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 |  موضوع: كتاب Design and Analysis of Experiments الثلاثاء 05 أكتوبر 2021, 12:48 am | |
| 
أخواني في الله
أحضرت لكم كتاب
Design and Analysis of Experiments
Second Edition
Angela Dean, Daniel Voss
Danel Draguljić
و المحتوى كما يلي :
Contents
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 2
1.1.4 Randomization 3
1.2 Analysis: Basic Principles and Techniques 4
2 Planning Experiments . 7
2.1 Introduction . 7
2.2 A Checklist for Planning Experiments . 7
2.3 A Real Experiment—Cotton-Spinning Experiment 13
2.4 Some Standard Experimental Designs . 16
2.4.1 Completely Randomized Designs 17
2.4.2 Block Designs . 17
2.4.3 Designs with Two or More Blocking
Factors 17
2.4.4 Split-Plot Designs 19
2.5 More Real Experiments . 20
2.5.1 Soap Experiment . 20
2.5.2 Battery Experiment . 24
2.5.3 Cake-Baking Experiment . 27
Exercises . 29
3 Designs with One Source of Variation . 31
3.1 Introduction . 31
3.2 Randomization . 31
3.3 Model for a Completely Randomized Design 32
3.4 Estimation of Parameters 34
3.4.1 Estimable Functions of Parameters . 34
3.4.2 Notation . 34
3.4.3 Obtaining Least Squares Estimates . 35
3.4.4 Properties of Least Squares Estimators 37
3.4.5 Estimation of r2 . 39
3.4.6 Confidence Bound for r2 . 39
3.5 One-Way Analysis of Variance 41
3.5.1 Testing Equality of Treatment Effects 41
3.5.2 Use of p-Values . 453.6 Sample Sizes 45
3.6.1 Expected Mean Squares for Treatments . 46
3.6.2 Sample Sizes Using Power of a Test . 47
3.7 A Real Experiment—Soap Experiment, Continued 49
3.7.1 Checklist, Continued 50
3.7.2 Data Collection and Analysis 50
3.7.3 Discussion by the Experimenter . 52
3.7.4 Further Observations by the Experimenter . 52
3.8 Using SAS Software . 52
3.8.1 Randomization 52
3.8.2 Analysis of Variance 54
3.8.3 Calculating Sample Size Using Power
of a Test . 56
3.9 Using R Software . 57
3.9.1 Randomization 59
3.9.2 Reading and Plotting Data 60
3.9.3 Analysis of Variance 62
3.9.4 Calculating Sample Size Using Power
of a Test . 64
Exercises . 65
4 Inferences for Contrasts and Treatment Means 69
4.1 Introduction . 69
4.2 Contrasts . 69
4.2.1 Pairwise Comparisons . 70
4.2.2 Treatment Versus Control . 71
4.2.3 Difference of Averages . 72
4.2.4 Trends 72
4.3 Individual Contrasts and Treatment Means 74
4.3.1 Confidence Interval for a Single Contrast 74
4.3.2 Confidence Interval for a Single
Treatment Mean . 76
4.3.3 Hypothesis Test for a Single Contrast
or Treatment Mean . 77
4.3.4 Equivalence of Tests and Confidence
Intervals (Optional) . 79
4.4 Methods of Multiple Comparisons 81
4.4.1 Multiple Confidence Intervals 81
4.4.2 Bonferroni Method for Preplanned
Comparisons 83
4.4.3 Scheffé Method of Multiple Comparisons 85
4.4.4 Tukey Method for All Pairwise
Comparisons 87
4.4.5 Dunnett Method for Treatment-VersusControl Comparisons 90
4.4.6 Combination of Methods . 92
4.4.7 Methods Not Controlling Experimentwise
Error Rate . 92
4.5 Sample Sizes 924.6 Using SAS Software . 94
4.6.1 Inferences on Individual Contrasts . 94
4.6.2 Multiple Comparisons . 95
4.7 Using R Software . 96
4.7.1 Inferences on Individual Contrasts . 97
4.7.2 Multiple Comparisons . 99
Exercises . 100
5 Checking Model Assumptions . 103
5.1 Introduction . 103
5.2 Strategy for Checking Model Assumptions 103
5.2.1 Residuals 104
5.2.2 Residual Plots . 104
5.3 Checking the Fit of the Model 106
5.4 Checking for Outliers 107
5.5 Checking Independence of the Error Terms . 108
5.6 Checking the Equal Variance Assumption 110
5.6.1 Detection of Unequal Variances 110
5.6.2 Data Transformations to Equalize
Variances 112
5.6.3 Analysis with Unequal Error Variances . 115
5.7 Checking the Normality Assumption 117
5.8 Using SAS Software . 119
5.8.1 Residual Plots . 119
5.8.2 Transforming the Data . 123
5.8.3 Implementing Satterthwaite’s Method . 124
5.9 Using R Software . 125
5.9.1 Residual Plots . 125
5.9.2 Transforming the Data . 129
5.9.3 Implementing Satterthwaite’s Method . 130
Exercises . 132
6 Experiments with Two Crossed Treatment Factors . 139
6.1 Introduction . 139
6.2 Models and Factorial Effects . 139
6.2.1 The Meaning of Interaction 139
6.2.2 Models for Two Treatment Factors 142
6.2.3 Checking the Assumptions on the Model 143
6.3 Contrasts . 144
6.3.1 Contrasts for Main Effects and Interactions . 144
6.3.2 Writing Contrasts as Coefficient Lists 146
6.4 Analysis of the Two-Way Complete Model . 149
6.4.1 Least Squares Estimators for the Two-Way
Complete Model . 149
6.4.2 Estimation of r2 for the Two-Way
Complete Model . 151
6.4.3 Multiple Comparisons for the Complete
Model 152
6.4.4 Analysis of Variance for the Complete
Model 1556.5 Analysis of the Two-Way Main-Effects Model . 161
6.5.1 Least Squares Estimators for the
Main-Effects Model . 161
6.5.2 Estimation of r2 in the Main-Effects
Model 165
6.5.3 Multiple Comparisons for the Main-Effects
Model 166
6.5.4 Unequal Variances 168
6.5.5 Analysis of Variance for Equal
Sample Sizes . 168
6.5.6 Model Building 170
6.6 Calculating Sample Sizes 171
6.7 Small Experiments 171
6.7.1 One Observation Per Cell . 171
6.7.2 Analysis Based on Orthogonal Contrasts 172
6.7.3 Tukey’s Test for Additivity 175
6.7.4 A Real Experiment—Air Velocity
Experiment . 176
6.8 Using SAS Software . 177
6.8.1 Analysis of Variance 177
6.8.2 Contrasts and Multiple Comparisons . 180
6.8.3 Plots . 182
6.8.4 One Observation Per Cell . 183
6.9 Using R Software . 184
6.9.1 Analysis of Variance 186
6.9.2 Contrasts and Multiple Comparisons . 187
6.9.3 Plots . 191
6.9.4 One Observation Per Cell . 192
Exercises . 193
7 Several Crossed Treatment Factors . 201
7.1 Introduction . 201
7.2 Models and Factorial Effects . 201
7.2.1 Models 201
7.2.2 The Meaning of Interaction 202
7.2.3 Separability of Factorial Effects . 205
7.2.4 Estimation of Factorial Contrasts 206
7.3 Analysis—Equal Sample Sizes 209
7.4 A Real Experiment—Popcorn–Microwave
Experiment 213
7.5 One Observation per Cell 219
7.5.1 Analysis Assuming that Certain Interaction
Effects are Negligible 219
7.5.2 Analysis Using Half-Normal Probability Plot
of Effect Estimates . 221
7.5.3 Analysis Using Confidence Intervals . 2237.6 Using SAS Software . 225
7.6.1 Half-Normal Probability Plots
of Contrast Estimates 225
7.6.2 Voss–Wang Confidence Interval Method 227
7.6.3 Experiments with Empty Cells . 228
7.7 Using R Software . 231
7.7.1 Half-Normal Probability Plots
of Contrast Estimates 231
7.7.2 Voss–Wang Confidence Interval Method 232
7.7.3 Experiments with Empty Cells . 234
Exercises . 237
8 Polynomial Regression 249
8.1 Introduction . 249
8.2 Models 250
8.3 Least Squares Estimation (Optional) 253
8.3.1 Normal Equations 253
8.3.2 Least Squares Estimates
for Simple Linear Regression 254
8.4 Test for Lack of Fit 254
8.5 Analysis of the Simple Linear Regression Model . 257
8.6 Analysis of Polynomial Regression Models . 260
8.6.1 Analysis of Variance 260
8.6.2 Confidence Intervals 262
8.7 Orthogonal Polynomials and Trend Contrasts
(Optional) 263
8.7.1 Simple Linear Regression . 263
8.7.2 Quadratic Regression 265
8.7.3 Comments . 266
8.8 A Real Experiment—Bean-Soaking Experiment 266
8.8.1 Checklist 267
8.8.2 One-Way Analysis of Variance
and Multiple Comparisons 270
8.8.3 Regression Analysis . 271
8.9 Using SAS Software . 273
8.10 Using R Software . 276
Exercises . 281
9 Analysis of Covariance 285
9.1 Introduction . 285
9.2 Models 285
9.2.1 Checking Model Assumptions
and Equality of Slopes . 287
9.2.2 Model Extensions 287
9.3 Least Squares Estimates . 287
9.3.1 Normal Equations (Optional) . 287
9.3.2 Least Squares Estimates
and Adjusted Treatment Means . 288
9.4 Analysis of Covariance . 2899.5 Treatment Contrasts and Confidence Intervals 293
9.5.1 Individual Confidence Intervals . 293
9.5.2 Multiple Comparisons . 294
9.6 Using SAS Software . 296
9.7 Using R Software . 299
Exercises . 301
10 Complete Block Designs . 305
10.1 Introduction . 305
10.2 Blocks, Noise Factors or Covariates? 305
10.3 Design Issues 306
10.3.1 Block Sizes . 306
10.3.2 Complete Block Design Definitions 307
10.3.3 The Randomized Complete Block Design 308
10.3.4 The General Complete Block Design . 309
10.3.5 How Many Observations? . 309
10.4 Analysis of Randomized Complete Block Designs 310
10.4.1 Model and Analysis of Variance 310
10.4.2 Multiple Comparisons . 313
10.5 A Real Experiment—Cotton-Spinning Experiment 314
10.5.1 Design Details . 314
10.5.2 Sample-Size Calculation 315
10.5.3 Analysis of the Cotton-Spinning
Experiment . 315
10.6 Analysis of General Complete Block Designs 318
10.6.1 Model and Analysis of Variance 318
10.6.2 Multiple Comparisons for the General
Complete Block Design 320
10.6.3 Sample-Size Calculations . 322
10.7 Checking Model Assumptions 323
10.8 Factorial Experiments 324
10.9 Using SAS Software . 327
10.10 Using R Software . 331
Exercises . 336
11 Incomplete Block Designs 349
11.1 Introduction . 349
11.2 Design Issues 349
11.2.1 Block Sizes . 349
11.2.2 Design Plans and Randomization 350
11.2.3 Estimation of Contrasts 351
11.3 Some Special Incomplete Block Designs . 352
11.3.1 Balanced Incomplete Block Designs . 352
11.3.2 Group Divisible Designs 354
11.3.3 Cyclic Designs 355
11.4 Analysis of General Incomplete Block Designs . 356
11.4.1 Contrast Estimators and Multiple
Comparisons 356
11.4.2 Analysis of Variance 35811.4.3 Analysis of Balanced Incomplete
Block Designs . 359
11.4.4 A Real Experiment—Detergent
Experiment . 360
11.4.5 Analysis of Group Divisible Designs . 365
11.4.6 Analysis of Cyclic Designs 366
11.5 A Real Experiment—Plasma Experiment . 366
11.6 Sample Sizes 371
11.7 Factorial Experiments 372
11.7.1 Factorial Structure 372
11.8 Using SAS Software . 376
11.8.1 Generation of Efficient Block Designs 376
11.8.2 Analysis of Variance, Contrasts,
and Multiple Comparisons 378
11.8.3 Plots . 381
11.9 Using R Software . 382
11.9.1 Generating Efficient Incomplete Block
Designs . 382
11.9.2 Analysis of Variance, Contrasts,
and Multiple Comparisons 384
11.9.3 Plots . 387
Exercises . 389
12 Designs with Two Blocking Factors . 399
12.1 Introduction . 399
12.2 Design Issues 400
12.2.1 Selection and Randomization
of Row–Column Designs . 400
12.2.2 Latin Square Designs 401
12.2.3 Youden Designs . 403
12.2.4 Cyclic and Other Row–Column Designs . 404
12.3 Analysis of Row–Column Designs . 405
12.3.1 Model for a Row–Column Design . 405
12.3.2 Analysis of Variance for a Row–Column
Design 406
12.3.3 Confidence Intervals and Multiple
Comparisons 407
12.4 Analysis of Latin Square Designs 408
12.4.1 Analysis of Variance for Latin
Square Designs 408
12.4.2 Confidence Intervals for Latin Square
Designs . 409
12.4.3 How Many Observations? . 411
12.5 Analysis of Youden Designs . 412
12.5.1 Analysis of Variance for Youden Designs 412
12.5.2 Confidence Intervals for Youden Designs 413
12.5.3 How Many Observations? . 413
12.6 Checking the Assumptions on the Model . 414
12.7 Factorial Experiments in Row–Column Designs 41612.8 Using SAS Software . 416
12.8.1 Factorial Model 417
12.8.2 Plots . 419
12.9 Using R Software . 420
12.9.1 Factorial Model 423
12.9.2 Plots . 424
Exercises . 425
13 Confounded Two-Level Factorial Experiments . 433
13.1 Introduction . 433
13.2 Single Replicate Factorial Experiments 433
13.2.1 Coding and Notation 433
13.2.2 Confounding 434
13.2.3 Analysis . 434
13.3 Confounding Using Contrasts . 435
13.3.1 Contrasts 435
13.3.2 Experiments in Two Blocks . 436
13.3.3 Experiments in Four Blocks . 441
13.3.4 Experiments in Eight Blocks . 443
13.3.5 Experiments in More Than Eight Blocks 443
13.4 Confounding Using Equations 444
13.4.1 Experiments in Two Blocks . 444
13.4.2 Experiments in More Than Two Blocks . 445
13.5 A Real Experiment—Mangold Experiment 447
13.6 Plans for Confounded 2p Experiments . 451
13.7 Multireplicate Designs 451
13.8 Complete Confounding: Repeated Single-Replicate
Designs 452
13.8.1 A Real Experiment—Decontamination
Experiment . 452
13.9 Partial Confounding . 455
13.10 Comparing the Multireplicate Designs . 458
13.11 Using SAS Software . 461
13.12 Using R Software . 463
Exercises . 465
14 Confounding in General Factorial Experiments 473
14.1 Introduction . 473
14.2 Confounding with Factors at Three Levels 473
14.2.1 Contrasts 473
14.2.2 Confounding Using Contrasts 474
14.2.3 Confounding Using Equations 475
14.2.4 A Real Experiment—Dye Experiment 478
14.2.5 Plans for Confounded 3p Experiments 481
14.3 Designing Using Pseudofactors 482
14.3.1 Confounding in 4p Experiments . 482
14.3.2 Confounding in 2p 4q Experiments . 483
14.4 Designing Confounded Asymmetric Experiments . 48314.5 Using SAS Software . 486
14.6 Using R Software . 489
Exercises . 491
15 Fractional Factorial Experiments 495
15.1 Introduction . 495
15.2 Fractions from Block Designs; Factors
with 2 Levels 495
15.2.1 Half-Fractions of 2p Experiments;
2p−1 Experiments . 495
15.2.2 Resolution and Notation 498
15.2.3 A Real Experiment—Soup Experiment 499
15.2.4 Quarter-Fractions of 2p Experiments;
2p−2 Experiments . 501
15.2.5 Smaller Fractions of 2p Experiments . 505
15.3 Fractions from Block Designs; Factors
with 3 Levels 507
15.3.1 One-Third Fractions of 3p Experiments;
3p−1 Experiments . 507
15.3.2 One-Ninth Fractions of 3p Experiments;
3p−2 Experiments . 511
15.4 Fractions from Block Designs; Other Experiments . 511
15.4.1 2p 4q Experiments 511
15.4.2 2p 3q Experiments 512
15.5 Blocked Fractional Factorial Experiments . 513
15.6 Fractions from Orthogonal Arrays 516
15.6.1 2p Orthogonal Arrays 516
15.6.2 2p 4q Orthogonal Arrays 521
15.6.3 3p Orthogonal Arrays 522
15.7 Design for the Control of Noise Variability . 523
15.7.1 A Real Experiment—Inclinometer
Experiment . 525
15.8 Small Screening Designs: Orthogonal Main
Effect Plans . 529
15.8.1 Saturated Designs 529
15.8.2 Supersaturated Designs . 533
15.8.3 Saturated Orthogonal Main Effect Plans
Plus Interactions . 536
15.8.4 Definitive Screening Designs 537
15.9 Using SAS Software . 538
15.9.1 Fractional Factorials . 538
15.9.2 Design for the Control of Noise Variability . 539
15.9.3 Analysis of Small Screening Designs . 542
15.10 Using R Software . 543
15.10.1 Fractional Factorials . 543
15.10.2 Design for the Control of Noise Variability . 546
15.10.3 Analysis of Small Screening Designs . 547
Exercises . 54916 Response Surface Methodology 565
16.1 Introduction . 565
16.2 First-Order Designs and Analysis 567
16.2.1 Models 567
16.2.2 Standard First-Order Designs 568
16.2.3 Least Squares Estimation . 569
16.2.4 Checking Model Assumptions 570
16.2.5 Analysis of Variance 570
16.2.6 Tests for Lack of Fit 572
16.2.7 Path of Steepest Ascent 576
16.3 Second-Order Designs and Analysis 577
16.3.1 Models and Designs . 577
16.3.2 Central Composite Designs 578
16.3.3 Generic Test for Lack of Fit
of the Second-Order Model 581
16.3.4 Analysis of Variance for a Second-Order
Model 581
16.3.5 Canonical Analysis of a Second-Order
Model 583
16.4 Properties of Second-Order Designs: CCDs . 585
16.4.1 Rotatability . 585
16.4.2 Orthogonality . 586
16.4.3 Orthogonal Blocking 587
16.5 A Real Experiment: Flour Production Experiment,
Continued 589
16.6 Box–Behnken Designs 592
16.7 Using SAS Software . 594
16.7.1 Analysis of a Standard First-Order Design . 594
16.7.2 Analysis of a Second-Order Design 597
16.8 Using R Software . 599
16.8.1 Analysis of a Standard First-Order Design . 599
16.8.2 Analysis of a Second-Order Design 602
16.8.3 Generating Designs . 606
Exercises . 608
17 Random Effects and Variance Components . 615
17.1 Introduction . 615
17.2 Some Examples 615
17.3 One Random Effect 618
17.3.1 The Random-Effects One-Way Model 618
17.3.2 Estimation of r2 . 619
17.3.3 Estimation of r2
T . 620
17.3.4 Testing Equality of Treatment Effects 622
17.3.5 Confidence Intervals
for Variance Components . 625
17.4 Sample Sizes for an Experiment
with One Random Effect 628
17.5 Checking Assumptions on the Model . 63117.6 Two or More Random Effects 632
17.6.1 Models and Examples . 632
17.6.2 Checking Model Assumptions 634
17.6.3 Estimation of r2 . 634
17.6.4 Estimation of Variance Components 635
17.6.5 Confidence Intervals for Variance
Components 637
17.6.6 Hypothesis Tests for Variance
Components 640
17.6.7 Sample Sizes . 642
17.7 Mixed Models . 642
17.7.1 Expected Mean Squares
and Hypothesis Tests 643
17.7.2 Confidence Intervals in Mixed Models 645
17.8 Rules for Analysis of Random-Effects
and Mixed Models 647
17.8.1 Rules—Equal Sample Sizes . 647
17.8.2 Controversy (Optional) . 648
17.9 Block Designs and Random Block Effects 649
17.10 Using SAS Software . 652
17.10.1 Checking Assumptions on the Model . 652
17.10.2 Estimation and Hypothesis Testing 654
17.10.3 Sample Size Calculations . 657
17.11 Using R Software . 659
17.11.1 Checking Assumptions on the Model . 659
17.11.2 Estimation and Hypothesis Testing 661
17.11.3 Sample Size Calculations . 664
Exercises . 665
18 Nested Models 671
18.1 Introduction . 671
18.2 Examples and Models 671
18.3 Analysis of Nested Fixed Effects 674
18.3.1 Least Squares Estimates 674
18.3.2 Estimation of r2 . 675
18.3.3 Confidence Intervals 675
18.3.4 Hypothesis Testing . 676
18.4 Analysis of Nested Random Effects . 679
18.4.1 Expected Mean Squares 679
18.4.2 Estimation of Variance Components 682
18.4.3 Hypothesis Testing . 683
18.4.4 Some Examples 683
18.5 Using SAS Software . 687
18.5.1 Voltage Experiment . 68718.6 Using R Software . 691
18.6.1 Voltage Experiment . 692
18.6.2 Analysis Using Least Squares Estimates
and aov . 694
18.6.3 Analysis Using Restricted Maximum
Likelihood Estimation . 695
Exercises . 695
19 Split-Plot Designs 703
19.1 Introduction . 703
19.2 Designs and Models . 703
19.3 Analysis of a Split-Plot Design
with Complete Blocks 705
19.3.1 Split-Plot Analysis 706
19.3.2 Whole-Plot Analysis 707
19.3.3 Contrasts Within and Between
Whole Plots 708
19.3.4 A Real Experiment—Oats Experiment 709
19.4 Split-Split-Plot Designs . 711
19.5 Split-Plot Confounding . 713
19.6 A Real Experiment—UAV Experiment 713
19.6.1 Analysis of Variance 715
19.6.2 Multiple Comparisons . 716
19.7 A Real Experiment—Mobile Computing Field Study . 717
19.7.1 Analysis of Variance 719
19.7.2 Multiple Comparisons . 721
19.7.3 Analysis as a Split-Split-Plot Design . 721
19.7.4 Design Construction . 724
19.8 Using SAS Software . 727
19.8.1 The Analysis of Variance Approach 727
19.8.2 Simple Contrasts . 732
19.8.3 The Restricted Maximum Likelihood
Approach 733
19.8.4 Recovery of Inter-block Information . 736
19.8.5 ReML and Unbalanced Data . 742
19.9 Using R Software . 745
19.9.1 The Analysis of Variance Approach 745
19.9.2 Simple Contrasts . 746
19.9.3 The Restricted Maximum Likelihood
Approach 747
19.9.4 Recovery of Inter-block Information . 753
19.9.5 ReML and Unbalanced Data . 756
Exercises . 758
20 Computer Experiments 765
20.1 Introduction . 765
20.2 Models for Computer Experiments . 767
20.3 Gaussian Stochastic Process Model . 76820.4 Design . 772
20.4.1 Space-Filling and Non-collapsing Designs . 772
20.4.2 Construction of Latin Hypercube Designs 774
20.5 A Real Experiment—Neuron Experiment . 776
20.6 Using SAS Software . 778
20.6.1 Maximin Latin Hypercube Designs 779
20.6.2 Fitting the GaSP Model 781
20.7 Using R Software . 784
20.7.1 Maximin Latin Hypercube Designs 784
20.7.2 Fitting the GaSP Model 785
Exercises . 786
Appendix A: Tables . 793
Bibliography . 821
Index of Authors 825
Index of Experiments 829
Index of Subjects . 833
Index of Experiments
A
Abrasive wear, 244
Absorbancy, paper towel, 303
Acid copper pattern plating, 574, 579, 582, 584, 586, 594,
599, 606
Air freshener, 427, 428
Air rifle, 396
Air velocity, 176, 183, 192, 200
Alchohol, 665
Alloy, metal, 350, 356
Alloy, titanium, 698, 699
Ammunition, 632, 638, 642
Anatase, 554, 559
Antifungal antibiotic, 243
B
Balloon, 66, 108, 292, 294, 296, 299
Banana, 325
Battery, 40, 44, 45, 71, 72, 89, 94, 96, 101, 102, 107, 112,
118, 146, 150, 173, 194
Bean-soaking, 93, 266, 273, 276, 283
Beef, 392
Bicycle, 134, 281
Bicycle, exercise, 404, 416, 420
Biscuit, 343
Biscuit, buttermilk, 666
Bleach, 154, 195, 196
Bread-baking, 308
Breathalyzer, 306, 349
Buttermilk biscuit, 666
C
Caffeine, 429
Candle, 667
Catalyst, 134, 303
Catalytic reaction, 469, 470
Chemical, 340
Cigarette, 760
Clean wool, 616
Coating, 240
Coil, 456, 462, 464
Colorfastness, 323, 344
Cotton-spinning, 100, 314, 327, 331, 347
D
Dairy cow, 409, 410, 415
DCIS, 309, 319, 321, 336
Decontamination (alpha), 452
Decontamination (beta), 466, 549
Dessert, 135
Detergent, 360, 378, 384, 390
Drill advance, 220, 222, 224, 225, 227, 231, 232
Drug, 758
Dye, 478, 486, 489, 491, 550
E
Effervescent, 344
Efficiency, 673
Exercise bicycle, 404, 416, 420
F
Fabric stain, 395
Field, 437, 466, 468
Film viscosity, 610
Filter, 78, 84, 86
Fishing line, 759
Flour, 513, 524, 551, 607
Flour early, 555
Flour production, 587, 589, 611
Fractionation, 609, 610
G
Golf ball, 668
Golf driver, 430830 Index of Experiments
H
Handwheel, 551
Heart–lung pump, 37, 66, 73, 76, 77, 259, 284
I
Ice cream, 621, 624, 626, 627, 630, 657, 665, 666, 669
Ice melting, 246
Inclinometer, 525, 541, 546
Injection molding, 555, 761
Ink, 197
Insole cushion, 345
L
Lactic acid, 531
Length perception, 341
Light bulb, 337
Lithium bioavailability, 393
Load-carrying, 342
M
Machine head, 672, 683
Mangold, 447, 466, 550
Margarine, 133
Meat cooking, 67, 68, 100, 132, 198
Memory, 196
Memory recall, 339
Metal alloy, 350, 356
Mobile computing field study, 717, 742, 756, 763, 764
Mung bean, 120
N
Nail varnish, 162, 166, 167, 170
Neuron, 778, 783, 787
O
Oats, 709, 728, 736, 745, 753
Operator, 699
P
PAH recovery, 589, 597, 602
Paint, 553, 569, 571, 572, 576, 606, 608
Paint followup, 608
Paper towel absorbancy, 303
Paper towel strength, 240, 244
Peas, 468
Penicillin, 467
Perception, length, 341
Perception, quantity, 428
Plasma, 366, 380, 387, 394
Plastic, 678
Popcorn–microwave, 213, 238
Projectile, 465
Prosthetic elbow, 767
Q
Quantity perception, 428
R
Rail weld, 228, 234
Reaction time, 100, 133, 151, 153, 160, 177, 184, 341
Red blood cell, 700
Refinery, 507
Resin impurity, 612
Resin moisture, 613
Respiratory exchange ratio, 336
Resting metabolic rate, 311, 312, 336
Rocket, 241
Rust, 391
S
Sludge, 502, 538, 544
Soap, 49, 54, 60, 62, 91, 101, 132
Soil, 684
Soup, 499
Spaghetti sauce, 137
Spectrometer, 242, 556
Steel bar, 245
Step, 373, 392
Sugar beet, 492, 551
Survival, 198
Systolic blood pressure, 282
T
Temperature, 650, 654, 661, 669
Titanium alloy, 698, 699
Tool coating, 791
Trout, 67, 68, 101, 102, 105, 111, 116, 124, 130, 282
UU
AV experiment, 713, 732, 746, 762
UAV switch experiment, 734, 749, 762, 763
V
Vaccine, 538
Video game, 426, 427
Viscosity, 695
Viscosity, film, 610
Voltage, 687, 692, 695
W
Wafer, 519
Water boiling, 200
Water heating, 338
Weathering, 238, 239Index of Experiments 831
Weight lifting, 194
Weld strength, 194, 195
Welding, 505
Wildflower, 136
Y
Yeast, 346
Z
Zinc plating, 302A
Acid copper pattern plating, 599
Additive model, 143
Adjusted block sum of squares, 359
Adjusted means, 289
Adjusted treatment sum of squares, 358, 412
Adjusted treatment total, 358
Aliased effects, 495, 496
Aliasing scheme, 497
Analysis of covariance, 285, 289, 296, 299, 656
adjusted means, 289
assumption checking, 287
centered model, 286
confidence intervals, 294
least squares estimators, 288
model extensions, 287
multiple comparisons, 294
normal equations, 288
uncentered model, 286
Analysis of variance, 177, 186
balanced incomplete block designs, 358, 379, 385
confounding in factorial experiments, 435, 462, 464,
488, 489
crossed treatment factors, 159, 169, 177, 184, 211,
217
fixed effects, 41, 44, 54, 62
fractional factorial experiments, 538, 541, 544, 546
incomplete block designs, 358, 359, 380, 387
mixed effects, 648, 654, 661
nested factors, 676, 679, 683, 687, 691
one source of variation, 44, 623
one-way, 41, 44, 54, 62, 623
polynomial regression, 261, 273, 277
random effects, 623, 654
randomized complete block design, 311, 327, 331
response surface methods, 571, 581, 594, 597, 599,
603
row–column designs, 407, 408, 412, 416, 421
split-plot designs, 706, 709, 713, 715, 719, 729
split-split-plot designs, 712, 722
two-way, 159, 169, 177, 184
Assumption checking, 103, 104, 143
constant error variance, 110
independent errors, 108
lack of fit, 252
lack-of-fit test, 254, 276, 280
model fit, 106
normality of errors, 117
normality of random effects, 631
outliers, 107
random-effects model, 634
residual plots, 103
strategy, 103
Asymmetric factorial experiments, 433, 483, 511
Average reciprocal distance designs, 791
Axial points, 579
Axial-points block, 588
B
Balanced incomplete block design, 352
analysis of variance, 358, 385
assumption checking, 356
confidence intervals, 379, 386
contrast estimators, 360
factorial experiments, 372, 459
inter-block estimates, 739, 753
intra-block analysis, 738, 753
intra-block estimates, 738, 753
multiple comparisons, 360, 379, 386
necessary conditions for existence, 354
plotting data adjusted for block effects, 362
randomization, 353
sample sizes, 371
Balanced incomplete block designs
analysis of variance, 379
orthogonal contrasts, 360
Best linear unbiased predictor (BLUP), 772
Binary, 350
Block designs, 305, 349
Index834 Index of Subjects
Blocking factors, 305, 306, 597
crossed, 399
Blocks, 306
Block sizes, 306, 349
Block–treatment model, 356, 434
Blom’s normal scores, 117
Bonferroni method, 82, 83
Borehole function, 792
Box–Behnken designs, 592
orthogonal blocking, 592, 593
rotatable, 592, 593
Branching column, 534
C
Canonical analysis, 583, 597, 604
Canonical axes, 585
Canonical coefficients, 583, 585
Canonical form, 583
Carryover effects, 402
Cell-means model, 142, 201
Center points, 568
Centered covariate, 286, 296, 299
Centered linear regression model, 264
Centered regressors, 264
Central composite designs, 578
orthogonal, 586
orthogonal blocking, 588
rotatable, 586
Checking model assumptions, 103, see also Assumption
checking
Coefficient list, 146, 207
Coefficient of determination, 262
Coefficient of multiple determination, 262
Complete block designs, 305, 307, see also Randomized
complete block designs
Complete confounding, 451, 452, 459
Complete model, 142
Completely randomized designs, 31, 139, see also
Fractional factorial experiments; One source
of variation; Several crossed treatment factors;
Two crossed treatment factors
Composite design, 726
Computer simulator, 767
Confidence band, 258
Confidence bounds, 76
Confidence intervals, 74, 213, 223, 263, 276, 293, 638
Confidence region, 85
Confirmatory experiment, 451
Confounded, 434, 495
Confounding, 434, 713
complete, 451, 452, 459
partial, 451, 455
Confounding equations, 444
Confounding in factorial experiments, 433, 473
analysis of variance, 435, 462, 464, 488, 489
asymmetric factorial experiments, 483
block–treatment model, 434
complete confounding, 451, 459
confidence intervals, 462, 465, 489
confounding using contrasts, 435, 474
confounding using equations, 444, 475
four-level factors, 482
least squares estimators, 462, 465
partial confounding, 451, 460, 475
plans, 451, 481
pseudofactors, 482, 483
randomization, 436
three-level factors, 473, 475
two-level factors, 433
Confounding scheme, 443
Confounding using contrasts, 435, 474
Confounding using equations, 444, 475
Connected design, 352
Connectivity graph, 352
Contrast, 34, 69
coefficients, 70
difference of averages, 72
interaction, 144, 206
least squares estimator, 211
main-effect, 206
normalized, 70
pairwise comparison, 70
pairwise difference, 70
preplanned, 82
simple, 145
standard error, 70
sum of squares, 77, 212
three-factor interaction, 206
treatment, 69
treatment versus control, 71
trend, 72, 147, 266
two-factor interaction, 206
variance, 212
Control of noise variability, 523
Control treatment, 71
Covariates, 285, 305, 656
Critical coefficient, 83
Critical value, 597
Crossed array, 484
Crossed blocking factors, 399
Crossed treatment factors, 139
Crossover experiments, 401
Cubic correlation function, 789
Cyclic designs, 355
least squares estimators, 366
multiple comparisons, 366
randomization, 355
Cyclic Latin squares, 401
Cyclic row–column designs, 404, see also Row–column
designs
Cyclic Youden designs, 403
Cycling treatment labels, 355
D
Data adjusted for block effects, 362
Data snooping, 82Index of Subjects 835
Data transformation, 112
Decision rule, 77
Defining contrast, 496
Defining relation, 496
Definitive screening design, 537
Degrees of freedom, 209
Design, 31
Design matrix, 774
Design space, 768
Difference-of-averages contrast, 72
Difficult-to-change factors, 589, 703
Disconnected designs, 352, 355
Dunnett method, 82, 90
E
Effect sparsity, 172, 219, 222, 223, 533
Eigenvalues, 585, 597, 598, 604
Eigenvectors, 585, 597, 604
Empirical best linear unbiased predictor (eBLUP), 772
Empty cells, 228, 234
Emulator, 768
Error assumptions, 33, 104
constant variance, 110
independence, 108
normality, 117
Error sum of squares, 39, 210
Error variable, 32
Estimability of contrasts, 352
Estimable functions, 34
Estimated generalized least squares, 734, 749
Estimation rules, 209, see also Rules for estimation and
testing
Euclidean distance, 789
Experimental design, 31, 350
Experimental plan, 350
Experimentwise error rate, 81, 152
F
Factorial experiments, 201, 324, 372, 416, 433
asymmetric, 433, 511
balanced incomplete block designs, 459
confounding, 433, 473
fractions, 495
incomplete block designs, 433, 473
single replicate, 433
symmetric, 433
three-level factors, 473
two-level factors, 433
Factorial points, 568
Factorial structure, 372
Factorial-points block, 588
First associates, 354
First-order designs, 568
orthogonal, 569
First-order response surface regression model, 567
Fixed effects, 615
Fixed-effects models, 615
Fractional factorial experiments, 495, 498, 724
analysis of variance, 538, 541, 544, 546
asymmetric fractions, 724
asymmetrical fractions, 511, 512
blocking, 513
composite defining relation, 726
composite design, 726
free variables, 725
hypothesis tests, 541, 546
least squares estimators, 538, 545
nonregular fraction, 530
orthogonal arrays, 516, 521, 522
orthogonal main effect plan, 529
pseudofactors, 511, 719, 724
randomization, 495
regular fraction, 530
saturated design, 529
Taguchi experiments, 523, 539, 546
three-level factors, 507
two-level factors, 495, 516
Full model, 41
G
Gauss–Markov Theorem, 37
Gaussian correlation function, 788
Gaussian stochastic process, 770
Gaussian stochastic process model, 770
General complete block designs, 307, 309
Generalized least squares estimates, 734, 749
Generator, 530
Group divisible designs, 354, see also Incomplete block
designs
least squares estimators, 365
necessary conditions for existence, 355
H
Hadamard matrix, 534
Half-normal probability plots, 221, 225, 231
Half-normal scores, 221
Half-range, 568
Hypothesis testing rules, 209, see also Rules for
estimation and testing
Hypothesis tests, 212
I
Incomplete block designs, 307, 349
analysis of variance, 358, 359, 380, 387
assumption checking, 356
balanced incomplete block designs, 352
block sizes, 349
block–treatment model, 356
cyclic designs, 355
estimability of contrasts, 352
factorial experiments, 372
group divisible designs, 354
least squares estimators, 357, 365836 Index of Subjects
multiple comparisons, 357, 380, 387
plotting data adjusted for block effects, 362, 381, 387
R design generation, 382
randomization, 350
sample sizes, 371
SAS design generation, 376
two-level factorial experiments, 433
Independent contrasts, 443
Initial block, 355
Input combinations, 767
Input points, 767
Input space, 768
Interaction contrasts, 144, 206
Interaction line graph, 205
Interaction plots, 140, 202, 217
Interactions, 139, 141
three-factor, 202
two-factor, 139
L
Lack of fit, 106, 252
Lack-of-fit sum of squares, 572
Lack-of-fit test, 254, 581, 597, 600
Latin hypercube design (LHD), 776, 781, 786, 790
maximin, 778, 781, 786
minimax, 790
minimum average reciprocal, 791
Latin square designs, 401, see also Row–column designs
analysis of variance, 407, 408
assumption checking, 414
confidence intervals, 410
least squares estimators, 408, 410
multiple comparisons, 410
randomization, 401
replication, 402
row–column–treatment model, 405
sample sizes, 411
Latin squares, 401
Least squares estimators, 36, 149, 161, 163, 164, 253,
264, 265, 288, 313
Line graph, 205
Linear effect, 568
Linear model, 33
Linear trend contrast, 264
Local experiment, 566
Local linear effect, 568
Loss of information, 451
Lower confidence bound, 76
M
Main effects, 141
Main-effect contrasts, 152, 206
Main-effects model, 143, 161, 202
Maximin Latin Hypercube designs, 790
Maximum likelihood estimation, 771
Maximum likelihood estimator, 733, 749
Mean square, 210
Mesh size, 783
Method of least squares, 35
Midrange, 568
Minimax designs, 790
Minimum significant difference, 83
Mixed arrays, 523
Mixed models, 615, 642, 673
analysis of variance, 648, 654, 661
confidence intervals, 647, 648, 655, 662
expected mean squares, 643, 648, 654
hypothesis tests, 643, 648, 654, 661
least squares estimators, 655, 662
test statistic denominator, 648
Mixed models analysis
analysis of variance approach, 727, 745
restricted maximum likelihood approach, 734, 749
Mixed-models controversy, 648
Model building, 170
Modulo, 444, 476
Multiple comparisons, 81, 152, 166, 180, 187, 213, 294,
320, 321
Bonferroni method, 82, 83
combination of methods, 92
Dunnett method, 82, 90
Games–Howell method, 115
other methods, 92
Scheffé method, 82, 85
split-plot designs, 716, 721
split-split-plot designs, 722
summary of methods, 82
Tukey method, 82, 87
N
Nested blocking structure, 703
Nested factors, 671
analysis of variance, 676, 679, 683, 687, 691
assumption checking, 674
confidence intervals, 676, 678, 679, 682
expected mean squares, 679, 682, 687
fixed-effects model, 674
least squares estimators, 674
mixed effects, 682
rules for estimation and testing, 678, 679
test statistic denominator, 683
two-way nested models, 672, 673
Nested fixed effects, 674
Nested models, 671
Noise factors, 305, 513, 523, 541, 546
Noncollapsing design, 774
Normal equations, 35, 164, 253, 264, 265, 288, 412
Normal probability plots, 117
Normal scores, 117
Normalized contrasts, 70
Nuisance factors, 285, 305
O
One source of variation, 31, 41, 618Index of Subjects 837
fixed-effects model, 33, 265
analysis of variance, 41, 44, 54, 62
assumption checking, 103
confidence intervals, 74, 76, 94, 97
hypothesis tests, 77, 78, 94, 97
least squares estimates, 36
multiple comparisons, 81, 83, 86, 88, 90, 95, 99
normal equations, 35
randomization, 31, 52, 59
residual plots, 104
sample sizes, 45, 48, 92
random-effects model, 618
analysis of covariance, 656
analysis of variance, 623, 654
assumption checking, 631, 652, 659
confidence intervals, 625, 627
expected mean squares, 654
hypothesis tests, 654
least squares estimates, 36
normal equations, 35
randomization, 31, 52, 59
sample sizes, 628
variance-components estimators, 619, 621
One-way analysis of covariance, 289
One-way analysis of variance, 41, see also One source of
variation
Orthogonal arrays, 436, 495, 516
asymmetrical, 521
three-level factors, 522
two-level factors, 516
Orthogonal blocking, 587, 588
Orthogonal central composite designs, 586
Orthogonal contrasts, 172, 360, 435
Orthogonal first-order designs, 569
Orthogonal main-effect plan, 529, 530
Orthogonal polynomials, 266
Orthogonal second-order designs, 586
Outliers, 107
Overall confidence level, 81
Overall significance level, 81
Overfit, 251
P
Pairwise comparisons, 70
Pairwise differences, 70
Partial confounding, 451, 455, 460, 475
Partitioning principle, 80
Path of steepest ascent, 566, 576
Pearson product-moment correlation, 262
Plackett–Burman design, 530
Polynomial regression, 249
analysis of variance, 261, 273, 277
assumption checking, 252
confidence intervals, 258, 263, 276
hypothesis testing, 274, 277
lack of fit, 252
lack-of-fit test, 254, 276, 280
least squares estimators, 251, 253, 254, 264, 265
model, 250, 567
normal equations, 253, 254, 264, 265
orthogonal polynomials, 266
prediction intervals, 258, 276
quadratic regression, 251, 265
simple linear regression, 250, 257, 263
Pooled sample variance, 255
Power, 47
Power exponential correlation function, 788
Prediction intervals, 258, 276
Preplanned contrasts, 82
Product arrays, 523, 589
Pseudofactors, 482, 511, 719
Pure error, 255, 572
P-value, 45
Q
Quadratic regression, 251, 265
Quasi mean squared error, 223
R
Random block effects, 649, 739, 753
Random effects, 615, 618, 632, 679
Random numbers, 794, 796
Random two-way main-effects model, 632
Random-effects models, 615
Random-effects one-way model, 618
Random-effects two-way complete model, 632
Randomization, 31, 52, 59, 308, 350, 353
Randomized complete block designs, 305, 307, 308, 704
analysis of variance, 311, 318, 327, 331
assessment of blocking, 311
assumption checking, 323
block–treatment interaction model, 318, 325
block–treatment model, 310, 318, 325
factorial experiments, 324
least squares estimators, 313
multiple comparisons, 313, 320, 321
randomization, 308
sample sizes, 309, 322
Recovery of inter-block information, 736, 753
Reduced model, 41
Regression model, 249
Residual effects, 402
Residual maximum likelihood, 734, 749
Residual plots, 103, 104, 252, see also Assumption
checking
Residuals, 39, 104
scaled, 104
standardized, 104
Studentized, 104
Resolution, 498
Response curve, 249
Response surface, 249, 565
Response surface methods, 565
analysis of variance, 571, 581, 594, 597, 599, 603
analysis with blocking factors, 597838 Index of Subjects
assumption checking, 570
Box–Behnken designs, 592
canonical analysis, 583, 597, 604
central composite designs, 578
first-order designs, 568, 569
first-order model, 567
lack-of-fit test, 581, 597
orthogonal blocking, 587, 588
orthogonal designs, 586
path of steepest ascent, 576
rotatable designs, 585, 586
second-order designs, 578
second-order model, 573, 597, 602
Restricted maximum likelihood, 656, 664, 734, 743, 749,
756
Robust design, 523
Rotatable central composite designs, 586
Rotatable second-order designs, 585
Row–column designs, 399, 401, 403, 404
analysis of variance, 407, 416, 421
assumption checking, 414
confidence intervals, 417, 422
factorial experiments, 416
least squares estimators, 419, 425
multiple comparisons, 407
plotting data adjusted for block effects, 419, 425
randomization, 400
row–column–treatment model, 405
Row–column–treatment model, 405
R software, 57
analysis of covariance, 299
analysis of variance, 62
assumption checking, 125
confidence intervals, 97
data frame, 59
factor variable, 62
Games–Howell method, 130
hypothesis tests, 97
keyboard data entry, 61
least squares means, 62
library loading, 63
means, 128
mixed models, 661
multiple comparisons, 99
nested effects, 691
package installation, 63
plots, 60
plotting data, 61
regression, 276
residual plots, 125
Satterthwaite’s method, 130
transforming data, 129
updating the software, 58
user-defined function, 130
working directory, 58
Rules for estimation and testing, 209, 637, 647, 678, 682,
683
analysis of variance, 211, 648, 678, 683
confidence intervals, 213, 648, 682
contrast sum of squares, 212
contrast variance, 212
degrees of freedom, 209, 678
error sum of squares, 210
expected mean squares, 637, 648, 679, 682
hypothesis tests, 212, 648
least squares estimators, 211
mean square, 210
multiple comparisons, 213
test statistic denominator, 648, 683
total sum of squares, 210
Run order, 110
S
Saddle point, 578
Sample correlation, 262
Sample sizes, 45, 92, 171, 309, 322, 371, 628, 642, 657,
664, 665
SAS software
analysis of covariance, 296
analysis of variance, 54
assumption checking, 119
classification variable, 55
confidence intervals, 94
data input, 53
Games–Howell method, 124
hypothesis tests, 94
least squares means, 56
means, 122
multiple comparisons, 95
nested effects, 687
pdf file output, 55
plotting data, 55
random effects, 654
regression, 273
residual plots, 119
Satterthwaite’s method, 124
transforming data, 123
Satterthwaite’s approximation, 115, 124, 130, 154, 168,
655, 664, 691, 717, 733, 743, 746
Scaled residuals, 104
Scheffé method, 82, 85
Screening experiments, 497
Second associates, 354
Second-order designs, 578
orthogonal, 586
rotatable, 585
Second-order response surface regression model, 573,
597, 602
Separability of factorial effects, 205
Sequential sums of squares, 179, 273, 277
Several crossed treatment factors, 201
analysis of variance, 211, 217, 220
cell-means model, 201
confidence intervals, 213
hypothesis tests, 212
interaction plots, 202, 217
least squares estimators, 211Index of Subjects 839
main-effects model, 202
multiple comparisons, 213
rules for estimation and testing, 209
single replicate experiment, 219
three-way complete model, 202
Significance level, 43
Simple contrasts, 145, 732, 746
Simple linear regression, 250, 263
Simple pairwise differences, 145, 717
Simultaneous confidence intervals, 81, 223
Simultaneous hypothesis tests, 81
Single replicate experiments, 171, 183, 192, 219, 221,
223, 433
Split plots, 703
Split-plot designs, 703, 714, 718
analysis of variance, 706, 709, 713, 715, 719, 729
confidence intervals, 709
confounding, 724
expected mean squares, 728, 729, 745
least squares estimators, 708
models, 705, 718, 735, 750
multiple comparisons, 709, 716, 721, 729, 745
randomization, 703
split-plot analysis, 706
split-plot confounding, 713
type I analysis, 728
type III analysis, 729, 745
whole-plot analysis, 707
Split-split-plot designs, 711, 721
analysis of variance, 712, 722
model, 712, 722
multiple comparisons, 722
Standard error, 70
Standard first-order designs, 568
Standard Latin squares, 401
Star points, 579
Stationary point, 578
Studentized range distribution, 88
Studentized residuals, 104
Sum of products, 288
Sum of squares
blocks adjusted for treatments, 359
contrast, 77
error, 39
lack of fit, 255, 572
pure error, 572
total, 44
treatments, 42
treatments adjusted for blocks, 358, 412
Type I, 178, 187, 273, 277
Type III, 178, 187
Supersaturated designs, 533
Symmetric factorial experiments, 433
T
Taguchi experiments, 523
T-distribution approximation, 83
Test for lack of fit, 254
Test power, 47
Three-factor interaction contrast, 206
Three-way complete model, 202
Total sum of squares, 44, 210
Transformation, 112
Treatment contrasts, 34, 69, 293, 435
Treatments adjusted for blocks, 358, 461, 463
Treatment sum of squares, 42
Treatment-versus-control contrast, 71
Trend contrasts, 72, 147, 266
Tukey method, 82, 87
Tukey’s test for additivity, 175
Two crossed treatment factors, 139
analysis of variance, 155, 159, 168, 169, 177, 184, 186
assumption checking, 143, 182, 191
cell-means model, 142
complete model, 142
confidence intervals, 144, 152
interaction plots, 140
least squares estimators, 149, 161, 163, 164
main-effects model, 143, 161
multiple comparisons, 144, 152, 166, 180, 187
randomization, 139
residual plots, 182, 191
sample sizes, 171
single replicate experiment, 171, 183, 192
Two or more random effects, 632
analysis of variance, 648, 654
assumption checking, 634
confidence intervals, 638, 648
expected mean squares, 637, 648, 654
hypothesis tests, 640, 648, 654
intermediate random-effects model, 633
random-effects two-way complete model, 632
random two-way main-effects model, 632
sample sizes, 642
test statistic denominator, 648
variance-components estimators, 637
Two-factor interaction, 139
Two-factor interaction contrast, 206
Two-level factorial experiments, 433
Two-way analysis of variance, 159, see also Two crossed
treatment factors
Two-way nested model, 672
Type I sums of squares, 178, 187
Type III sums of squares, 178, 187
U
Unadjusted estimator, 356
Unadjusted mean, 289
Unconfounded, 307
Unequal variances, 154, 168
Upper confidence bound, 40, 76
V
Variance component estimation
analysis of variance estimates, 620, 625, 635, 637,
655, 664, 682, 727, 745840 Index of Subjects
restricted maximum likelihood estimates, 656, 664,
695, 733, 742, 748, 755, 776
Variance components, 618
Voss–Wang method, 223, 227, 232
W
Washout periods, 402
Websites
Dean Voss Draguljic, 54, 58
R-project, 57
RStudio, 57
Whole plots, 703
Words, 498
Y
Youden designs, 403, see also Row–column designs
analysis of variance, 407, 412
assumption checking, 414
confidence intervals, 413
least squares estimators, 412
multiple comparisons, 413
randomization, 403
replication, 403
row–column–treatment model, 405
sample sizes, 413
Youden square, 403
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