Design and Analysis of Experiments Set

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.

• 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 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