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