Design and Analysis of Experiments Set
1st Edition
Will be published approx. on 4. July 2008
Book
Hardback
1411 pages
978-0-470-38551-7 (ISBN)
Description
This set includes Design and Analysis of Experiments, Volume 1, Introduction to Experimental Design, 2nd Edition & Design and Analysis of Experiments, Volume 2, Advanced Experimental Design.
Design and Analysis of Experiments, Volume 1, Second Edition provides a general introduction to the philosophy, theory, and practice of designing scientific comparative experiments and also details the intricacies that are often encountered throughout the design and analysis processes. With the addition of extensive numerical examples and expanded treatment of key concepts, this book further addresses the needs of practitioners and successfully provides a solid understanding of the relationship between the quality of experimental design and the validity of conclusions.
Design and Analysis of Experiments, Volume 2: Advanced Experimental Design is the second of a two-volume body of work that builds upon the philosophical foundations of experimental design set forth half a century ago by Oscar Kempthorne, and features the latest developments in the field.
Design and Analysis of Experiments, Volume 1, Second Edition provides a general introduction to the philosophy, theory, and practice of designing scientific comparative experiments and also details the intricacies that are often encountered throughout the design and analysis processes. With the addition of extensive numerical examples and expanded treatment of key concepts, this book further addresses the needs of practitioners and successfully provides a solid understanding of the relationship between the quality of experimental design and the validity of conclusions.
Design and Analysis of Experiments, Volume 2: Advanced Experimental Design is the second of a two-volume body of work that builds upon the philosophical foundations of experimental design set forth half a century ago by Oscar Kempthorne, and features the latest developments in the field.
More details
Series
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Product notice
sewn/stitched
Cloth over boards
Dimensions
Height: 244 mm
Width: 162 mm
Thickness: 88 mm
Weight
2422 gr
ISBN-13
978-0-470-38551-7 (9780470385517)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Klaus Hinkelmann, PhD, is Emeritus Professor of Statistics in the Department of Statistics at Virginia Polytechnic Institute and State University. A Fellow of the American Statistical Association and the American Association for the Advancement of Science, Dr. Hinkelmann has published extensively in the areas of design of experiments, statistical methods, and biometry.
The late Oscar Kempthorne, ScD, was Emeritus Professor of Statistics and Emeritus Distinguished Professor of Liberal Arts and Sciences at Iowa State University. He was the recipient of many honors within the statistics profession.
The late Oscar Kempthorne, ScD, was Emeritus Professor of Statistics and Emeritus Distinguished Professor of Liberal Arts and Sciences at Iowa State University. He was the recipient of many honors within the statistics profession.
Content
VOLUME 1 TOC:
1. The Processes of Science. 1.1 Introduction.
1.2 Development of Theory.
1.3 The Nature and Role of Theory in Science.
1.4 Varieties of Theory.
1.5 The Problem of General Science.
1.6 Causality.
1.7 The Upshot.
1.8 What Is An Experiment?.
1.9 Statistical Inference.
2. Principles of Experimental Design.
2.1 Confirmatory and Exploratory Experiments.
2.2 Steps of Designed Investigations.
2.3 The Linear Model.
2.4 Illustrating Individual Steps: Study 1.
2.5 Three Principles of Experimental Design.
2.6 The Statistical Triangle and Study 2.
2.7 Planning the Experiment.
2.8 Cooperation between Scientist and Statistician.
2.9 General Principle of Inference.
2.10 Other Considerations for Experimental Designs.
3. Survey of Designs and Analyses.
3.1 Introduction.
3.2 Error-Control Designs.
3.3 Treatment Designs.
3.4 Combining Ideas.
3.5 Sampling Designs.
3.6 Analysis and Statistical Software.
3.7 Summary.
4. Linear Model Theory.
4.1 Introduction.
4.2 Representation of Linear Models.
4.3 Functional and Classificatory Linear Models.
4.4 The Fitting Of Y .= X_.
4.5 The Moore-Penrose Generalized Inverse.
4.6 The Conditioned Linear Model.
4.7 The Two-Part Linear Model.
4.8 A Special Case of a Partitioned Model.
4.9 Three-Part Models.
4.10 The Two-Way Classification Without Interaction.
4.11 The K-Part Linear Model.
4.12 Balanced Classificatory Structures.
4.13 Unbalanced Data Structures.
4.14 Analysis of Covariance Model.
4.15 From Data Analysis to Statistical Inference.
4.16 The Simple Normal Stochastic Linear Model.
4.17 Distribution Theory with GMNLM.
4.18 Mixed Models.
5. Randomization.
5.1 Introduction.
5.2 The Tea Tasting Lady.
5.3 A Triangular Experiment.
5.4 The Simple Arithmetical Experiment.
5.5 Randomization Ideas for Intervention Experiments.
5.6 The General Idea of the Experiment Randomization Test.
5.7 Introduction to Subsequent.
6. The Completely Randomized Design.
6.1 Introduction and Definition.
6.2 The Randomization Process.
6.3 The Derived Linear Model.
6.4 Analysis Of Variance.
6.5 Statistical Tests.
6.6 Approximating the Randomization Test.
6.7 CRD with Unequal Numbers of Replications.
6.8 Number of Replications.
6.9 Subsampling In A CRD.
6.10 Transformations.
6.11 Examples Using SASR.
7. Comparisons of Treatments.
7.1 Introduction.
7.2 Comparisons for Qualitative Treatments.
7.3 Orthogonality and Orthogonal Comparisons.
7.4 Comparisons for Quantitative Treatments.
7.5 Multiple Comparison Procedures.
7.6 Grouping Treatments.
7.7 Examples Using SAS.
8. Use of Supplementary Information.
8.1 Introduction.
8.2 Motivation of the Procedure.
8.3 Analysis of Covariance Procedure.
8.4 Treatment Comparisons.
8.5 Violation of Assumptions.
8.6 Analysis of Covariance with Subsampling.
8.7 The Case of Several Covariates.
8.8 Examples Using SASR.
9. Randomized Block Designs.
9.1 Introduction.
9.2 Randomized Complete Block Design.
9.3 Relative Efficiency of the RCBD.
9.4 Analysis of Covariance.
9.5 Missing Observations.
9.6 Nonadditivity in the RCBD.
9.7 The Generalized Randomized Block Design.
9.8 Incomplete Block Designs.
9.9 Systematic Block Designs.
9.10 Examples Using SASR.
10. Latin Square Type Designs.
10.1 Introduction and Motivation.
10.2 Latin Square Design.
10.3 Replicated Latin Squares.
10.4 Latin Rectangles.
10.5 Incomplete Latin Squares.
10.6 Orthogonal Latin Squares.
10.7 Change-Over Designs.
10.8 Examples Using SAS.
11. Factorial Experiments: Basic Ideas.
11.1 Introduction.
11.2 Inferences from Factorial Experiments.
11.3 Experiments with Factors at Two Levels.
11.4 The Interpretation of Effects and Interactions.
11.5 Interactions: A Case Study.
11.6 2n Factorials in Incomplete Blocks.
11.7 Fractions of 2n Factorials.
11.8 Orthogonal Main Effect Plans for 2n Factorials.
11.9 Experiments with Factors at Three Levels.
11.10experimentswith Factors at Two and Three Levels.
11.11examples Using SAS.
12. Response Surface Designs.
12.1 Introduction.
12.2 Formulation of the Problem.
12.3 First-Order Models and Designs.
12.4 Second-Order Models and Designs.
12.5 Integrated Mean Squared Error Designs.
12.6 Searching For an Optimum.
12.7 Experiments with Mixtures.
12.8 Examples Using SAS.
13. Split-Plot Type Designs.
13.1 Introduction.
13.2 The Simple Split-Plot Design.
13.3 Relative Efficiency of Split-Plot Design.
13.4 Other Forms of Split-Plot Designs.
13.5 Split-Block Design.
13.6 The Split-Split-Plot Design.
13.7 Examples Using SAS.
14. Designs with Repeated Measures.
14.1 Introduction.
14.2 Methods for Analyzing Repeated Measures Data.
14.3 Examples Using SAS.
14.4 Exercises.
VOLUME 2 TOC:
Preface xix
1 General Incomplete Block Design 1
1.1 Introduction and Examples 1
1.2 General Remarks on the Analysis of Incomplete Block Designs 3
1.3 The Intrablock Analysis 4
1.4 Incomplete Designs with Variable Block Size 13
1.5 Disconnected Incomplete Block Designs 14
1.6 Randomization Analysis 16
1.7 Interblock Information in an Incomplete Block Design 23
1.8 Combined Intra- and Interblock Analysis 27
1.9 Relationships Among Intrablock Interblock and Combined Estimation 31
1.10 Estimation of Weights for the Combined Analysis 36
1.11 Maximum-Likelihood Type Estimation 39
1.12 Efficiency Factor of an Incomplete Block Design 43
1.13 Optimal Designs 48
1.14 Computational Procedures 52
2 Balanced Incomplete Block Designs 71
2.1 Introduction 71
2.2 Definition of the BIB Design 71
2.3 Properties of BIB Designs 72
2.4 Analysis of BIB Designs 74
2.5 Estimation of ? 77
2.6 Significance Tests 79
2.7 Some Special Arrangements 89
2.8 Resistant and Susceptible BIB Designs 98
3 Construction of Balanced Incomplete Block Designs 104
3.1 Introduction 104
3.2 Difference Methods 104
3.3 Other Methods 113
3.4 Listing of Existing BIB Designs 115
4 Partially Balanced Incomplete Block Designs 119
4.1 Introduction 119
4.2 Preliminaries 119
4.3 Definition and Properties of PBIB Designs 123
4.4 Association Schemes and Linear Associative Algebras 127
4.5 Analysis of PBIB Designs 131
4.6 Classification of PBIB Designs 137
4.7 Estimation of ? for PBIB(2) Designs 155
5 Construction of Partially Balanced Incomplete Block Designs 158
5.1 Group-Divisible PBIB(2) Designs 158
5.2 Construction of Other PBIB(2) Designs 165
5.3 Cyclic PBIB Designs 167
5.4 Kronecker Product Designs 172
5.5 Extended Group-Divisible PBIB Designs 178
5.6 Hypercubic PBIB Designs 187
6 More Block Designs and Blocking Structures 189
6.1 Introduction 189
6.2 Alpha Designs 190
6.3 Generalized Cyclic Incomplete Block Designs 193
6.4 Designs Based on the Successive Diagonalizing Method 194
6.5 Comparing Treatments with a Control 195
6.6 Row-Column Designs 213
7 Two-Level Factorial Designs 241
7.1 Introduction 241
7.2 Case of Two Factors 241
7.3 Case of Three Factors 248
7.4 General Case 253
7.5 Interpretation of Effects and Interactions 260
7.6 Analysis of Factorial Experiments 262
8 Confounding in 2 n Factorial Designs 279
8.1 Introduction 279
8.2 Systems of Confounding 283
8.3 Composition of Blocks for a Particular System of Confounding 289
8.4 Detecting a System of Confounding 291
8.5 Using SAS for Constructing Systems of Confounding 293
8.6 Analysis of Experiments with Confounding 293
8.7 Interblock Information in Confounded Experiments 303
8.8 Numerical Example Using SAS 311
9 Partial Confounding in 2 n Factorial Designs 312
9.1 Introduction 312
9.2 Simple Case of Partial Confounding 312
9.3 Partial Confounding as an Incomplete Block Design 318
9.4 Efficiency of Partial Confounding 323
9.5 Partial Confounding in a 23 Experiment 324
9.6 Partial Confounding in a 24 Experiment 327
9.7 General Case 329
9.8 Double Confounding 335
9.9 Confounding in Squares 336
9.10 Numerical Examples Using SAS 338
10 Designs with Factors at Three Levels 359
10.1 Introduction 359
10.2 Definition of Main Effects and Interactions 359
10.3 Parameterization in Terms of Main Effects and Interactions 365
10.4 Analysis of 3n Experiments 366
10.5 Confounding in a 3n Factorial 368
10.6 Useful Systems of Confounding 374
10.7 Analysis of Confounded 3n Factorials 380
10.8 Numerical Example 387
11 General Symmetrical Factorial Design 393
11.1 Introduction 393
11.2 Representation of Effects and Interactions 395
11.3 Generalized Interactions 396
11.4 Systems of Confounding 398
11.5 Intrablock Subgroup 400
11.6 Enumerating Systems of Confounding 402
11.7 Fisher Plans 403
11.8 Symmetrical Factorials and Finite Geometries 409
11.9 Parameterization of Treatment Responses 410
11.10 Analysis of pn Factorial Experiments 412
11.11 Interblock Analysis 421
11.12 Combined Intra- and Interblock Information 426
11.13 The sn Factorial 431
11.14 General Method of Confounding for the Symmetrical Factorial Experiment 447
11.15 Choice of Initial Block 463
12 Confounding in Asymmetrical Factorial Designs 466
12.1 Introduction 466
12.2 Combining Symmetrical Systems of Confounding 467
12.3 The GC/n Method 477
12.4 Method of Finite Rings 480
12.5 Balanced Factorial Designs (BFD) 491
13 Fractional Factorial Designs 507
13.1 Introduction 507
13.2 Simple Example of Fractional Replication 509
13.3 Fractional Replicates for 2n Factorial Designs 513
13.4 Fractional Replicates for 3n Factorial Designs 524
13.5 General Case of Fractional Replication 529
13.6 Characterization of Fractional Factorial Designs of Resolution III IV and V 536
13.7 Fractional Factorials and Combinatorial Arrays 547
13.8 Blocking in Fractional Factorials 549
13.9 Analysis of Unreplicated Factorials 558
14 Main Effect Plans 564
14.1 Introduction 564
14.2 Orthogonal Resolution III Designs for Symmetrical Factorials 564
14.3 Orthogonal Resolution III Designs for Asymmetrical Factorials 582
14.4 Nonorthogonal Resolution III Designs 594
15 Supersaturated Designs 596
15.1 Introduction and Rationale 596
15.2 Random Balance Designs 596
15.3 Definition and Properties of Supersaturated Designs 597
15.4 Construction of Two-Level Supersaturated Designs 598
15.5 Three-Level Supersaturated Designs 603
15.6 Analysis of Supersaturated Experiments 604
16 Search Designs 608
16.1 Introduction and Rationale 608
16.2 Definition of Search Design 608
16.3 Properties of Search Designs 609
16.4 Listing of Search Designs 615
16.5 Analysis of Search Experiments 617
16.6 Search Probabilities 630
17 Robust-Design Experiments 633
17.1 Off-Line Quality Control 633
17.2 Design and Noise Factors 634
17.3 Measuring Loss 635
17.4 Robust-Design Experiments 636
17.5 Modeling of Data 638
18 Lattice Designs 649
18.1 Definition of Quasi-Factorial Designs 649
18.2 Types of Lattice Designs 653
18.3 Construction of One-Restrictional Lattice Designs 655
18.4 General Method of Analysis for One-Restrictional Lattice Designs 657
18.5 Effects of Inaccuracies in the Weights 661
18.6 Analysis of Lattice Designs as Randomized Complete Block Designs 666
18.7 Lattice Designs as Partially Balanced Incomplete Block Designs 669
18.8 Lattice Designs with Blocks of Size Kl 670
18.9 Two-Restrictional Lattices 671
18.10 Lattice Rectangles 678
18.11 Rectangular Lattices 679
18.12 Efficiency Factors 682
19 Crossover Designs 684
19.1 Introduction 684
19.2 Residual Effects 685
19.3 The Model 685
19.4 Properties of Crossover Designs 687
19.5 Construction of Crossover Designs 688
19.6 Optimal Designs 695
19.7 Analysis of Crossover Designs 699
19.8 Comments on Other Models 706
Appendix A Fields and Galois Fields 716
Appendix B Finite Geometries 721
Appendix C Orthogonal and Balanced Arrays 724
Appendix D Selected Asymmetrical Balanced Factorial Designs 728
Appendix E Exercises 736
References 749
Author Index 767
Subject Index 771
1. The Processes of Science. 1.1 Introduction.
1.2 Development of Theory.
1.3 The Nature and Role of Theory in Science.
1.4 Varieties of Theory.
1.5 The Problem of General Science.
1.6 Causality.
1.7 The Upshot.
1.8 What Is An Experiment?.
1.9 Statistical Inference.
2. Principles of Experimental Design.
2.1 Confirmatory and Exploratory Experiments.
2.2 Steps of Designed Investigations.
2.3 The Linear Model.
2.4 Illustrating Individual Steps: Study 1.
2.5 Three Principles of Experimental Design.
2.6 The Statistical Triangle and Study 2.
2.7 Planning the Experiment.
2.8 Cooperation between Scientist and Statistician.
2.9 General Principle of Inference.
2.10 Other Considerations for Experimental Designs.
3. Survey of Designs and Analyses.
3.1 Introduction.
3.2 Error-Control Designs.
3.3 Treatment Designs.
3.4 Combining Ideas.
3.5 Sampling Designs.
3.6 Analysis and Statistical Software.
3.7 Summary.
4. Linear Model Theory.
4.1 Introduction.
4.2 Representation of Linear Models.
4.3 Functional and Classificatory Linear Models.
4.4 The Fitting Of Y .= X_.
4.5 The Moore-Penrose Generalized Inverse.
4.6 The Conditioned Linear Model.
4.7 The Two-Part Linear Model.
4.8 A Special Case of a Partitioned Model.
4.9 Three-Part Models.
4.10 The Two-Way Classification Without Interaction.
4.11 The K-Part Linear Model.
4.12 Balanced Classificatory Structures.
4.13 Unbalanced Data Structures.
4.14 Analysis of Covariance Model.
4.15 From Data Analysis to Statistical Inference.
4.16 The Simple Normal Stochastic Linear Model.
4.17 Distribution Theory with GMNLM.
4.18 Mixed Models.
5. Randomization.
5.1 Introduction.
5.2 The Tea Tasting Lady.
5.3 A Triangular Experiment.
5.4 The Simple Arithmetical Experiment.
5.5 Randomization Ideas for Intervention Experiments.
5.6 The General Idea of the Experiment Randomization Test.
5.7 Introduction to Subsequent.
6. The Completely Randomized Design.
6.1 Introduction and Definition.
6.2 The Randomization Process.
6.3 The Derived Linear Model.
6.4 Analysis Of Variance.
6.5 Statistical Tests.
6.6 Approximating the Randomization Test.
6.7 CRD with Unequal Numbers of Replications.
6.8 Number of Replications.
6.9 Subsampling In A CRD.
6.10 Transformations.
6.11 Examples Using SASR.
7. Comparisons of Treatments.
7.1 Introduction.
7.2 Comparisons for Qualitative Treatments.
7.3 Orthogonality and Orthogonal Comparisons.
7.4 Comparisons for Quantitative Treatments.
7.5 Multiple Comparison Procedures.
7.6 Grouping Treatments.
7.7 Examples Using SAS.
8. Use of Supplementary Information.
8.1 Introduction.
8.2 Motivation of the Procedure.
8.3 Analysis of Covariance Procedure.
8.4 Treatment Comparisons.
8.5 Violation of Assumptions.
8.6 Analysis of Covariance with Subsampling.
8.7 The Case of Several Covariates.
8.8 Examples Using SASR.
9. Randomized Block Designs.
9.1 Introduction.
9.2 Randomized Complete Block Design.
9.3 Relative Efficiency of the RCBD.
9.4 Analysis of Covariance.
9.5 Missing Observations.
9.6 Nonadditivity in the RCBD.
9.7 The Generalized Randomized Block Design.
9.8 Incomplete Block Designs.
9.9 Systematic Block Designs.
9.10 Examples Using SASR.
10. Latin Square Type Designs.
10.1 Introduction and Motivation.
10.2 Latin Square Design.
10.3 Replicated Latin Squares.
10.4 Latin Rectangles.
10.5 Incomplete Latin Squares.
10.6 Orthogonal Latin Squares.
10.7 Change-Over Designs.
10.8 Examples Using SAS.
11. Factorial Experiments: Basic Ideas.
11.1 Introduction.
11.2 Inferences from Factorial Experiments.
11.3 Experiments with Factors at Two Levels.
11.4 The Interpretation of Effects and Interactions.
11.5 Interactions: A Case Study.
11.6 2n Factorials in Incomplete Blocks.
11.7 Fractions of 2n Factorials.
11.8 Orthogonal Main Effect Plans for 2n Factorials.
11.9 Experiments with Factors at Three Levels.
11.10experimentswith Factors at Two and Three Levels.
11.11examples Using SAS.
12. Response Surface Designs.
12.1 Introduction.
12.2 Formulation of the Problem.
12.3 First-Order Models and Designs.
12.4 Second-Order Models and Designs.
12.5 Integrated Mean Squared Error Designs.
12.6 Searching For an Optimum.
12.7 Experiments with Mixtures.
12.8 Examples Using SAS.
13. Split-Plot Type Designs.
13.1 Introduction.
13.2 The Simple Split-Plot Design.
13.3 Relative Efficiency of Split-Plot Design.
13.4 Other Forms of Split-Plot Designs.
13.5 Split-Block Design.
13.6 The Split-Split-Plot Design.
13.7 Examples Using SAS.
14. Designs with Repeated Measures.
14.1 Introduction.
14.2 Methods for Analyzing Repeated Measures Data.
14.3 Examples Using SAS.
14.4 Exercises.
VOLUME 2 TOC:
Preface xix
1 General Incomplete Block Design 1
1.1 Introduction and Examples 1
1.2 General Remarks on the Analysis of Incomplete Block Designs 3
1.3 The Intrablock Analysis 4
1.4 Incomplete Designs with Variable Block Size 13
1.5 Disconnected Incomplete Block Designs 14
1.6 Randomization Analysis 16
1.7 Interblock Information in an Incomplete Block Design 23
1.8 Combined Intra- and Interblock Analysis 27
1.9 Relationships Among Intrablock Interblock and Combined Estimation 31
1.10 Estimation of Weights for the Combined Analysis 36
1.11 Maximum-Likelihood Type Estimation 39
1.12 Efficiency Factor of an Incomplete Block Design 43
1.13 Optimal Designs 48
1.14 Computational Procedures 52
2 Balanced Incomplete Block Designs 71
2.1 Introduction 71
2.2 Definition of the BIB Design 71
2.3 Properties of BIB Designs 72
2.4 Analysis of BIB Designs 74
2.5 Estimation of ? 77
2.6 Significance Tests 79
2.7 Some Special Arrangements 89
2.8 Resistant and Susceptible BIB Designs 98
3 Construction of Balanced Incomplete Block Designs 104
3.1 Introduction 104
3.2 Difference Methods 104
3.3 Other Methods 113
3.4 Listing of Existing BIB Designs 115
4 Partially Balanced Incomplete Block Designs 119
4.1 Introduction 119
4.2 Preliminaries 119
4.3 Definition and Properties of PBIB Designs 123
4.4 Association Schemes and Linear Associative Algebras 127
4.5 Analysis of PBIB Designs 131
4.6 Classification of PBIB Designs 137
4.7 Estimation of ? for PBIB(2) Designs 155
5 Construction of Partially Balanced Incomplete Block Designs 158
5.1 Group-Divisible PBIB(2) Designs 158
5.2 Construction of Other PBIB(2) Designs 165
5.3 Cyclic PBIB Designs 167
5.4 Kronecker Product Designs 172
5.5 Extended Group-Divisible PBIB Designs 178
5.6 Hypercubic PBIB Designs 187
6 More Block Designs and Blocking Structures 189
6.1 Introduction 189
6.2 Alpha Designs 190
6.3 Generalized Cyclic Incomplete Block Designs 193
6.4 Designs Based on the Successive Diagonalizing Method 194
6.5 Comparing Treatments with a Control 195
6.6 Row-Column Designs 213
7 Two-Level Factorial Designs 241
7.1 Introduction 241
7.2 Case of Two Factors 241
7.3 Case of Three Factors 248
7.4 General Case 253
7.5 Interpretation of Effects and Interactions 260
7.6 Analysis of Factorial Experiments 262
8 Confounding in 2 n Factorial Designs 279
8.1 Introduction 279
8.2 Systems of Confounding 283
8.3 Composition of Blocks for a Particular System of Confounding 289
8.4 Detecting a System of Confounding 291
8.5 Using SAS for Constructing Systems of Confounding 293
8.6 Analysis of Experiments with Confounding 293
8.7 Interblock Information in Confounded Experiments 303
8.8 Numerical Example Using SAS 311
9 Partial Confounding in 2 n Factorial Designs 312
9.1 Introduction 312
9.2 Simple Case of Partial Confounding 312
9.3 Partial Confounding as an Incomplete Block Design 318
9.4 Efficiency of Partial Confounding 323
9.5 Partial Confounding in a 23 Experiment 324
9.6 Partial Confounding in a 24 Experiment 327
9.7 General Case 329
9.8 Double Confounding 335
9.9 Confounding in Squares 336
9.10 Numerical Examples Using SAS 338
10 Designs with Factors at Three Levels 359
10.1 Introduction 359
10.2 Definition of Main Effects and Interactions 359
10.3 Parameterization in Terms of Main Effects and Interactions 365
10.4 Analysis of 3n Experiments 366
10.5 Confounding in a 3n Factorial 368
10.6 Useful Systems of Confounding 374
10.7 Analysis of Confounded 3n Factorials 380
10.8 Numerical Example 387
11 General Symmetrical Factorial Design 393
11.1 Introduction 393
11.2 Representation of Effects and Interactions 395
11.3 Generalized Interactions 396
11.4 Systems of Confounding 398
11.5 Intrablock Subgroup 400
11.6 Enumerating Systems of Confounding 402
11.7 Fisher Plans 403
11.8 Symmetrical Factorials and Finite Geometries 409
11.9 Parameterization of Treatment Responses 410
11.10 Analysis of pn Factorial Experiments 412
11.11 Interblock Analysis 421
11.12 Combined Intra- and Interblock Information 426
11.13 The sn Factorial 431
11.14 General Method of Confounding for the Symmetrical Factorial Experiment 447
11.15 Choice of Initial Block 463
12 Confounding in Asymmetrical Factorial Designs 466
12.1 Introduction 466
12.2 Combining Symmetrical Systems of Confounding 467
12.3 The GC/n Method 477
12.4 Method of Finite Rings 480
12.5 Balanced Factorial Designs (BFD) 491
13 Fractional Factorial Designs 507
13.1 Introduction 507
13.2 Simple Example of Fractional Replication 509
13.3 Fractional Replicates for 2n Factorial Designs 513
13.4 Fractional Replicates for 3n Factorial Designs 524
13.5 General Case of Fractional Replication 529
13.6 Characterization of Fractional Factorial Designs of Resolution III IV and V 536
13.7 Fractional Factorials and Combinatorial Arrays 547
13.8 Blocking in Fractional Factorials 549
13.9 Analysis of Unreplicated Factorials 558
14 Main Effect Plans 564
14.1 Introduction 564
14.2 Orthogonal Resolution III Designs for Symmetrical Factorials 564
14.3 Orthogonal Resolution III Designs for Asymmetrical Factorials 582
14.4 Nonorthogonal Resolution III Designs 594
15 Supersaturated Designs 596
15.1 Introduction and Rationale 596
15.2 Random Balance Designs 596
15.3 Definition and Properties of Supersaturated Designs 597
15.4 Construction of Two-Level Supersaturated Designs 598
15.5 Three-Level Supersaturated Designs 603
15.6 Analysis of Supersaturated Experiments 604
16 Search Designs 608
16.1 Introduction and Rationale 608
16.2 Definition of Search Design 608
16.3 Properties of Search Designs 609
16.4 Listing of Search Designs 615
16.5 Analysis of Search Experiments 617
16.6 Search Probabilities 630
17 Robust-Design Experiments 633
17.1 Off-Line Quality Control 633
17.2 Design and Noise Factors 634
17.3 Measuring Loss 635
17.4 Robust-Design Experiments 636
17.5 Modeling of Data 638
18 Lattice Designs 649
18.1 Definition of Quasi-Factorial Designs 649
18.2 Types of Lattice Designs 653
18.3 Construction of One-Restrictional Lattice Designs 655
18.4 General Method of Analysis for One-Restrictional Lattice Designs 657
18.5 Effects of Inaccuracies in the Weights 661
18.6 Analysis of Lattice Designs as Randomized Complete Block Designs 666
18.7 Lattice Designs as Partially Balanced Incomplete Block Designs 669
18.8 Lattice Designs with Blocks of Size Kl 670
18.9 Two-Restrictional Lattices 671
18.10 Lattice Rectangles 678
18.11 Rectangular Lattices 679
18.12 Efficiency Factors 682
19 Crossover Designs 684
19.1 Introduction 684
19.2 Residual Effects 685
19.3 The Model 685
19.4 Properties of Crossover Designs 687
19.5 Construction of Crossover Designs 688
19.6 Optimal Designs 695
19.7 Analysis of Crossover Designs 699
19.8 Comments on Other Models 706
Appendix A Fields and Galois Fields 716
Appendix B Finite Geometries 721
Appendix C Orthogonal and Balanced Arrays 724
Appendix D Selected Asymmetrical Balanced Factorial Designs 728
Appendix E Exercises 736
References 749
Author Index 767
Subject Index 771