Design and Analysis of Experiments, Volume 2

KLAUS HINKELMANN, PHD, is Emeritus Professor of Statistics at Virginia Polytechnic Institute and State University Department of Statistics, where he also served as both graduate administrator and department head. In addition to being a Fellow of both the American Statistical Association and the American Association for the Advancement of Science, Professor Hinkelmann is a member of the International Statistical Institute, and has served as a council member of the International Biometric Society. He was editor of Biometrics and the Current Index to Statistics.OSCAR KEMPTHORNE, SCD, was Emeritus Professor of Statistics and Emeritus Distinguished Professor of Liberal Arts and Sciences at Iowa State University. He was a Fellow of the American Statistical Association, the Institute of Mathematical Statistics, and the American Association for the Advancement of Science, as well as an Honorary Fellow of the Royal Statistical Society and a member of the International Statistical Institute. In addition, Dr. Kempthorne was a past president of the Eastern North American Region (ENAR) of the International Biometric Society, a former chairman of statistics within the American Association for the Advancement of Science, and a past president of the Institute of Mathematical Statistics.

• Preface xix1 General Incomplete Block Design 11.1 Introduction and Examples 11.2 General Remarks on the Analysis of Incomplete Block Designs 31.3 The Intrablock Analysis 41.4 Incomplete Designs with Variable Block Size 131.5 Disconnected Incomplete Block Designs 141.6 Randomization Analysis 161.7 Interblock Information in an Incomplete Block Design 231.8 Combined Intra- and Interblock Analysis 271.9 Relationships Among Intrablock Interblock and Combined Estimation 311.10 Estimation of Weights for the Combined Analysis 361.11 Maximum-Likelihood Type Estimation 391.12 Efficiency Factor of an Incomplete Block Design 431.13 Optimal Designs 481.14 Computational Procedures 522 Balanced Incomplete Block Designs 712.1 Introduction 712.2 Definition of the BIB Design 712.3 Properties of BIB Designs 722.4 Analysis of BIB Designs 742.5 Estimation of ρ 772.6 Significance Tests 792.7 Some Special Arrangements 892.8 Resistant and Susceptible BIB Designs 983 Construction of Balanced Incomplete Block Designs 1043.1 Introduction 1043.2 Difference Methods 1043.3 Other Methods 1133.4 Listing of Existing BIB Designs 1154 Partially Balanced Incomplete Block Designs 1194.1 Introduction 1194.2 Preliminaries 1194.3 Definition and Properties of PBIB Designs 1234.4 Association Schemes and Linear Associative Algebras 1274.5 Analysis of PBIB Designs 1314.6 Classification of PBIB Designs 1374.7 Estimation of ρ for PBIB(2) Designs 1555 Construction of Partially Balanced Incomplete Block Designs 1585.1 Group-Divisible PBIB(2) Designs 1585.2 Construction of Other PBIB(2) Designs 1655.3 Cyclic PBIB Designs 1675.4 Kronecker Product Designs 1725.5 Extended Group-Divisible PBIB Designs 1785.6 Hypercubic PBIB Designs 1876 More Block Designs and Blocking Structures 1896.1 Introduction 1896.2 Alpha Designs 1906.3 Generalized Cyclic Incomplete Block Designs 1936.4 Designs Based on the Successive Diagonalizing Method 1946.5 Comparing Treatments with a Control 1956.6 Row–Column Designs 2137 Two-Level Factorial Designs 2417.1 Introduction 2417.2 Case of Two Factors 2417.3 Case of Three Factors 2487.4 General Case 2537.5 Interpretation of Effects and Interactions 2607.6 Analysis of Factorial Experiments 2628 Confounding in 2 n Factorial Designs 2798.1 Introduction 2798.2 Systems of Confounding 2838.3 Composition of Blocks for a Particular System of Confounding 2898.4 Detecting a System of Confounding 2918.5 Using SAS for Constructing Systems of Confounding 2938.6 Analysis of Experiments with Confounding 2938.7 Interblock Information in Confounded Experiments 3038.8 Numerical Example Using SAS 3119 Partial Confounding in 2 n Factorial Designs 3129.1 Introduction 3129.2 Simple Case of Partial Confounding 3129.3 Partial Confounding as an Incomplete Block Design 3189.4 Efficiency of Partial Confounding 3239.5 Partial Confounding in a 23 Experiment 3249.6 Partial Confounding in a 24 Experiment 3279.7 General Case 3299.8 Double Confounding 3359.9 Confounding in Squares 3369.10 Numerical Examples Using SAS 33810 Designs with Factors at Three Levels 35910.1 Introduction 35910.2 Definition of Main Effects and Interactions 35910.3 Parameterization in Terms of Main Effects and Interactions 36510.4 Analysis of 3n Experiments 36610.5 Confounding in a 3n Factorial 36810.6 Useful Systems of Confounding 37410.7 Analysis of Confounded 3n Factorials 38010.8 Numerical Example 38711 General Symmetrical Factorial Design 39311.1 Introduction 39311.2 Representation of Effects and Interactions 39511.3 Generalized Interactions 39611.4 Systems of Confounding 39811.5 Intrablock Subgroup 40011.6 Enumerating Systems of Confounding 40211.7 Fisher Plans 40311.8 Symmetrical Factorials and Finite Geometries 40911.9 Parameterization of Treatment Responses 41011.10 Analysis of pn Factorial Experiments           41211.11 Interblock Analysis 42111.12 Combined Intra- and Interblock Information 42611.13 The sn Factorial 43111.14 General Method of Confounding for the Symmetrical Factorial Experiment 44711.15 Choice of Initial Block 46312 Confounding in Asymmetrical Factorial Designs 46612.1 Introduction 46612.2 Combining Symmetrical Systems of Confounding 46712.3 The GC/n Method 47712.4 Method of Finite Rings 48012.5 Balanced Factorial Designs (BFD) 49113 Fractional Factorial Designs 50713.1 Introduction 50713.2 Simple Example of Fractional Replication 50913.3 Fractional Replicates for 2n Factorial Designs 51313.4 Fractional Replicates for 3n Factorial Designs 52413.5 General Case of Fractional Replication 52913.6 Characterization of Fractional Factorial Designs of Resolution III IV and V 53613.7 Fractional Factorials and Combinatorial Arrays 54713.8 Blocking in Fractional Factorials 54913.9 Analysis of Unreplicated Factorials 55814 Main Effect Plans 56414.1 Introduction 56414.2 Orthogonal Resolution III Designs for Symmetrical Factorials 56414.3 Orthogonal Resolution III Designs for Asymmetrical Factorials 58214.4 Nonorthogonal Resolution III Designs 59415 Supersaturated Designs 59615.1 Introduction and Rationale 59615.2 Random Balance Designs 59615.3 Definition and Properties of Supersaturated Designs 59715.4 Construction of Two-Level Supersaturated Designs 59815.5 Three-Level Supersaturated Designs 60315.6 Analysis of Supersaturated Experiments 60416 Search Designs 60816.1 Introduction and Rationale 60816.2 Definition of Search Design 60816.3 Properties of Search Designs 60916.4 Listing of Search Designs 61516.5 Analysis of Search Experiments 61716.6 Search Probabilities 63017 Robust-Design Experiments 63317.1 Off-Line Quality Control 63317.2 Design and Noise Factors 63417.3 Measuring Loss 63517.4 Robust-Design Experiments 63617.5 Modeling of Data 63818 Lattice Designs 64918.1 Definition of Quasi-Factorial Designs 64918.2 Types of Lattice Designs 65318.3 Construction of One-Restrictional Lattice Designs 65518.4 General Method of Analysis for One-Restrictional Lattice Designs 65718.5 Effects of Inaccuracies in the Weights 66118.6 Analysis of Lattice Designs as Randomized Complete Block Designs 66618.7 Lattice Designs as Partially Balanced Incomplete Block Designs 66918.8 Lattice Designs with Blocks of Size Kl 67018.9 Two-Restrictional Lattices 67118.10 Lattice Rectangles 67818.11 Rectangular Lattices 67918.12 Efficiency Factors 68219 Crossover Designs 68419.1 Introduction 68419.2 Residual Effects 68519.3 The Model 68519.4 Properties of Crossover Designs 68719.5 Construction of Crossover Designs 68819.6 Optimal Designs 69519.7 Analysis of Crossover Designs 69919.8 Comments on Other Models 706Appendix A Fields and Galois Fields 716Appendix B Finite Geometries 721Appendix C Orthogonal and Balanced Arrays 724Appendix D Selected Asymmetrical Balanced Factorial Designs 728Appendix E Exercises 736References 749Author Index 767Subject Index 771

"…a massively impressive work of scholarship…" (Short Book Reviews, December 2006) "...a broad and in-depth book...covers not only classic but also up-to-date results and references, making it convenient for researchers. It is one of the very few advanced textbooks on experimental design..." (Technometrics, November 2006)"I suspect this excellent book will be used most often by specialists in design...the book's importance is largely as a reference for experts...or as an independent learning tool…" (Journal of the American Statistical Association, June 2006)"I would expect HK to attain essentially the same stature and appeal to virtually the same markets as the 1952 edition." (Journal of Quality Technology, January 2006)"…the authors have done a commendable job in putting together the vast amount of literature that is available on the topics…of great value to students, and also to teachers and researchers." (Mathematical Reviews, 2006b)