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1．Principles and Techniques1

1.1．Design:Basic Principles and Techniques1

1.1.1．The Art of Experimentation1

1.1.2．Replication2

1.1.3．Blocking3

1.1.4．Randomization3

1.2．Analysis:Basic Principles and Techniques5

2．Planning Experiments7

2.1．Introduction7

2.2．A Checklist for Planning Experiments7

2.3．A Real Experiment—Cotton-Spinning Experiment14

2.4．Some Standard Experimental Designs17

2.4.1．Completely Randomized Designs18

2.4.2．Block Designs18

2.4.3．Designs with Two or More Blocking Factors19

2.4.4．Split-Plot Designs21

2.5．More Real Experiments22

2.5.1．Soap Experiment22

2.5.2．Battery Experiment26

2.5.3．Cake-Baking Experiment29

Exercises31

3．Designs with One Source of Variation33

3.1．Introduction33

3.2．Randomization34

3.3．Model for a Completely Randomized Design35

3.4．Estimation of Parameters37

3.4.1．Estimable Functions of Parameters37

3.4.2．Notation37

3.4.3．Obtaining Least Squares Estimates38

3.4.4．Properties of Least Squares Estimators40

3.4.5．Estimation of σ242

3.4.6．Confidence Bound for σ243

3.5．One-Way Analysis of Variance44

3.5.1．Testing Equality of Treatment Effects44

3.5.2．Use of p-Values48

3.6．Sample Sizes49

3.6.1．Expected Mean Squares for Treatments50

3.6.2．Sample Sizes Using Power of a Test51

3.7．A Real Experiment—Soap Experiment,Continued53

3.7.1．Checklist,Continued53

3.7.2．Data Collection and Analysis54

3.7.3．Discussion by the Experimenter56

3.7.4．Further Observations by the Experimenter56

3.8．Using SAS Software57

3.8.1．Randomization57

3.8.2．Analysis of Variance58

Exercises61

4．Inferences for Contrasts and Treatment Means67

4.1．Introduction67

4.2．Contrasts68

4.2.1．Pairwise Comparisons69

4.2.2．Treatment Versus Control70

4.2.3．Difference of Averages70

4.2.4．Trends71

4.3．Individual Contrasts and Treatment Means73

4.3.1．Confidence Interval for a Single Contrast73

4.3.2．Confidence Interval for a Single Treatment Mean75

4.3.3．Hypothesis Test for a Single Contrast or Treatment Mean75

4.4．Methods of Multiple Comparisons78

4.4.1．Multiple Confidence Intervals78

4.4.2．Bonferroni Method for Preplanned Comparisons80

4.4.3．Scheffé Method of Multiple Comparisons83

4.4.4．Tukey Method for All Pairwise Comparisons85

4.4.5．Dunnett Method for Treatment-Versus-Control Comparisons87

4.4.6．Hsu Method for Multiple Comparisons with the Best Treatment89

4.4.7．Combination of Methods91

4.4.8．Methods Not Controlling Experimentwise Error Rate92

4.5．Sample Sizes92

4.6．Using SAS Software94

4.6.1．Inferences on Individual Contrasts94

4.6.2．Multiple Comparisons96

Exercises97

5．Checking Model Assumptions103

5.1．Introduction103

5.2．Strategy for Checking Model Assumptions104

5.2.1．Residuals104

5.2.2．Residual Plots105

5.3．Checking the Fit of the Model107

5.4．Checking for Outliers107

5.5．Checking Independence of the Error Terms109

5.6．Checking the Equal Variance Assumption111

5.6.1．Detection of Unequal Variances112

5.6.2．Data Transformations to Equalize Variances113

5.6.3．Analysis with Unequal Error Variances116

5.7．Checking the Normality Assumption119

5.8．Using SAS Software122

5.8.1．Using SAS to Generate Residual Plots122

5.8.2．Transforming the Data126

Exercises127

6．Experiments with Two Crossed Treatment Factors135

6.1．Introduction135

6.2．Models and Factorial Effects136

6.2.1．The Meaning of Interaction136

6.2.2．Models for Two Treatment Factors138

6.2.3．Checking the Assumptions on the Model140

6.3．Contrasts141

6.3.1．Contrasts for Main Effects and Interactions141

6.3.2．Writing Contrasts as Coefficient Lists143

6.4．Analysis of the Two-Way Complete Model145

6.4.1．Least Squares Estimators for the Two-Way Complete Model146

6.4.2．Estimation of σ2 for the Two-Way Complete Model147

6.4.3．Multiple Comparisons for the Complete Model149

6.4.4．Analysis of Variance for the Complete Model152

6.5．Analysis of the Two-Way Main-Effects Model158

6.5.1．Least Squares Estimators for the Main-Effects Model158

6.5.2．Estimation of σ2 in the Main-Effects Model162

6.5.3．Multiple Comparisons for the Main-Effects Model163

6.5.4．Unequal Variances165

6.5.5．Analysis of Variance for Equal Sample Sizes165

6.5.6．Model Building168

6.6．Calculating Sample Sizes168

6.7．Small Experiments169

6.7.1．One Observation per Cell169

6.7.2．Analysis Based on Orthogonal Contrasts169

6.7.3．Tukey's Test for Additivity172

6.7.4．A Real Experiment—Air Velocity Experiment173

6.8．Using SAS Software175

6.8.1．Contrasts and Multiple Comparisons177

6.8.2．Plots181

6.8.3．One Observation per Cell182

Exercises183

7．Several Crossed Treatment Factors193

7.1．Introduction193

7.2．Models and Factorial Effects194

7.2.1．Models194

7.2.2．The Meaning of Interaction195

7.2.3．Separability of Factorial Effects197

7.2.4．Estimation of Factorial Contrasts199

7.3．Analysis—Equal Sample Sizes201

7.4．A Real Experiment—Popcorn-Microwave Experiment205

7.5．One Observation per Cell211

7.5.1．Analysis Assuming That Certain Interaction Effects Are Negligible211

7.5.2．Analysis Using Normal Probability Plot of Effect Estimates213

7.5.3．Analysis Using Confidence Intervals215

7.6．Design for the Control of Noise Variability217

7.6.1．Analysis of Design-by-Noise Interactions218

7.6.2．Analyzing the Effects of Design Factors on Variability221

7.7．Using SAS Software223

7.7.1．Normal Probability Plots of Contrast Estimates224

7.7.2．Voss-Wang Confidence Interval Method224

7.7.3．Identification of Robust Factor Settings226

7.7.4．Experiments with Empty Cells227

Exercises231

8．Polynomial Regression243

8.1．Introduction243

8.2．Models244

8.3．Least Squares Estimation(Optional)248

8.3.1．Normal Equations248

8.3.2．Least Squares Estimates for Simple Linear Regression248

8.4．Test for Lack of Fit249

8.5．Analysis of the Simple Linear Regression Model251

8.6．Analysis of Polynomial Regression Models255

8.6.1．Analysis of Variance255

8.6.2．Confidence Intervals257

8.7．Orthogonal Polynomials and Trend Contrasts(Optional)258

8.7.1．Simple Linear Regression258

8.7.2．Quadratic Regression260

8.7.3．Comments261

8.8．A Real Experiment—Bean-Soaking Experiment262

8.8.1．Checklist262

8.8.2．One-Way Analysis of Variance and Multiple Comparisons264

8.8.3．Regression Analysis267

8.9．Using SAS Software268

Exercises273

9．Analysis of Covariance277

9.1．Introduction277

9.2．Models278

9.2.1．Checking Model Assumptions and Equality of Slopes279

9.2.2．Model Extensions279

9.3．Least Squares Estimates280

9.3.1．Normal Equations(Optional)280

9.3.2．Least Squares Estimates and Adjusted Treatment Means281

9.4．Analysis of Covariance282

9.5．Treatment Contrasts and Confidence Intervals286

9.5.1．Individual Confidence Intervals286

9.5.2．Multiple Coinparisons287

9.6．Using SAS Software288

Exercises292

10．Complete Block Designs295

10.1．Introduction295

10.2．Blocks,Noise Factors or Covariates?296

10.3．Design Issues297

10.3.1．Block Sizes297

10.3.2．Complete Block Design Definitions298

10.3.3．The Randomized Complete Block Design299

10.3.4．The General Complete Block Design300

10.3.5．How Many Observations?301

10.4．Analysis of Randomized Complete Block Designs301

10.4.1．Model and Analysis of Variance301

10.4.2．Multiple Comparisons305

10.5．A Real Experiment—Cotton-Spinning Experiment306

10.5.1．Design Details306

10.5.2．Sample-Size Calculation307

10.5.3．Analysis of the Cotton-Spinning Experiment307

10.6．Analysis of General Complete Block Designs309

10.6.1．Model and Analysis of Variance309

10.6.2．Multiple Comparisons for the General Complete Block Design312

10.6.3．Sample-Size Calculations315

10.7．Checking Model Assumptions316

10.8．Factorial Experiments317

10.9．Using SAS Software320

Exercises324

11．Incomplete Block Designs339

11.1．Introduction339

11.2．Design Issues340

11.2.1．Block Sizes340

11.2.2．Design Plans and Randomization340

11.2.3．Estimation of Contrasts(Optional)342

11.2.4．Balanced Incomplete Block Designs343

11.2.5．Group Divisible Designs345

11.2.6．Cyclic Designs346

11.3．Analysis of General Incomplete Block Designs348

11.3.1．Contrast Estimators and Multiple Comparisons348

11.3.2．Least Squares Estimation(Optional)351

11.4．Analysis of Balanced Incomplete Block Designs354

11.4.1．Multiple Comparisons and Analysis of Variance354

11.4.2．A Real Experiment—Detergent Experiment355

11.5．Analysis of Group Divisible Designs360

11.5.1．Multiple Comparisons and Analysis of Variance360

11.6．Analysis of Cyclic Designs362

11.7．A Real Experiment—Plasma Experiment362

11.8．Sample Sizes368

11.9．Factorial Experiments369

11.9.1．Factorial Structure369

11.10．Using SAS Software372

11.10.1．Analysis of Variance and Estimation of Contrasts372

11.10.2．Plots377

Exercises378

12．Designs with Two Blocking Factors387

12.1．Introduction387

12.2．Design Issues388

12.2.1．Selection and Randomization of Row-Column Designs388

12.2.2．Latin Square Designs389

12.2.3．Youden Designs391

12.2.4．Cyclic and Other Row-Column Designs392

12.3．Model for a Row-Column Design394

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 Comparisons401

12.5．Analysis of Latin Square Designs401

12.5.1．Analysis of Variance for Latin Square Designs401

12.5.2．Confidence Intervals for Latin Square Designs403

12.5.3．How Many Observations?405

12.6．Analysis of Youden Designs406

12.6.1．Analysis of Variance for Youden Designs406

12.6.2．Confidence Intervals for Youden Designs407

12.6.3．How Many Observations?407

12.7．Analysis of Cyclic and Other Row-Column Designs408

12.8．Checking the Assumptions on the Model409

12.9．Factorial Experiments in Row-Column Designs410

12.10．Using SAS Software410

12.10.1．Factorial Model413

12.10.2．Plots415

Exercises415

13．Confounded Two-Level Factorial Experiments421

13.1．Introduction421

13.2．Single replicate factorial experiments422

13.2.1．Coding and notation422

13.2.2．Confounding422

13.2.3．Analysis423

13.3．Confounding Using Contrasts424

13.3.1．Contrasts424

13.3.2．Experiments in Two Blocks425

13.3.3．Experiments in Four Blocks430

13.3.4．Experiments in Eight Blocks432

13.3.5．Experiments in More Than Eight Blocks433

13.4．Confounding Using Equations433

13.4.1．Experiments in Two Blocks433

13.4.2．Experiments in More Than Two Blocks435

13.5．A Real Experiment—Mangold Experiment437

13.6．Plans for Confounded 2p Experiments441

13.7．Multireplicate Designs441

13.8．Complete Confounding:Repeated Single-Replicate Designs442

13.8.1．A Real Experiment—Decontamination Experiment442

13.9．Partial Confounding446

13.10．Comparing the Multireplicate Designs449

13.11．Using SAS Software452

Exercises454

14．Confounding in General Factorial Experiments461

14.1．Introduction461

14.2．Confounding with Factors at Three Levels462

14.2.1．Contrasts462

14.2.2．Confounding Using Contrasts463

14.2.3．Confounding Using Equations464

14.2.4．A Real Experiment—Dye Experiment467

14.2.5．Plans for Confounded 3p Experiments470

14.3．Designing Using Pseudofactors471

14.3.1．Confounding in 4p Experiments471

14.3.2．Confounding in 2p×4q Experiments472

14.4．Designing Confounded Asymmetrical Experiments472

14.5．Using SAS Software475

Exercises477

15．Fractional Factorial Experiments483

15.1．Introduction483

15.2．Fractions from Block Designs;Factors with 2 Levels484

15.2.1．Half-Fractions of 2p Experiments;2p-1 Experiments484

15.2.2．Resolution and Notation487

15.2.3．A Real Experiment—Soup Experiment487

15.2.4．Quarter-Fractions of 2p Experiments;2p-2 Experiments490

15.2.5．Smaller Fractions of 2p Experiments494

15.3．Fractions from Block Designs;Factors with 3 Levels496

15.3.1．One-Third Fractions of 3p Experiments;3p-1 Experiments496

15.3.2．One-Ninth Fractions of 3p Experiments;3p-2 Experiments501

15.4．Fractions from Block Designs;Other Experiments501

15.4.1．2p×4q Experiments501

15.4.2．2p×3q Experiments502

15.5．Blocked Fractional Factorial Experiments503

15.6．Fractions from Orthogonal Arrays506

15.6.1．2p Orthogonal Arrays506

15.6.2．Saturated Designs512

15.6.3．2p×4q Orthogonal Arrays513

15.6.4．3p Orthogonal Arrays514

15.7．Design for the Control of Noise Variability515

15.7.1．A Real Experiment—Inclinometer Experiment516

15.8．Using SAS Software521

15.8.1．Fractional Factorials521

15.8.2．Design for the Control of Noise Variability524

Exercises529

16．Response Surface Methodology547

16.1．Introduction547

16.2．First-Order Designs and Analysis549

16.2.1．Models549

16.2.2．Standard First-Order Designs551

16.2.3．Least Squares Estimation552

16.2.4．Checking Model Assumptions553

16.2.5．Analysis of Variance553

16.2.6．Tests for Lack of Fit554

16.2.7．Path of Steepest Ascent559

16.3．Second-Order Designs and Analysis561

16.3.1．Models and Designs561

16.3.2．Central Composite Designs562

16.3.3．Generic Test for Lack of Fit of the Second-Order Model564

16.3.4．Analysis of Variance for a Second-Order Model564

16.3.5．Canonical Analysis of a Second-Order Model566

16.4．Properties of Second-Order Designs:CCDs569

16.4.1．Rotatability569

16.4.2．Orthogonality570

16.4.3．Orthogonal Blocking571

16.5．A Real Experiment:Flour Production Experiment,Continued573

16.6．Box-Behnken Designs576

16.7．Using SAS Software579

16.7.1．Analysis of a Standard First-Order Design579

16.7.2．Analysis of a Second-Order Design582

Exercises586

17．Random Effects and Variance Components593

17.1．Introduction593

17.2．Some Examples594

17.3．One Random Effect596

17.3.1．The Random-Effects One-Way Model596

17.3.2．Estimation of σ2597

17.3.3．Estimation of σ2 T598

17.3.4．Testing Equality of Treatment Effects601

17.3.5．Confidence Intervals for Variance Components603

17.4．Sample Sizes for an Experiment with One Random Effect607

17.5．Checking Assumptions on the Model610

17.6．Two or More Random Effects610

17.6.1．Models and Examples610

17.6.2．Checking Model Assumptions613

17.6.3．Estimation of σ2613

17.6.4．Estimation of Variance Components614

17.6.5．Confidence Intervals for Variance Components616

17.6.6．Hypothesis Tests for Variance Components620

17.6.7．Sample Sizes622

17.7．Mixed Models622

17.7.1．Expected Mean Squares and Hypothesis Tests622

17.7.2．Confidence Intervals in Mixed Models625

17.8．Rules for Analysis of Random and Mixed Models627

17.8.1．Rules—Equal Sample Sizes627

17.8.2．Controversy(Optional)628

17.9．Block Designs and Random Blocking Factors630

17.10．Using SAS Software632

17.10.1．Checking Assumptions on the Model632

17.10.2．Estimation and Hypothesis Testing635

Exercises639

18．Nested Models645

18.1．Introduction645

18.2．Examples and Models646

18.3．Analysis of Nested Fixed Effects648

18.3.1．Least Squares Estimates648

18.3.2．Estimation of σ2649

18.3.3．Confidence Intervals650

18.3.4．Hypothesis Testing650

18.4．Analysis of Nested Random Effects654

18.4.1．Expected Mean Squares654

18.4.2．Estimation of Variance Components656

18.4.3．Hypothesis Testing657

18.4.4．Some Examples658

18.5．Using SAS Software662

18.5.1．Voltage Experiment662

Exercises667

19．Split-Plot Designs675

19.1．Introduction675

19.2．Designs and Models676

19.3．Analysis of a Split-Plot Design with Complete Blocks678

19.3.1．Split-Plot Analysis678

19.3.2．Whole-Plot Analysis680

19.3.3．Contrasts Within and Between Whole Plots681

19.3.4．A Real Experiment—Oats Experiment681

19.4．Split-Split-Plot Designs684

19.5．Split-Plot Confounding686

19.6．Using SAS Software687

Exercises691

A.Tables695

Bibliography725

Index of Authors731

Index of Experiments733

Index of Subjects735