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عدد المساهمات : 18928 التقييم : 35294 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
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أخواني في الله أحضرت لكم كتاب Design and Analysis of Experiments Second Edition Angela Dean, Daniel Voss Danel Draguljić
![كتاب Design and Analysis of Experiments D_a_a_13](https://i.servimg.com/u/f61/15/36/74/14/d_a_a_13.jpg) 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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