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 |  موضوع: كتاب Design and Analysis of Experiments - Volume 1 الثلاثاء 11 يناير 2022, 1:58 am | |
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أحضرت لكم كتاب
Design and Analysis of Experiments - Volume 1
Introduction to Experimental Design
Second Edition
Klaus Hinkelmann
Virginia Polytechnic Institute and State University
Department of Statistics
Blacksburg, VA
Oscar Kempthorne
Iowa State University
Department of Statistics
Ames, IA
و المحتوى كما يلي :
Contents
Preface to the Second Edition
Preface to the First Edition
xxi
1 The Processes of Science
1.1 INTRODUCTION .
1.1 . 1 Observations in Science
1.1.2 Two Types of Observations .
1.1.3 From Observation to Law .
1.2 DEVELOPMENT OF THEORY
1.2.1 The Basic Syllogism
1.2.2 Induction, Deduction, and Hypothesis .
1.3 THE NATURE AND ROLE OF THEORY IN SCIENCE .
1.3.1 What Is Science?
1.3.2 Two Types of Science .
1.4 VARIETIES OF THEORY .
1.4.1 Two Types of Theory
1.4.2 What Is a Theory? .
THE PROBLEM OF GENERAL SCIENCE
1.5.1 Two Problems .
1 S.2 The Role of Data Analysis .
1 S.3 The Problem of Inference .
1.6 CAUSALITY
1.6.1 Defining Cause. Causation. and Causality .
1.6.2 The Role of Comparative Experiments .
1.7 THEUPSHOT .
1.8 WHAT IS AN EXPERIMENT?
Absolute and Comparative Experiments
1.8.2 Three Types of Experiments
1.9 STATISTICAL INFERENCE
1.9.1 Drawing Inference .
1.9.2 Notions of Probability .
1.9.3 Variability and Randomization .
1.5
1.8.1
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26 vi CONTENTS
2 Principles of Experimental Design 29
2.1 CONFIRMATORY AND EXPLORATORY EXPERIMENTS 29
2.2 STEPS OF DESIGNED INVESTIGATIONS . 30
2.2.1 Statement of the Problem 31
2.2.2 Subject Matter Model . 32
2.2.3 Three Aspects of Design 33
2.2.4 Modeling the Response . 35
2.2.5 Choosing the Response . 36
2.2.6 Principles of Analysis . 36
2.3 THE LINEAR MODEL . 37
2.3.1 Three Types of Effects . 37
2.3.2 Experimental and Observational Units . 38
2.3.3 Outline of a Model . 40
2.4.1 The Questions and Hypotheses . 41
2.4.2 The Experiment and a Model 41
2.4.3 Analysis 42
2.4 ILLUSTRATING INDIVIDUAL STEPS: STUDY 1 . 41
2.4.4 Alternative Experimental Setup 44
2.5 THREE PRINCIPLES OF EXPERIMENTAL DESIGN 45
2.6 THE STATISTICAL TRIANGLE: STUDY 2 . 46
2.6.1 Statement of the Problem 46
2.6.2 Four Experimental Situations . 46
2.7 PLANNING THE EXPERIMENT: THINGS TO THINK ABOUT 5 1
2.8 COOPERATION BETWEEN SCIENTIST AND STATISTICIAN . . 53
2.9 GENERAL PRINCIPLE OF INFERENCE AND TYPES OF
STATISTICAL ANALYSES 56
2.9.1 General Model . 56
2.9.2 Outline of the ANOVA . 56
2.10 OTHER CONSIDERATIONS FOR EXPERIMENTAL DESIGNS . . 58
3 Survey of Designs And Analyses 61
3.1 INTRODUCTION . 61
3.2 ERROR-CONTROL DESIGNS 62
3.3 TREATMENT DESIGNS 64
3.4 COMBINING IDEAS FROM ERROR-CONTROL AND
TREATMENT DESIGNS 65
3.5 SAMPLING DESIGNS . 68
3.6 ANALYSIS AND STATISTICAL SOFTWARE 68
3.7 SUMMARY., . 69
4 Linear Model Theory 71
4.1 INTRODUCTION . 71
4.1.1 The Concept of a Model 71
4.1.2 Comparative and Absolute Experiments 73
4.2 REPRESENTATION OF LINEAR MODELS . 73
4.3 FUNCTIONAL AND CLASSIFICATORY LINEAR MODELS . 74 CONTENTS vii
4.3.1 Functional Models . 74
4.3.2 Classificatory Models . 74
4.3.3
Components 75
4.4 THE FITTING OF y = Xp 76
4.4.1 The Notion of Identifiability 76
4.4.3 The Method of Least Squares . 77
4.4.4 Theory of Linear Equations 81
4.5 MOORE-PENROSE GENERALIZED INVERSE . 84
4.6 CONDITIONED LINEAR MODEL 85
4.6.1 Affine Linear Model 85
4.6.2 Normal Equations for the Conditioned Model . 87
4.6.3 Different Types of Conditions . 88
4.6.4 General Case 89
4.7 TWO-PART LINEAR MODEL 90
4.7.1 Ordered Linear Models . 90
4.7.2 Using Orthogonal Projections . 91
4.7.3 Orthogonal ANOVA 93
Models with Classificatory and Functional
4.4.2 The Notion of Estimability . 77
4.8 SPECIAL CASE OF A PARTITIONED MODEL . 94
4.9 THREE-PART MODELS 94
4.10 TWO-WAY CLASSIFICATION WITHOUT INTERACTION 95
4.1 1 K-PART LINEAR MODEL . 97
4.11.1 The General Model and Its Sums of Squares 97
4.1 1.2 The Means Model . 99
4.12 BALANCED CLASSIFICATORY STRUCTURES 100
4.12.1 Factors, Levels, and Partitions . 101
4.12.2 Nested, Crossed, and Confounded Factors . 101
4.12.3 The Notion of Balance . 102
4.12.4 Balanced One-way Classification . 102
4.12.5 Two-way Classification with Equal Numbers . 103
4.12.6 Experimental versus Observational Studies 104
4.12.7 General Classificatory Structure 106
4.12.8 The Well-Formulated Model 109
112
4.13.1 Two-Fold Nested Classification 112
4.13.2 Two-way Cross-Classification . 113
4.13.3 Two-way Classification without Interaction 116
4.14 ANALYSIS OF COVARIANCE MODEL . 118
4.14.1 The Question of Explaining Data . 118
4.14.2 Obtaining the ANOVA Table 120
4.14.3 The Case of One Covariate . 121
4.14.4 The Case of Several Covariates 121
4.15 FROM DATA ANALYSIS TO STATISTICAL INFERENCE . 122
4.16 SIMPLE NORMAL STOCHASTIC LINEAR MODEL 123
4.16.1 The Notion of Estimability . 123
4.13 UNBALANCED DATA STRUCTURES ...
V l l l CONTENTS
4.16.2 Gauss-Markov Linear Model
4.16.3 Ordinary Least Squares and Best Linear Unbiased Estimators
4.16.4 Expectation of Quadratic Forms
4.17.1 Distributional Properties of X'P
4.17.2 Distribution of Sums of Squares
4.17.3 Testing of Hypotheses .
4.18 MIXED MODELS .
4.18.1 The Notion of Fixed, Mixed and Random Models .
4.18.2 Aitken-like Model .
4.18.3 Mixed Models in Experimental Design
4.17 DISTRIBUTION THEORY WITH GXNLM .
5 Randomization
5.1 INTRODUCTION .
5.1.1 Observational versus Intervention Studies .
5.1.2 Historical Controls versus Repetitions .
5.2 THE TEA TASTING LADY
5.3 TRIANGULAR EXPERIMENT
5.3.1 Medical Example
5.3.2 Randomization. Probabilities. and Beliefs .
5.4 SIMPLE ARITHMETICAL EXPERIMENT
5.4.1 Noisy Experiments .
Investigative Experiments and Beliefs .
5.4.3 Randomized Experiments .
5.5 RANDOMIZATION IDEAS
5.6 EXPERIMENT RANDOMIZATION TEST
5.7 INTRODUCTION TO SUBSEQUENT CHAPTERS .
5.4.2
6 Completely Randomized Design
6.1 INTRODUCTION AND DEFINITION
6.2 RANDOMIZATION PROCESS
Use of Random Numbers
6.2.2 Design Random Variables .
6.3 DERIVED LINEAR MODEL .
Conceptual Responses and Observations
6.3.2 Distributional Properties
6.3.3 Additivity in the Broad Sense .
6.3.4 Error Structure .
6.3.5 Summary of Results
6.4 ANALYSIS OF VARIANCE
6.4.1 Deriving the ANOVA Table
Obtaining Expected Mean Squares .
6.5 STATISTICAL TESTS .
6.5.1 Enumerating Randomizations .
6.5.2 Randomization Test
6.6 APPROXIMATING THE RANDOMIZATION TEST .
6.2.1
6.3.1
6.4.2
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174 CONTENTS ix
6.6.1 Moments of the Test Statistic 174
6.6.2 Approximation by the F-Test 177
6.6.3 Simulation Study 177
6.7 CRD WITH UNEQUAL NUMBERS OF REPLICATIONS 179
6.7.1 Randomization . 180
6.7.2 The Model and ANOVA 180
6.7.3 Comparing Randomization Test and F-Test 180
6.8 NUMBER OF REPLICATIONS 180
6.8.1 Power of the F-Test . 182
6.8.2 Smallest Detectable Difference . 184
6.8.3 Practical Considerations 185
6.9 SUBSAMPLING IN A CRD 191
6.9.1 Subsampling Model 191
6.9.2 Inferences with Subsampling 193
6.9.3 Comparison of CRDs without and with Subsampling . 193
6.10 TRANSFORMATIONS . 196
6.10.1 Nonadditivity in the General Sense 196
6.10.2 Nonconstancy of Variances . 197
6.10.3 Choice of Transformation . 198
6.10.4 Power Transformations . 200
6.1 1 EXAMPLES USING SAS@ 201
6.12 EXERCISES 204
7 Comparisons of Treatments 213
7.1 INTRODUCTION . 213
7.2 COMPARISONS FOR QUALITATIVE TREATMENTS . 213
7.2.1 Treatment Contrasts 214
7.2.2 Orthogonal Contrasts 214
7.2.3 Partitioning the Treatment Sum of Squares 215
7.3 ORTHOGONALITY AND ORTHOGONAL COMPARISONS 218
7.4 COMPARISONSFORQUANTITATIVETREATMENTS 219
7.4.1 Comparisons for Treatments with Equidistant Levels . 219
7.4.2 Use of Orthogonal Polynomials 220
7.4.3 Contrast Sums of Squares and the ANOVA 223
7.5 MULTIPLE COMPARISON PROCEDURES . 224
7.5.1 Multiple Comparisons and Error Rates . 224
7.5.2 Least Significant Difference Test 225
7.5.3 Bonferroni t-Statistics . 225
7.5.4 Studentized Range Procedure . 226
7.5.5 Duncan’s Multiple Range Test . 226
7.5.6 Scheffk’s Procedure 227
7.5.7 Comparisons with a Control 227
7.5.8 Alternatives to Tests Based on Normality . 228
7.6 GROUPING TREATMENTS 229
7.7 EXAMPLES USING SAS@ 230
7.8 EXERCISES 236 X CONTENTS
8 Use of Supplementary Information
8.1 INTRODUCTION .
8.2 MOTIVATION OF THE PROCEDURE
8.3 ANALYSIS OF COVARIANCE PROCEDURE
8.3.1 Basic Model
8.3.2 Least Squares Analysis .
8.3.3 Least Squares Means
8.3.4 Formulation in Matrix Notation
8.3.5 ANOVA Table .
8.4 TREATMENT COMPARISONS
8.4.1 Preplanned Comparisons
8.4.2 Multiple Comparison Procedures .
8.5 VIOLATION OF ASSUMPTIONS .
8.5.1 Linear Relationship between x and y
8.5.2 Common Slope .
8.5.3 Covariates Affected by Treatments .
8.5.4 Normality Assumption .
8.6 ANALYSIS OF COVARIANCE WITH
SUBS AMPLING
8.7 CASE OF SEVERAL COVARIATES .
8.7.1 General Case
8.7.2 Two Covariates .
8.8 EXAMPLES USING SAS@
8.9 EXERCISES
9 Randomized Block Designs
9.1 INTRODUCTION .
9.2 RANDOMIZED COMPLETE BLOCK DESIGN .
9.2.1 Definition
9.2.2 Derived Linear Model .
9.2.3 Estimation of Treatment Contrasts .
9.2.4 Analysis of Variance
9.2.5 Randomization Test and F-Test
9.2.6 Additivity in the Broad Sense .
9.2.7 Subsampling in an RCBD .
9.3 RELATIVE EFFICIENCY OF THE RCBD
9.3.1 Question of Effectiveness of Blocking .
9.3.2 Use of Uniformity Trials
9.3.3 Interpretation and Use of Relative Efficiency .
9.4 ANALYSIS OF COVARIANCE
9.4.1 TheModel .
9.4.2 Least Squares Analysis .
9.4.3 The ANOVA Table .
9.5 MISSING OBSERVATIONS
9.5.1 Estimating a Missing Observation .
9.5.2 Using the Estimated Missing Observation .
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297 CONTENTS xi
9.5.3 Several Missing Observations . 298
9.6 NONADDITIVITY IN THE RCBD 300
9.6.1 The Problem of Nonadditivity . 300
9.6.2 General Model for Nonadditivity 300
Nonadditivity 302
9.6.4 Testing for Nonadditivity 303
9.6.6 Generalizations . 305
9.6.7 Several Blocking Factors 306
9.6.8 Dealing with Block-Treatment Interaction . 312
9.7 GENERALIZED RANDOMIZED BLOCK DESIGN . 314
9.7.1 Definition 314
9.7.2 Derived Linear Model . 314
9.7.3 TheANOVATable . 317
9.7.4 Analyzing Block-Treatment Interaction 319
9.7.5 A More General Formulation 323
9.7.6 Random Block Effects . 324
9.7.7 Using Satterthwaite’s Procedure 326
9.8 INCOMPLETE BLOCK DESIGNS 328
Blocks . 328
9.8.2 Balanced Incomplete Block Designs 330
9.8.3 BalancedTreatment IncompleteBlockDesigns 333
9.8.4 Partially Balanced Incomplete Block Designs . 335
9.8.5 Extended Block Designs 337
9.8.6 Some General Remarks . 338
9.9 SYSTEMATIC BLOCK DESIGNS 340
9.9.1 Dealing with Trends 340
9.9.2 Trend-free Designs . 341
9.10 EXAMPLES USING SAS@ 343
9.11 EXERCISES 366
9.6.3 One Blocking Factor: A Specific Model for
9.6.5 Tukey’s Test for Nonadditivity . 303
9.8.1 General Notion of Designs with Incomplete
10 Latin Square Type Designs 373
10.1 INTRODUCTION AND MOTIVATION 373
10.2 LATIN SQUARE DESIGN . 374
10.2.1 Definition 374
10.2.2 Transformation Sets and Randomization 376
10.2.3 Derived Linear Model . 377
10.2.4 Estimation of Treatment Contrasts . 380
10.2.5 Analysis of Variance 382
The Model under Additivity in the Broad Sense
10.2.7 Consequences of Nonadditivity 386
10.2.8 Investigating Nonadditivity . 387
10.2.9 Miscellaneous Remarks 389
10.3 REPLICATED LATIN SQUARES . 390
10.2.6 385 xii CONTENTS
10.3.1 Different Scenarios for Replication 390
10.3.2 Rows and Columns Crossed with
10.3.3 Rows Nested in and Columns Crossed with
10.3.4 Rows and Columns Nested in Replications 392
10.3.5 Replication x Treatment Interaction 392
10.4 LATIN RECTANGLES . 393
10.5 INCOMPLETE LATIN SQUARES 394
10.6 ORTHOGONAL LATIN SQUARES 395
10.6.1 Graco-Latin Squares 395
10.6.2 Mutually Orthogonal Latin Squares 396
10.7.1 Two-Treatment Change-Over Design . 398
10.7.2 Change-Over Designs for More than Two Treatments . 401
10.7.3 Some Variations and Extensions 402
10.9 EXERCISES 414
Replications 391
Replications 391
10.7 CHANGE-OVER DESIGNS 397
10.8 EXAMPLES USING SAS@ 404
11 Factorial Experiments: Basic Ideas 419
11.1 INTRODUCTION . 419
1 1.2 INFERENCES FROM FACTORIAL EXPERIMENTS 420
11.3 EXPERIMENTS WITH FACTORS AT TWO LEVELS 422
11.3.1 Definition of Main Effects and Interactions 422
1 1.3.2 Estimation of Main Effects and Interactions 425
11.3.3 Sums of Squares for Main Effects and Interactions 426
1 1.4 INTERPRETATION OF EFFECTS AND INTERACTIONS . 426
11.5 INTERACTIONS: A CASE STUDY 428
1 1.5.1 The Experiment . 428
1 1.5.2 The Model . 428
1 1 S.3 The Analysis 430
11.5.4 Separate Analyses . 439
1 1 S.5 Blocking by Intrinsic Factor Only . 440
1 1 S.6 Using the Half-normal Plot Technique . 441
1 1 S.7 The Analysis 443
11.5.8 Summary 446
1 1.6 2n FACTORIALS IN INCOMPLETE BLOCKS 446
11.6.1 23 Factorial in Blocks of Size 4 446
11.6.2 23 Factorial in Blocks of Size 2 447
1 1.6.3 Partial Confounding 449
1 1.7 FRACTIONS OF 2n FACTORIALS 451
11.7.1 Rationale for Fractional Replication 451
1 1.7.2 1/2 Fraction of the 23 Factorial . 454
11.7.3 The Alias Structure . 454
11.7.4 1/4 Fraction of the 28 Factorial . 456
11.7.5 Systems of Confounding for Fractional Factorials . 457 CONTENTS Xlll ...
11.8 ORTHOGONAL MAIN EFFECT PLANS FOR 2n FACTORIALS . . 462
11.9 EXPERIMENTS WITH FACTORS AT THREE LEVELS 464
11.9.1 The 3' Factorial 465
11.9.2 Extensions . 468
11.9.4 Systems of Confounding for the 3" Factorial . 470
1 1.9.5 Fractions of 3" Factorials . 472
11.9.6 Highly Fractionated 3" Factorials . 475
11.9.3 Formal Definition of Main Effects and Interactions 468
11.9.7 Systems of Confounding for Fractions of 3n
Factorials 475
476
11.10.1 Asymmetrical Factorial Experiments . 476
11 . 10.2 Confounding in 2" x 3n Factorials 477
Blocks of Size 18: . 478
Blocks of Size 12: . 478
Blocks of Size 9: 478
Blocks of Size 6: 478
Blocks of Size 4: 478
479
11.1 1 EXAMPLES USING SAS@ 481
11.12 EXERCISES 492
11.10 FACTORS AT TWO AND THREE LEVELS .
11.10.3 Fractions of 2m x 3n Factorials
12 Response Surface Designs 497
12.2 FORMULATION OF THE PROBLEM 498
12.3 FIRST-ORDER MODELS AND DESIGNS 500
12.3.1 First-Order Regression Model . 500
12.3.2 Least Squares Analysis .
12.3.3 Alternative Designs . 503
12.4 SECOND-ORDER MODELS AND DESIGNS 504
12.4.1 Second-Order Linear Regression 504
12.4.2 Possible Designs 505
12.4.3 Central Composite Designs 506
Blocking in Central Composite Designs
12.4.5 Box-Behnken Designs . 509
Hard-to-Change versus Easy-to-Change Factors
12.5 INTEGRATED MEAN SQUARED ERROR DESIGNS
12.5.1 Variance and Bias for the One-Factor Case 514
12.5.2 Choice of Design
12.6 SEARCHING FOR AN OPTIMUM 518
12.7 EXPERIMENTS WITH MIXTURES . 519
12.7.1 Defining the Problem 519
12.7.2 Simplex-Lattice Designs 520
12.7.3 Simplex-Centroid Designs . 521
12.7.4 Axial Designs 521
12.7.5 Canonical Polynomials . 521
12.1 INTRODUCTION . 497
500
12.4.4
12.4.6
507
511
513
517 xiv CONTENTS
12.7.6 Including Process Variables 523
12.8 EXAMPLES USING SAS@ 523
12.9 EXERCISES 531
13 Split-Plot Type Designs 533
13.1 INTRODUCTION . 533
13.2 SIMPLE SPLIT-PLOT DESIGN 534
13.2.1 Superimposing Two Randomized Complete Block Designs . . 534
13.2.2 Derived Linear Model . 537
13.2.3 Testing of Hypotheses . 538
13.2.4 Estimating Treatment Contrasts 539
13.2.5 Testing Hypotheses about Treatment Contrasts 542
13.3 RELATIVEEFFICIENCY OFSPLIT-PLOTDESIGN 543
13.4 OTHER FORMS OF SPLIT-PLOT DESIGNS . 544
13.4.2 Split-Plot Design in Time . 545
13.4.4 SPD(LSD, RCBD) . 548
13.4.5 SPD(CRD, IBD) 549
13.4.6 SPD(GRBD, RCBD) 550
13.4.7 SPD(GRBD, IBD) . 552
13.4.1 SPD(CRD, RCBD) . 545
13.4.3 SPD(CRD, LSD) 547
13.4.8 SPD(IBD, RCBD) . 553
13.4.9 SPD(RCBD, GRBD) 554
13.4.10 Summary 555
13.5.1 The Layout . 555
13.5.2 Linear Model and ANOVA . 557
13.5.3 Estimating Treatment Contrasts 557
13.7 EXAMPLES USING SAS@ 562
13.8 EXERCISES 569
13.5 SPLIT-BLOCK DESIGN 555
13.6 SPLIT-SPLIT-PLOT DESIGN . 560
14 Designs with Repeated Measures 573
14.1 INTRODUCTION . 573
14.2 METHODS FOR ANALYZING REPEATED MEASURES DATA . . 574
14.2.1 Comparisons at Separate Time Points . 574
14.2.2 Use of Summary Measures . 575
14.2.3 Trend Analysis . 575
14.2.4 The ANOVA Method 577
14.2.5 Mixed Model Analysis . 578
14.4 EXERCISES 593
14.3 EXAMPLES USING SAS@ 580
Epilogue 595 CONTENTS
Bibliography
Abbreviations
Author Index
Subject Index
Author Index
Addelman, S., 109,480
Afsarinejad, K., 401-402, 573
Aikins, D., 33
Alcorn, J. S., 308
Algina, J., 574
Alldredge, J. R., 407
Altman, D. G., 574
Amaranthus, M. P., 33
Anderson, V. L., 479
Androne, A. S., 32
Arnold, J. C., 292, 389
Balaam, L. N., 399,403
Balakrishnan, N., 175
Bancroft, T. A., 256,313
Bartlett, M. S., 198
Bechhofer, R. E., 333, 335
Behnken, D. W., 509,511
Belsley, D. A., 258
Beyer, W. H., 221
Birch, J. B., 257
Blaisdell, E. A., Jr., 403
Borkowski, J. J., 51 I
Bose, R. C., 335, 396-397
Bowman, K. O., 184, 190, 196,292
Box, G. E. P., 200, 455, 497, 499, 504,
Bradley, R. A., 341-342
Buehler, R. J., 519
Burman, J. P., 464
Burton, R. D., 306
506-507,509,5 17-5 19
Calinski, T., 229-230
Campbell, M. J., 575
Carlson, S. R., 307
Carmella, S. G., 38
Carmer, S. G., 225
Carter, W. H., Jr., 497
CASS Principal Investigators, 20
Clatworthy, W. H., 335-336, 509
Cochran, W. G., 239, 253, 331, 395-396,
400,542
Coggin, C. J., 20
Coleman, D. E., 30
Connor, W.J., 479
Conover, W. J., 258
Coons, I., 295, 389
Cornell, J. A., 499, 504, 507, 517-519,
Corsten, L. C. A., 229-230,306
Cotterill, P. P., 306
521-522
COX, D. R., 35, 151, 200, 252-253, 260,
292,341
COX, G. M., 331, 395-396,400,542
Craske, M. G., 33
Crowder, M., 573
Daniel, C., 441
Dean, C. A., 306
DCnes, J., 376
De Palluel, C., 374
Dick, I. D., 303
Diers, B. W., 307
Doerfler, T. E., 127, 178, 286
Draper, N. R., 499, 507,509,517-518
Dryden, G. McL., 33
Duncan, D. B., 226
Dunlap, W. P., 230
Dunnett, C. W., 227-228
615 616 AUTHOR INDEX
Eisenhart, C., 132, 326
Ellis, R. L., 3, 7
Euler, L., 374
Evans, M. A., 407
Everitt, B. S., 574
Federer, W. T., 59, 338
Feldt, L. S., 545, 577
Finney, D. J., 574, 579
Fisher, L. D.. 20.313. 319
Fisher, R. A., 68, 139-140, 148-150, 177,
221, 225, 239, 278, 286, 374,
377,396,420
Folks, L., 11, 27
Fox, M., 184
Freeman, M. F., 200
Frison, L., 573, 575
Fritz, V. A., 38
Gallie, W. B., 7
Gardner, G. M., 38
Geisser, S., 577
Gersh, B. J., 20
Glass, S., 389
Glenn, W. A., 298
Graybill, F. A., 305-306
Greenhouse, S., 577
Hand, D., 573
Harter, H. L., 226-227
Hartley, H. O., 184, 221, 323, 395
Harville, D. A., 130
Heagerty, P. J., 20, 313, 319
Heath, D. D., 3, 7
Hecht, S. S., 38
Hedayat, A., 338,401,573
Hering, F., 560
Hext, G. R., 519
Hinkelmann, K., xix, 35, 38, 41, 55, 292,
Hinsworth, F. R., 519
Hochberg, Y., 225-226, 228, 252
Hocking, R. R., 99-100, 134,258
Hryniewicz, K., 32
Hsu, J. C., 225
Huber, P. J., 228, 257
295,308,389,428,509
Hudaihed, A., 32
Hunter, J. S., 455,499, 506-507
Huynh, H., 545,577
Iman, R. L., 258
Jacroux, M., 342
Jo, J., 509
John, J. A., 366
John, P. W. M., 338
Johnson, D. E., 305-306, 570-571
Johnson, N. L., 175
Jones, B., 400
Kabelka, E. A., 307
Kastenbaum, M. A., 184, 190, 196,292
Katz, S. D., 32
Keedwell, A. I., 376
Kempthorne, O., xxii, 11, 27, 109, 127,
151, 157, 161, 174, 178, 197-
198, 228, 285- 286, 291, 300,
312, 323-324, 377, 386-387,
419,468,480,519
Kenney, P. M., 38
Kenward, M. G., 400
Keppel, G., 548
Keselman, H. J., 574
Keynes, J. M., 25
Khuri, A. I., 499, 504, 507, 517-518
Kiefer, J., 59
Kii, W. Y., 33
Kirk, R. E., 307
Knott, M., 229
Konnerth, T. K., 230
Kotz, S., 175
Kowalchuk, R. K., 574
Kowalski, S. M., 512
Kramer, C. Y., 226,251-252, 298, 389
Kress, L. W., 41
Kuehl, R. O., 232
Kuh, E., 258
Lane, P. W., 245
Lang, A. J., 33
Lencina, V. B., 134
Lentner, M., 292, 389 AUTHOR INDEX 617
Lucas, H. L., 400,403
Lucas, J. M., 5 11
Lumley, T., 20, 313, 319
Majumdar, D., 342
Mandel, J., 302-303, 305-306,440
Marasinghe, M. G., 306
Mathon, R., 331
Matthews, J. N. S., 575
McCarthy, M. D., 197
McCullagh, P., 253,260
McLean, R. A., 479
Mead, R., 497
Mejza, S., 560
Miller, R. G., 225-228, 251
Milliken, G. A., 245, 570-571
Montgomery, D. E., 30, 499, 507
Myers, R. H., 74, 257-258, 263. 498-499,
Myers, W. D., 20
Mystkowski, J. L., 33
507
Nair, K. R., 335
Nair, M. G., 33
Narula, S. C., 224
Nelder, J. A., 134, 245
Neyman, J., 140, 197,341,387
Northrop, F. S. C., 24
Notz, W. I., 342
Nowell-Smith, P. H., 18
Oberman, A., 20
Odeh, R. E., 184,342
Parker, E. T., 396
Parker, P. A., 512
Patterson, H. D., 402-403
Pauling, L., 14
Pearce, S. C., 35,277,333,428
Pearson, E. S., 184, 221
Peirce, C. S., 19
Perry, C. O., 295
Pike, D. J., 497
Pitman, E. J. G., 177,286
Plackett, R. L., 464
Pocock, S. J., 573,575
Powell, R. S., 230
Preece, D. A., 59
Quenouille, M. H., 366
Raghavarao, D., 33 1,403
Rao, C. R. 127
Ratkowsky, D. A., 407
Reid, T. C., 33
Richards, W., 176
Ringland, J. T., 228
Robinson, J., 248, 305, 549-550
Rogers, W. J., 20
Rojas, B. A., 387
Rom, D., 225
Rosa, A., 331
Rosen, C. J., 38
Rosenbaum, P. R., 240
Roux, C. Z . , 303
Rowell, J. G., 575
Roy, R. K., 477
Royston, P., 575
Runes, D. D., 17
Russell, B., 7, 12-13
SAS Institute, Inc., xviii, 69, 86, 98, 154,
180, 185, 201, 343, 451,459,
578
Satterthwaite, F. E., 326, 542, 561
Savage, L. J., 26
Scheffk, H., 184, 228, 260, 303, 305, 388,
519
Scheffler, I., 24
Scott, A. J., 229
Searle, S. F., 245
Shah, B. V., 59, 519
Shah, R. K., 342
Sheffield, L. T., 20
Shrikhande, S. S., 396
Singer, J. M., 134
Skelly, J. M., 41
Smith, C. A. B., 399
Smith, H. F., 240, 256
Snedecor, G. W., 229
Snee, R. D., 312
Spedding, J., 3, 7 618 AUTHOR INDEX
Speed, F. M., 100,245
Spendley, W., 5 19
Srivastava, J., 60, 387
Stablein, D. M., 497
Stanek, E. J., 111, 134
Stebbing, L. S., 21
Steinfeld. D., 33
Stevens, W. L., 397
Stewart, M. J., 308
Stoline, M. R., 225
Street, A. P., 374
Street, D. J., 374
Stufken, J., 342
Swanson, M. R., 225
Taguchi, G., 463-464,477
Tamhane, A. C., 225-226, 228, 252, 333,
335
Tang, P. C., 184
Throckmorton, T. N., 109
Tobias, R. D., 225
Tukey, J. W., 200,224,226,302-303,305,
387-388,440
van Belle, G., 20, 313, 319
van Eijnsbergen, A. C., 306
Venn, J., 25
Vining, G. G., 498,512
Voss, D. T., 134
Wagenaar, W. A., 402,547
Walters, D. E., 575
Wampler, J. L., 497
Wang, Y. C., 387
Ward, G. C., 303
Watson, G. S., 127
Webb, D. F., 51 1
Welch, B. L., 177, 286, 384-385
Welsch, R. E., 258
Westfall, P. H., 225
White, R. F., 109
Wilk,M. B., 161,300,317,323-324,386-
Williams, E. J., 401,403, 547
Wilson, K. B., 497,499, 506,518-519
Wolfinger, R. D., 225
387
Yates, F., 59,221,290-291,295, 330,377,
Yeh, C. M., 341-342
Youden, W. J., 394
Young, S., 479
394-396,420,468, 534, 549
Zahn, D. A., 441
Zedek, S., 548
Zyshnd, G., 107-109, 127,323 Subject Index
Additivity
in the broad sense, 161, 164, 218,
286, 300,329,385,425
in the strict sense, 158, 161, 164,
171, 218,280,286,300,377
transformation to, 388
unit-treatment, 40, 197, 329, 377,
425, 537
Aitken
equation, 125-127
theorem, 125- 127
matrix, 516
structure, 454-455,473-475
approximate, 295
cluster, 229
of data, 29
of experiments, 20-22, 26
mixed model, 578
nonparametric, 68
regression, 220,491. See also
statistical, 30, 36, 43, 55-57
trend, 575
Alias
Analysis
Regression, analysis
Analysis of covariance, 118, 121, 239,
242, 258-260, 292, 295, 389
algebra of, 12 1
model, 118
with subsampling, 258
table, 248-249, 294
technique, 295
Analysis of variance (ANOVA), 36, 42-
46, 68, 79, 92, 95, 99-101,
112, 115, 130, 151, 165-166,
177
auxiliary, 122, 242
between-and-within subjects de-
CRD, 167
BIBD, 361-364
sign, 566
with orthogonal contrasts,
with orthogonal polynom-
with repeated measures,
with subsampling, 194
with unequal numbers, 182
217,233
ials, 224, 235
58 1
cross-over design, 410
first-order design, 501-502, 525
GRBD, 317-318,324,357
Graco-Latin square, 397
IBD, 330
LSD, 383,405
orthogonal, 93-94
preliminary, 433
replicated, 391-393,408
RCBD, 282-284,344
with crossed blocking fac-
tors, 3 11
with nested blocking fac-
tors, 309-310, 354
under nonadditivity, 304
with subsampling, 289,
310,349,354
second order design, 505
SPD(BIBD, RCBD), 555
SPD(CRD,BIBD), 551
619 620 SUBJECT INDEX
SPD(CRD, LSD), 548
SPD(CRD, RCBD), 545
with repeated measures,
589
SPD(GRBD, BIBD), 553
SPD(GRBD, IBD), 554
SPD(GRBD, RCBD), 552
SPD(LSD, RCBD), 549
SPD(RCBD, GRBD), 556
SPD(RCBD, RCBD), 536
split-block design, 5.58
split-plot design, 536, 563
split-split-plot design, 561
table, 245-246, 259, 301, 430-43 1,
438,448,467
two-way classification, 105
uniformity trial, 291, 544
Anaximander, 12
Anaximenes, 12
Aphorism, 3,7,
Aquinas, 13, 17
Aristotle, 9, 12-13, 17
Arrangement(s)
existential, 9
random, 340
systematic, 341
first, 336
second, 336
Association scheme, 336
Avicenna, 13
Associates
Bacon, 4-7, 13, 19
Balance, 102
Balancedness, 59
Basis
inductive, 420
inferential, 64
approach, 123
empirical, 139
hierarchical, 123
calculus, 26
rational, 25
Bayes
Belief(s), 141, 144
Bernoulli, 2.5
random variable, 155
trial, 25
Bertrand, 25
Bias, 514-515
Block(s)
squared, 5 15
design, see Design
effect, see Effect, block
incomplete, 328, 446
size, 329
effectiveness of, 288
factors, see Factor(s)
orthogonal, 390, 507-508, 5 11
in two directions, 390
inequality, 225
procedure, 225,228
t-statistic, 225-226
Blocking, 61
Bonferroni
Borel. 25
Boyle, 13
Causality, 16-19
Causation, see Causality
Cause, see Causality
Central limit theorem, 148
Classification
Aristotelian, 5
models, 74-75
one-way, 102-103, 109
two-fold nested, 109, 112, 193
two-way, 95, 103-106, 109, 112-
116,329
Collinearity, 263
Comparison(s), see also Contrast(s)
a priori, 2 13
with a control, 227
multiple, 224, 251-252, 269, 286
orthogonal, 214-215,218
pairwise, 224
preplanned, 213, 219, 250
split-plot treatment, 543-544
treatment, 59, 165, 250, 332, 377
estimated, 21 8
whole-plot treatment, 543-544, 549
post-hoc, 225 SUBJECT INDEX 62 1
Component(s)
covariance, 133, 578
design, 56
error, 56
treatment, 56
variance, 133, 578
Comprehensiveness, 420
Computer packages, see SAS
Confidence interval(s), 27, 542
estimation, 37
simultaneous, 226-228
complete, 449
partial, 449,452
system of, 447, 457, 472, 475,
Confounding
507-508,5 11,552-554
Connectedness, 59, 329
Contrast(s), see also Comparison(s)
among treatment effects, 160
cubic, 223
defining, 455-456
orthogonal, 214-215,424
quadratic, 223
single-d.f., 441-442
standardized, 2 15
treatment, 214, 282, 380
historical, 139, 148
local, 45, 278
statistical, 24
paper, 520
system, 519
complete set of, 214
Control
Coordinate
Copernicus, 13
Correlation, epistemic, 11- 12
Covariate(s), 76, 240, 292
affected by treatments, 256
multiple, 259, 263
Darwin, 3, 9
Data
analysis, 5 , 11-12, 15, 100, 122
collection, 34, 38
longitudinal, 573
observational, 137
snooping, 227
structure, 100, See also Structure,
data
Deduction, 6-7
Degrees of freedom (d.f.), 79, 166, 183
denominator, 195
loss of, 290
Democritus, 12
Descartes, 9, 12
Design. see also Experiment(s),
all-bias, 517
all-variance, 5 17
axial, 506-508, 520-521
balanced incomplete block (BIBD),
63, 330-335, 359, 304, 549,
552-554
balanced residual effect, 401
balanced treatment incomplete
block (BTIBD), 63,333
between-and-within subjects, 545-
548
binary, 330, 342
Box-Behnken, 65,506
carry-over, 397
central composite (CCD), 506-508,
change-over, 397,400
complete block, 341
completely randomized (CRD),
512-514,524, 527-529
34,62, 106, 151-153,218,
529
with subsampling, 191
with unequal numbers,
179,219
connected, 339
construction of, 23
counterbalanced, 397,545
cross-over, 63, 397,573
diagram-balanced, 545
disconnected, 339
economical, 5 1 1
effects, see Effects,
equireplicate, 330, 343
equivalent estimation, 5 12
error-control, 33-41, 45, 53-56, 61-
65, 153, 277-278, 298, 328, 622 SUBJECT INDEX
377, 390, 421, 475, 497-499,
573,580
error-reduction, 277,419,446
of experiments, 1, 16, 20-22,26, 29
extended block, 63, 337-338, 554
factorial, see Factorial(s)
first-order, 506-507, 513, 525
generalized randomized block
(GRBD), 63, 106, 312-314,
323,353,554
Graeco-Latin square, 63-64, 395-
396
incomplete block (IBD), 34,65, 113
134, 295, 328-329, 421-422,
446,457,509, 549,552-554
Kronecker product, 477
Latin rectangle, 62, 393-394
Latin square (LSD), 34, 45, 62-64,
149-151, 374, 377, 387. See
also Latin square(s)
extended, 395
incomplete, 63-64, 394-
mutually orthogonal, 63,
replicated, 63, 390, 548
type, 62-63,373-375
395
395-396
lattice, 63-65
mixture, 5 19
model, 260
moments, 506, 515-516
nonorthogonal, 332,422
observation, 333-334,573
optimal, 517
orthogonal, 421,425, 504-506,539
pairwise balanced, 338
parameter, 477
partially balanced incomplete block
proper, 330, 342
randomized block, 34,62-63,277
replicated, 62-63
randomized complete block
(PBIBD), 63,335-337,552
(RCBD), 34, 63, 151, 278,
428,543
with subsampling, 288
repeated measures, 65, 397, 545,
balanced, 40 1
resolution 111,455, 475
resolution IV, 457, 475
resolution V, 457,475,505
resolvable, 5 1 1
response surface, 65, 497. See also
row-column, 34, 374
sampling, 33-37, 61
second-order, 504-505, 513
simplex, 504
centroid, 520-521
lattice, 520
split-block, 555
incomplete, 560
split-plot, 38,45,512,528,534,539
in strips, 555
in time, 545, 577
type, 39, 65, 151, 511, 533
573,577
Response surface
split-split-plot, 51 1, 560
statistical, 30
switch-over, 397
systematic block, 340
treatment, 33-37, 45, 61, 64-65,
trend-free block, 341-342
unbalanced, 5 1 1
unbiased, 382, 387
variance balanced, 59,338
Williams, 402
Youden square, 34, 394-395
Dewey, 19
Diagrammatic representation, 109
Difference( s)
390,419,499,573
nearly, 342
minimum, 184
smallest detectable, 184
treatment, 184, 242
standardized, 184
adjusted, 242
Distribution
beta, 175-177
chi-squared, 129, 303
noncentral, 13 1 SUBJECT INDEX 623
F-, 132, 177
central, 132
noncentral, 132, 183
joint, 26, 72, 130
mathematical, 10
noninformative prior, 26
normal (Gaussian), 10,72
posterior, 25-26
prior, 26
probability, 26, 139
randomization, 177. See also
studentized range, 226
of sum of squares, 130
multivariate, 129-130
Randomization
t-, 131, 542
noncentral, 13 1
theory, 129
Effect(s)
block, 37-38, 134
random, 324
carry-over, 398,403
design, 37,40, 134
direct, 398-400
error, 37,40,57
fixed, 325
interaction, 37-38,419, 468
learning, 545
linear, 505
linear x linear, 505
main, 37-38,419-425,468-470
multiplicity, 224
order, 548
quadratic, 505
random, 57,134
residual, 398-400
second order, 513,517
simple, 423
size, 184
systematic, 57
treatment, 37,40,46-47
second-order, 403
differential, 171-173
Efficiency, 59
factor, 333, 336
relative (RE), 288-291, 389,543
estimated (ERE), 290-292,
389,543
Einstein, 13
Equation( s)
Aitken, 125-127
linear, 81
normal (NE), 77, 80-83, 87, 115-
117, 125 242, 246, 254, 293,
329,500
-like, 133,578
conjugate, 77, 129
reduced (RNE), 90, 121,
329,360
theory of, 81
components, 162
estimation of, 137, 148
experimental, 37-48,68, 163-165,
mean squared, 5 14
measurement, 10, 14, 23, 39-40,
observational, 24, 39-48, 68, 191,
315
pure, 430, 502, 505
rates, 224
Error
191,258
integrated (IMSE), 516
161-162
comparisonwise, 224-225
familywise, 224-225
sampling, 39,42,48, 68, 161-162
selection, 161 - 162
space, 129
split-plot, 5 12
standard (se), 151
state, 161-162
structure, 162
technical, 161, 164
treatment, 38, 161-162, 315
unit, 40, 160, 239
variance, 5 15
whole-plot, 5 12
Estimability, 77, 123
Estimate
ANOVA-type, 133
best linear unbiased (BLUE), 125-
27, 160,242 624 SUBJECT INDEX
of error, 137, 148
generalized least squares (GLS),
126
interval, 165
ordinary least squares (OLS), 126-
point, 165
Estimation, see also Estimate
space, 129
Estimator, see Estimate
Expectation, posterior, 25
Experiment( s), see also Experimentation,
L I I - , 228, 257
127, 160
Studies
absolute, 22, 65, 73
agricultural, 148
agronomic, 65,420, 549, 556
arithmetical, 142
comparative, 14-15, 19-24, 65, 71-
confirmatory, 29-30
design of, 16, 20-22, 26, 29
exploratory, 29-30,475
factorial, 59, 64,419-422, 533
73,151,497,523
asymmetrical, 64
fractional, see Factorial(s)
symmetrical, 64
investigative, 144
Lady tasting tea, 139-140
mixture, 519, 523
noisy, 142
psychological, 545
randomized, 145
replicated randomized block, 307
triangular, 140
types of, 23
industrial, 30,420,497, 5 1 1, 543
scientific, 30, 46
sequential, 43
Experimentation
Explanation, 18
Factor( s)
between-subjects, 545
blocking, 32, 35, 106, 278, 306,
313,373,440,580
crossed, 308
nested, 308
classification, 32
confounded, 101
correction, 94
crossed, 101
easy-to-change, 5 11-512,543
efficiency, 333, 336
hard-to-change, 51 1-513,524,543
intrinsic, 35, 38-42,45, 5 1-53, 56,
106, 134, 278, 313-314, 325,
373,440,552
level, 54
nested, 106
nonspecific, 35, 38-42, 45, 56, 134,
278,373
qualitative, 52
quantitative, 52
split-plot, 534
treatment, 32-35,42, 51-53,422
whole-plot, 534
within-subjects, 545
Factorial(s), see also Design,
Experiment(s)
asymmetrical, 66, 476,479
complete, 5 1 1
fractional, 64-66, 453-455, 462-,
463,472,475,479,505-506
of resolution 111, 503
of resolution IV, 503
of resolution V, 503, 5 1 1
full, 503
highly fractionated, 475
mixed, 476,548
pure, 476
symmetrical, 66, 476
2n, 422,446,462,503,509
3n, 465,472,505,509
Faraday, 13
Fit
badness of, 76
lack of, 223, 502,505, 524
proportional, 96
relative, 10
Frequency (ies)
Frequentist approach, 123 SUBJECT INDEX 625
Function(s) loss of, 478
estimable, 78, 81, 125, 131, 242, supplementary, 59, 239-242, 248,
459,557
identifiable, 8 1
likelihood, 26
linear, 130
parametric, 137
polynomial, 498
quadratic, 130, 166
Games of chance, 25
Gauss -Markov
linear model (GMLM), 124- 125
normal linear model (GMNLM),
properties, 147
theorem, 124
128-131, 137, 147
Half-normal plot, 441-443
Heisenberg uncertainty principle, 2, I I
Heraclitus, 12
Heterogeneity, 239
elimination of, 395
of experimental units, 160
of groups, 229
Homogeneity, 193
Hume, 9
Huynh-Feldt condition, 545, 577
Hypothesis, 6-7
falsification of, 7
reductionist, 14
research, 32,41-44, 53
statistical, 32, 43
working, 32
Identifiability, 76, 1 14, 120
Induction, 4, 6-7
Inequality
Bonferroni. 225
Tchebycheff, 139
Bayesian, 26
statistical, 24, 57, 122, 151
Inference, 16
types of, 7,36
Information
inter-block, 134, 553
292
Interaction(s), 419, 470, 475
antidirectional, 319
antagonistic, 3 19
block-treatment, 278, 300-302, 306
codirectional, 313, 319
components, 468-470, 475
effects, see Effects, interaction
firs t-order, 42 1
generalized, 449, 456, 474-475
higher order, 420-42 1, 428
linear x linear, 505
lower order, 420
replication x treatment, 39 1-392
row-column, 379
simple, 424
synergistic, 313
three-factor, 457, 47 1, 504
treatment x design, 134
treatment-time, 575, 580
two-factor, 421,456,47 1, 504
unit-treatment, 300-301, 3 14
confidence, 27,217
-308, 312-314, 317-319, 338
plot, 320-321
Interval(s)
estimation, 37
simultaneous, 226-227
Intervention, see Studies, intervention
statistical, 137
Jeffreys, 26
Kant, 9. 17
Keeton, 17
Kepler, 4, 13
Knut Vik square, 149-150
Lagrange multipliers, 87
Latin rectangle, 393-394
Latin square(s), 62, 376, 548
completely counterbalanced, 402
complete orthogonalized, 397
cyclic, 402 626 SUBJECT INDEX
design (LSD), see Design, Latin
square
diagram-balanced, 547
Graeco-, 396
incomplete, 394,402
mutually orthogonal (MOLS), 397,
403
orthogonal, 395
principle, 62-64, 390, 393
reduced, 376
Lavoisier, 13
Law(s)
Kepler’s, 4
Mendel’s, 4
of succession, 25
analysis, 293-297, 335, 500
fitting, 76, 80,86, 119
generalized (GLS). 126, 512
mean (LSM), 244, 325-326,
method of, 37,57,77,220-221,
ordinary (OLS), 126, 512
Least squares
332,422
242,466
Leucippus, 132
Level( s)
coded, 500
equidistant, 219
significance, 172-173, 177-179, 183
function, 26
residual maximum (REML), 580
affine, 85-86
approximative, 77
classificatory, 74-75
conditional, 85, 99
derived, 68, 127, 159, 164, 278,
3 14,537
functional, 74
Gaussian, 26
Gauss-Markov (GMLN), 124-125
k-part, 97
ordered, 90-94
stochastic, 74, 77, 123
Likelihood, 11
Linear model, 37-38,44-46, 71-73
128-131, 137, 147
theory, 7 1
3-part, 94,329
Locke, 9
Logic, Aristotelian, 9
Loss
2 - p ~ t , 90
of degrees of freedom, 290
of information, 253
of power, 290
of sensitivity, 290
Mathematics, foundations of, 6
Matrix
design, 506
design-model, 466, 504
generalized inverse, 81-83, 125,332
idempotent symmetric (sip), 78,
84,87
incidence, 118, 329,333, 339, 509
information, 330
model, 73
Moore-Penrose (M-P) inverse,
orthogonal, 126, 216
projection, 91
variance-covariance, 124- 125, 578
84-86, 124
Maxwell, 13
Mean, admissible, 107-108, 115
Mean square(s)
expected, 168
synthetic error, 326-327
repeated, 23, 573-574, 578
summary, 575
process, 10,22-24
repeated, 23-24, 573
scale of, 34, 197
variability, 24
Measure(s),
Measurement(s)
Mendel, 4
Method(s)
ANOVA, 580
delta, 198
of parallel tangents (PARTAN), 5 19
of statistical differentials, 198
of steepest ascent, 518 SUBJECT INDEX 627
Mill, 18
Model(s), see also Linear model
approximate, 71, 74
classificatory, 34, 74
conditioned, 85-87
first-order, 500
fitting a, 76
fixed, 132-133, 323
full, 430
means, 99, 114
misspecification, 5 13
mixed, 132- 134,325
multiplicative, 303
nonlinear, 34
nonorthogonal, 332
overparameterized, 100, 115
partitioned, 94
polynomial, 5 19
probability, 10
random, 132-133, 325
randomization, 159
regression, 34
first-order, 500
second-order, 504
relative frequency, 10
statistical, 30, 34
testing of, 7
stochastic, 74, 128, 138
subject matter, 32, 35, 51, 54
subsampling, 191
three-part, 94
two-way classification, 329
well-formulated, 109-1 10, 115
Monte Car10 studies, 178
Multicollinearity, 74-75
Newton, 17
Nonadditivity, 196, 300-302, 312, 386-
387
testing for, 303
195
Noncentrality parameter, 131-132, 183,
Nonorthogonality, 400
Normality assumption, 257
adjusted, 241
high-leverage, 258
missing, 55, 295-298, 389
multivariate, 34
process, 1-2, 10
supplementary, 258
types of, 3
univariate, 34
validation of, 2
estimated, 297
Optimality, 59
A-, 59
D-, 59
E-, 59
Orthogonal array, 463-464
Orthogonality, 59, 218, 400-402
Period,
extra, 400
pre-, 400
wash-out, 398
main effect, 455,480
Plan
orthogonal, 462-463
saturated, 464
Plato, 12-13
Plot(s)
half-normal, 44 1-443
interaction, 320-321
split, 534, 537, 548, 556
split-split, 560
whole, 534, 537, 548, 556
PoincarC, 8, 25
Points,
axial, 506-508
center, 506-508
factorial, 506-508
canonical, 521-522
first-order, 499-500
low-order, 499
orthogonal, 220-222, 342, 441,
505,576
Tchebycheff, 221
Polynomial(s)
Popper, 7-8
Observation(s) Population, 628 S UB JECT INDEX
marginal mean, 245
reference, 323
target, 32, 60
explanatory 15
of F-test, 182
loss of, 290
transformation, 200
increase in, 253
of treatment comparisons, 278
Power
Precision
Predictive margin, 245
Principle(s)
of blocking, 34
of experimentation, 29
of indifference, 25
Latin square, 62-64, 390, 393
split-unit, 533
conditional, 25
continuous, 10
degrees of, 25
frequency theory of, 25-26
joint, 24
structure, 25
theory, 72
Bonferroni, 225,228
Calinski-Corsten, 23 1
Dunnett’s, 228
hierarchical agglomerative, 229
hypothesis falsification, 7
Johnson-Graybill, 306
Mandel’s, 302
multiple comparison, 224, 250-25 1
nonparametric, 228
optimization, 5 18
Satterthwaite, 326, 561
Scheffk, 227-228
stepwise, 229
studentized range, 226, 229
Tukey, 226,252
Tukey-Kramer, 226,252,269
control, 30
evolutionary, 1
Probability, 141
Procedure( s)
Process
manufacturing. 24
measurement, 10, 34
observational, 1-2, 10
production, 30
randomization, see Randomization,
of science, 1
sequential, 30
stochastic, 26, 72
matrix, 91
orthogonal, 9 1
Projector, orthogonal, 91
Protocol
process
Projection(s)
experimental, 55, 139
measurement, 10
observation, 2
Pythagoras, 12
Quadratic form, 128
Quality control, off-line, 477
Ramsey, 26
Randomization, 26, 34,45, 55-56, 6 1,
106, 137, 140-141, 147-151, 278,
376
analysis, 68-69, 180
distribution, 26
independent, 534,538
procedures, 27, 68, 111, 156-157,
180,377,380,533,548
process, 154, 157, 164, 171, 280-,
281,315,533,537
repetitions of, 158
restricted, 280, 291
test, 26,69, 150, 172-173, 180, 285,
385
approximation to the, 69,
173-174, 193,217,
248,286-288,317,
538
theory, 134, 177, 287, 303, 382
unrestricted, 29 1
Random numbers, 154
Random variable(s), 22-24
Bernoulli, 155 SUBJECT INDEX 629
design, 68, 154-155, 158, 280, 379,
Gaussian, 22 Sartre, 9
normal, 129 SAS, 69
Rotatability, 506
537
multivariate, 129 PROC FACTEX, 451,459,486-491
Range of validity, 60 PROC GLM, 201,230-232,264,
Region 269, 343, 348, 353, 404, 407,
experimental (ER), 498,503 430, 443, 446, 481, 523, 562,
operational (OR), 498 580
analysis, 220,497, 502
coefficient, 221, 304, 466-467, 505,
Regression PROC IML, 86
PROC MIXED, 201,343,348,353,
483,523, 562, 568,578-580
528 PROC PLAN, 154, 180,278-279,
line, 302 315-316, 377-378,481
polynomial, 262 PROC POWER, 185
second-order linear, 504 PROC REG, 523
Relation, see Relationship PROC RSREG, 523-524
Relationship Science(s)
defining, 455-456 descriptive, 9
functional, 498
identity, 455,475,479 general, 14
exact, 12
Reparameterization, 8 1 history, 5
Repetition(s), 139 physical, 14
process of, 1
type of, 9
Replication(s), 45, 61
Scientific objective, 58
Scope of validity, 277
Simplex
population of, 137-138
fractional, 451-453
number of 180, 184, 186-190, 193- Sensitivity of experiment, 45
195
coordinate system, 5 19
design, 504
k-dimensional, 504, 51 9
common, 253
effective, 45 1
unequal, 179-180
Residual, see Error
Response( s )
Slope( s)
conceptual, 157-158, 161,281,315,
379,537 equality of, 269
curve, 497,514
observed, 315, 379 Space
optimum, 499,503 column, 91
predicted, 501 error, 129
Response surface, 497-500 estimation, 129
design, 497-499 row, 76
first-order, 503
methodology (RSM), 497-499,5 19,
second-order, 509 Structure(s)
Socrates, 6, 12
Statistical Analysis System, see SAS
Statistical software, see SAS
523 Statistical triangle, 46
Rightmost bracket, 107, 11 1 alias, 454-455,473-475 630 SUBJECT INDEX
blocking, 45
classificatory, 100, 106
correlation, 577
covariance, 127, 160, 164, 168,545,
compound symmetry, 577-
first-order autoregressive,
spatial power, 579
unstructured, 579-580
balanced, 107-108, 11 1-
112,
classificatory, 99, 118
unbalanced, 112
nested, 353, 428, 440
balanced, 100-101
estimated, 588
575,578
580
578-580
data, 100
diagram(s), 110-1 11
error, 56
factor balanced, 112
factorial, 42, 64, 106, 419-421,
440,543,552. See also
Factorial (s)
asymmetrical, 64
symmetrical, 64
Latin square, 380
variance-covariance, 127
Studies, see also Experiment(s)
experimental, 104-106, 138, 149,
intervention, 106, 137-138, 149
observational, 104-106, 134, 137-
138, 149
preliminary, I 85, 191
simulation, 177, 286. See also
Subject matter knowledge, 328,422
Subsample, size of, 195
Subsampling, 34,40,67-68, 191-193,
Sub-subsampling, 67-68
Sum(s) of squares, 37,426
partial, 98, 550
sequential, 98
Type I, 98,330
Monte Carlo studies
288,353
Type 111, 98
basic, 5-6
Syllogism, 5-6
Symmetry, compound, 577-580
Synergism, 43
Taylor series expansion, 42 1
Test(s)
Bonferroni, 225
criterion, 151, 172
Duncans multiple range, 226, 25 1
F-, 151, 174, 177, 217, 285, 502,
538
power of, 182
Fishers protected LSD, 225
F-max, 323
of hypotheses, 7, 37, 57, 131, 171
lack-of-fit, 223,502-505
preliminary, 313, 323
randomization, 69, 177, 285. See
also Randomization, test
randomized triangular, 140
significance, 7, 37, 148-151, 165,
542
size of, 183
statistical, 137
studentized range, 226
t-like, 257
treatment, 226-227
Tukey’s, 303-305, 388
Tetrahedron, 504
Thales of Miletus, 12
Theorem
Aitken, 125-127
central limit, 148
Gauss-Markov, 125- 126
axiom, 13
development of, 4, 10
falsifiable, 14
Gauss-Markov normal linear model
mathematical, 11
normal, 285-286
Theory
(GMNLM), 174-176 SUBJECT INDEX
randomization, 176-177, 285-286. Tycho Brahe, 13
63 1
See also Randomization,
theory
scientific, 8
statistical, 11
types of, 11
Time series, 17
Transformation(s), 196- 199, 3 12
to additivity, 388
power, 200
sets, 376-377, 384
combinations, 420
control, 227
design, see Design, treatment
factorial. 64
mean,
qualitative, 52, 213, 497
quantitative, 52, 219,497
split-plot, 539-540, 543, 560
effect, 539
split-split-plot, 560, 561
test, 227
whole-pIot, 539-540, 543, 560
Treatment(s)
adjusted, 244
effect, 539-540
Trend, 340
analysis, 575
linear, 223, 34 1-343
overall, 577
agronomic, 278
Bernoulli, 25
binomial, 24
randomized clinical, 32, 35
uniformity, 290-291, 543
Trial
Triangle, equilateral, 504
Unbiasedness, 59
Unit(s)
error, 160
experimental (EU), 20, 34, 38,
68, 138,153, 533
observational (OU), 34, 38, 68
sampling, 68
Variability, see Variation
Variable(s)
classificatory, 1 18
coded, 514
concomitant, 15, 76, 118
explanatory, 35-38, 74, 151
function of, 71
mathematical, 1 1 - 12, 22
process, 523
random, see Random variable(s)
regressor, 302
response, 35-36, 52
average, 251-252, 336
estimator, 248, 562
experimental error, 317,557
nonconstancy of. 197
observational error, 3 17
prediction, 506
induced, 277
random, 38,239
sources of, see Analysis of variance,
table
systematic, 45, 62, 239
Variance(s), 514
component, 163, 193,288
component, 163, 193,288
Variation, 26
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