Design and Analysis of Experiments, Volume 2 - Klaus Hinkelmann

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Biographie:

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

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