Estimation of σ2 42

3.4.6．Confidence Bound for σ2 43

3.5．One-Way Analysis of Variance 44

3.5.1．Testing Equality of Treatment Effects 44

3.5.2．Use of p-Values 48

3.6．Sample Sizes 49

3.6.1．Expected Mean Squares for Treatments 50

3.6.2．Sample Sizes Using Power of a Test 51

3.7．A Real Experiment—Soap Experiment,Continued 53

3.7.1．Checklist,Continued 53

3.7.2．Data Collection and Analysis 54

3.7.3．Discussion by the Experimenter 56

3.7.4．Further Observations by the Experimenter 56

3.8．Using SAS Software 57

3.8.1．Randomization 57

3.8.2．Analysis of Variance 58

Exercises 61

4．Inferences for Contrasts and Treatment Means 67

4.1．Introduction 67

4.2．Contrasts 68

4.2.1．Pairwise Comparisons 69

4.2.2．Treatment Versus Control 70

4.2.3．Difference of Averages 70

4.2.4．Trends 71

4.3．Individual Contrasts and Treatment Means 73

4.3.1．Confidence Interval for a Single Contrast 73

4.3.2．Confidence Interval for a Single Treatment Mean 75

4.3.3．Hypothesis Test for a Single Contrast or Treatment Mean 75

4.4．Methods of Multiple Comparisons 78

4.4.1．Multiple Confidence Intervals 78

4.4.2．Bonferroni Method for Preplanned Comparisons 80

4.4.3．Scheffé Method of Multiple Comparisons 83

4.4.4．Tukey Method for All Pairwise Comparisons 85

4.4.5．Dunnett Method for Treatment-Versus-Control Comparisons 87

4.4.6．Hsu Method for Multiple Comparisons with the Best Treatment 89

4.4.7．Combination of Methods 91

4.4.8．Methods Not Controlling Experimentwise Error Rate 92

4.5．Sample Sizes 92

4.6．Using SAS Software 94

4.6.1．Inferences on Individual Contrasts 94

4.6.2．Multiple Comparisons 96

Exercises 97

5．Checking Model Assumptions 103

5.1．Introduction 103

5.2．Strategy for Checking Model Assumptions 104

5.2.1．Residuals 104

5.2.2．Residual Plots 105

5.3．Checking the Fit of the Model 107

5.4．Checking for Outliers 107

5.5．Checking Independence of the Error Terms 109

5.6．Checking the Equal Variance Assumption 111

5.6.1．Detection of Unequal Variances 112

5.6.2．Data Transformations to Equalize Variances 113

5.6.3．Analysis with Unequal Error Variances 116

5.7．Checking the Normality Assumption 119

5.8．Using SAS Software 122

5.8.1．Using SAS to Generate Residual Plots 122

5.8.2．Transforming the Data 126

Exercises 127

6．Experiments with Two Crossed Treatment Factors 135

6.1．Introduction 135

6.2．Models and Factorial Effects 136

6.2.1．The Meaning of Interaction 136

6.2.2．Models for Two Treatment Factors 138

6.2.3．Checking the Assumptions on the Model 140

6.3．Contrasts 141

6.3.1．Contrasts for Main Effects and Interactions 141

6.3.2．Writing Contrasts as Coefficient Lists 143

6.4．Analysis of the Two-Way Complete Model 145

6.4.1．Least Squares Estimators for the Two-Way Complete Model 146

6.4.2．Estimation of σ2 for the Two-Way Complete Model 147

6.4.3．Multiple Comparisons for the Complete Model 149

6.4.4．Analysis of Variance for the Complete Model 152

6.5．Analysis of the Two-Way Main-Effects Model 158

6.5.1．Least Squares Estimators for the Main-Effects Model 158

6.5.2．Estimation of σ2 in the Main-Effects Model 162

6.5.3．Multiple Comparisons for the Main-Effects Model 163

6.5.4．Unequal Variances 165

6.5.5．Analysis of Variance for Equal Sample Sizes 165

6.5.6．Model Building 168

6.6．Calculating Sample Sizes 168

6.7．Small Experiments 169

6.7.1．One Observation per Cell 169

6.7.2．Analysis Based on Orthogonal Contrasts 169

6.7.3．Tukey's Test for Additivity 172

6.7.4．A Real Experiment—Air Velocity Experiment 173

6.8．Using SAS Software 175

6.8.1．Contrasts and Multiple Comparisons 177

6.8.2．Plots 181

6.8.3．One Observation per Cell 182

Exercises 183

7．Several Crossed Treatment Factors 193

7.1．Introduction 193

7.2．Models and Factorial Effects 194

7.2.1．Models 194

7.2.2．The Meaning of Interaction 195

7.2.3．Separability of Factorial Effects 197

7.2.4．Estimation of Factorial Contrasts 199

7.3．Analysis—Equal Sample Sizes 201

7.4．A Real Experiment—Popcorn-Microwave Experiment 205

7.5．One Observation per Cell 211

7.5.1．Analysis Assuming That Certain Interaction Effects Are Negligible 211

7.5.2．Analysis Using Normal Probability Plot of Effect Estimates 213

7.5.3．Analysis Using Confidence Intervals 215

7.6．Design for the Control of Noise Variability 217

7.6.1．Analysis of Design-by-Noise Interactions 218

7.6.2．Analyzing the Effects of Design Factors on Variability 221

7.7．Using SAS Software 223

7.7.1．Normal Probability Plots of Contrast Estimates 224

7.7.2．Voss-Wang Confidence Interval Method 224

7.7.3．Identification of Robust Factor Settings 226

7.7.4．Experiments with Empty Cells 227

Exercises 231

8．Polynomial Regression 243

8.1．Introduction 243

8.2．Models 244

8.3．Least Squares Estimation(Optional) 248

8.3.1．Normal Equations 248

8.3.2．Least Squares Estimates for Simple Linear Regression 248

8.4．Test for Lack of Fit 249

8.5．Analysis of the Simple Linear Regression Model 251

8.6．Analysis of Polynomial Regression Models 255

8.6.1．Analysis of Variance 255

8.6.2．Confidence Intervals 257

8.7．Orthogonal Polynomials and Trend Contrasts(Optional) 258

8.7.1．Simple Linear Regression 258

8.7.2．Quadratic Regression 260

8.7.3．Comments 261

8.8．A Real Experiment—Bean-Soaking Experiment 262

8.8.1．Checklist 262

8.8.2．One-Way Analysis of Variance and Multiple Comparisons 264

8.8.3．Regression Analysis 267

8.9．Using SAS Software 268

Exercises 273

9．Analysis of Covariance 277

9.1．Introduction 277

9.2．Models 278

9.2.1．Checking Model Assumptions and Equality of Slopes 279

9.2.2．Model Extensions 279

9.3．Least Squares Estimates 280

9.3.1．Normal Equations(Optional) 280

9.3.2．Least Squares Estimates and Adjusted Treatment Means 281

9.4．Analysis of Covariance 282

9.5．Treatment Contrasts and Confidence Intervals 286

9.5.1．Individual Confidence Intervals 286

9.5.2．Multiple Coinparisons 287

9.6．Using SAS Software 288

Exercises 292

10．Complete Block Designs 295

10.1．Introduction 295

10.2．Blocks,Noise Factors or Covariates? 296

10.3．Design Issues 297

10.3.1．Block Sizes 297

10.3.2．Complete Block Design Definitions 298

10.3.3．The Randomized Complete Block Design 299

10.3.4．The General Complete Block Design 300

10.3.5．How Many Observations? 301

10.4．Analysis of Randomized Complete Block Designs 301

10.4.1．Model and Analysis of Variance 301

10.4.2．Multiple Comparisons 305

10.5．A Real Experiment—Cotton-Spinning Experiment 306

10.5.1．Design Details 306

10.5.2．Sample-Size Calculation 307

10.5.3．Analysis of the Cotton-Spinning Experiment 307

10.6．Analysis of General Complete Block Designs 309

10.6.1．Model and Analysis of Variance 309

10.6.2．Multiple Comparisons for the General Complete Block Design 312

10.6.3．Sample-Size Calculations 315

10.7．Checking Model Assumptions 316

10.8．Factorial Experiments 317

10.9．Using SAS Software 320

Exercises 324

11．Incomplete Block Designs 339

11.1．Introduction 339

11.2．Design Issues 340

11.2.1．Block Sizes 340

11.2.2．Design Plans and Randomization 340

11.2.3．Estimation of Contrasts(Optional) 342

11.2.4．Balanced Incomplete Block Designs 343

11.2.5．Group Divisible Designs 345

11.2.6．Cyclic Designs 346

11.3．Analysis of General Incomplete Block Designs 348

11.3.1．Contrast Estimators and Multiple Comparisons 348

11.3.2．Least Squares Estimation(Optional) 351

11.4．Analysis of Balanced Incomplete Block Designs 354

11.4.1．Multiple Comparisons and Analysis of Variance 354

11.4.2．A Real Experiment—Detergent Experiment 355

11.5．Analysis of Group Divisible Designs 360

11.5.1．Multiple Comparisons and Analysis of Variance 360

11.6．Analysis of Cyclic Designs 362

11.7．A Real Experiment—Plasma Experiment 362

11.8．Sample Sizes 368

11.9．Factorial Experiments 369

11.9.1．Factorial Structure 369

11.10．Using SAS Software 372

11.10.1．Analysis of Variance and Estimation of Contrasts 372

11.10.2．Plots 377

Exercises 378

12．Designs with Two Blocking Factors 387

12.1．Introduction 387

12.2．Design Issues 388

12.2.1．Selection and Randomization of Row-Column Designs 388

12.2.2．Latin Square Designs 389

12.2.3．Youden Designs 391

12.2.4．Cyclic and Other Row-Column Designs 392

12.3．Model for a Row-Column Design 394

12.4．Analysis of Row-Column Designs(Optional) 395

12.4.1．Least Squares Estimation(Optional) 395

12.4.2．Solution for Complete Column Blocks(Optional) 397

12.4.3．Formula for ssE(Optional) 398

12.4.4．Analysis of Variance for a Row-Column Design(Optional) 399

12.4.5．Confidence Intervals and Multiple Comparisons 401

12.5．Analysis of Latin Square Designs 401

12.5.1．Analysis of Variance for Latin Square Designs 401

12.5.2．Confidence Intervals for Latin Square Designs 403

12.5.3．How Many Observations? 405

12.6．Analysis of Youden Designs 406

12.6.1．Analysis of Variance for Youden Designs 406

12.6.2．Confidence Intervals for Youden Designs 407

12.6.3．How Many Observations? 407

12.7．Analysis of Cyclic and Other Row-Column Designs 408

12.8．Checking the Assumptions on the Model 409

12.9．Factorial Experiments in Row-Column Designs 410

12.10．Using SAS Software 410

12.10.1．Factorial Model 413

12.10.2．Plots 415

Exercises 415

13．Confounded Two-Level Factorial Experiments 421

13.1．Introduction 421

13.2．Single replicate factorial experiments 422

13.2.1．Coding and notation 422

13.2.2．Confounding 422

13.2.3．Analysis 423

13.3．Confounding Using Contrasts 424

13.3.1．Contrasts 424

13.3.2．Experiments in Two Blocks 425

13.3.3．Experiments in Four Blocks 430

13.3.4．Experiments in Eight Blocks 432

13.3.5．Experiments in More Than Eight Blocks 433

13.4．Confounding Using Equations 433

13.4.1．Experiments in Two Blocks 433

13.4.2．Experiments in More Than Two Blocks 435

13.5．A Real Experiment—Mangold Experiment 437

13.6．Plans for Confounded 2p Experiments 441

13.7．Multireplicate Designs 441

13.8．Complete Confounding:Repeated Single-Replicate Designs 442

13.8.1．A Real Experiment—Decontamination Experiment 442

13.9．Partial Confounding 446

13.10．Comparing the Multireplicate Designs 449

13.11．Using SAS Software 452

Exercises 454

14．Confounding in General Factorial Experiments 461

14.1．Introduction 461

14.2．Confounding with Factors at Three Levels 462

14.2.1．Contrasts 462

14.2.2．Confounding Using Contrasts 463

14.2.3．Confounding Using Equations 464

14.2.4．A Real Experiment—Dye Experiment 467

14.2.5．Plans for Confounded 3p Experiments 470

14.3．Designing Using Pseudofactors 471

14.3.1．Confounding in 4p Experiments 471

14.3.2．Confounding in 2p×4q Experiments 472

14.4．Designing Confounded Asymmetrical Experiments 472

14.5．Using SAS Software 475

Exercises 477

15．Fractional Factorial Experiments 483

15.1．Introduction 483

15.2．Fractions from Block Designs;Factors with 2 Levels 484

15.2.1．Half-Fractions of 2p Experiments;2p-1 Experiments 484

15.2.2．Resolution and Notation 487

15.2.3．A Real Experiment—Soup Experiment 487

15.2.4．Quarter-Fractions of 2p Experiments;2p-2 Experiments 490

15.2.5．Smaller Fractions of 2p Experiments 494

15.3．Fractions from Block Designs;Factors with 3 Levels 496

15.3.1．One-Third Fractions of 3p Experiments;3p-1 Experiments 496

15.3.2．One-Ninth Fractions of 3p Experiments;3p-2 Experiments 501

15.4．Fractions from Block Designs;Other Experiments 501

15.4.1．2p×4q Experiments 501

15.4.2．2p×3q Experiments 502

15.5．Blocked Fractional Factorial Experiments 503

15.6．Fractions from Orthogonal Arrays 506

15.6.1．2p Orthogonal Arrays 506

15.6.2．Saturated Designs 512

15.6.3．2p×4q Orthogonal Arrays 513

15.6.4．3p Orthogonal Arrays 514

15.7．Design for the Control of Noise Variability 515

15.7.1．A Real Experiment—Inclinometer Experiment 516

15.8．Using SAS Software 521

15.8.1．Fractional Factorials 521

15.8.2．Design for the Control of Noise Variability 524

Exercises 529

16．Response Surface Methodology 547

16.1．Introduction 547

16.2．First-Order Designs and Analysis 549

16.2.1．Models 549

16.2.2．Standard First-Order Designs 551

16.2.3．Least Squares Estimation 552

16.2.4．Checking Model Assumptions 553

16.2.5．Analysis of Variance 553

16.2.6．Tests for Lack of Fit 554

16.2.7．Path of Steepest Ascent 559

16.3．Second-Order Designs and Analysis 561

16.3.1．Models and Designs 561

16.3.2．Central Composite Designs 562

16.3.3．Generic Test for Lack of Fit of the Second-Order Model 564

16.3.4．Analysis of Variance for a Second-Order Model 564

16.3.5．Canonical Analysis of a Second-Order Model 566

16.4．Properties of Second-Order Designs:CCDs 569

16.4.1．Rotatability 569

16.4.2．Orthogonality 570

16.4.3．Orthogonal Blocking 571

16.5．A Real Experiment:Flour Production Experiment,Continued 573

16.6．Box-Behnken Designs 576

16.7．Using SAS Software 579

16.7.1．Analysis of a Standard First-Order Design 579

16.7.2．Analysis of a Second-Order Design 582

Exercises 586

17．Random Effects and Variance Components 593

17.1．Introduction 593

17.2．Some Examples 594

17.3．One Random Effect 596

17.3.1．The Random-Effects One-Way Model 596

17.3.2．Estimation of σ2 597

17.3.3．Estimation of σ2 T 598

17.3.4．Testing Equality of Treatment Effects 601

17.3.5．Confidence Intervals for Variance Components 603

17.4．Sample Sizes for an Experiment with One Random Effect 607

17.5．Checking Assumptions on the Model 610

17.6．Two or More Random Effects 610

17.6.1．Models and Examples 610

17.6.2．Checking Model Assumptions 613

17.6.3．Estimation of σ2 613

17.6.4．Estimation of Variance Components 614

17.6.5．Confidence Intervals for Variance Components 616

17.6.6．Hypothesis Tests for Variance Components 620

17.6.7．Sample Sizes 622

17.7．Mixed Models 622

17.7.1．Expected Mean Squares and Hypothesis Tests 622

17.7.2．Confidence Intervals in Mixed Models 625

17.8．Rules for Analysis of Random and Mixed Models 627

17.8.1．Rules—Equal Sample Sizes 627

17.8.2．Controversy(Optional) 628

17.9．Block Designs and Random Blocking Factors 630

17.10．Using SAS Software 632

17.10.1．Checking Assumptions on the Model 632

17.10.2．Estimation and Hypothesis Testing 635

Exercises 639

18．Nested Models 645

18.1．Introduction 645

18.2．Examples and Models 646

18.3．Analysis of Nested Fixed Effects 648

18.3.1．Least Squares Estimates 648

18.3.2．Estimation of σ2 649

18.3.3．Confidence Intervals 650

18.3.4．Hypothesis Testing 650

18.4．Analysis of Nested Random Effects 654

18.4.1．Expected Mean Squares 654

18.4.2．Estimation of Variance Components 656

18.4.3．Hypothesis Testing 657

18.4.4．Some Examples 658

18.5．Using SAS Software 662

18.5.1．Voltage Experiment 662

Exercises 667

19．Split-Plot Designs 675

19.1．Introduction 675

19.2．Designs and Models 676

19.3．Analysis of a Split-Plot Design with Complete Blocks 678

19.3.1．Split-Plot Analysis 678

19.3.2．Whole-Plot Analysis 680

19.3.3．Contrasts Within and Between Whole Plots 681

19.3.4．A Real Experiment—Oats Experiment 681

19.4．Split-Split-Plot Designs 684

19.5．Split-Plot Confounding 686

19.6．Using SAS Software 687

Exercises 691

A.Tables 695

Bibliography 725

Index of Authors 731

Index of Experiments 733

Index of Subjects 735