Incomplete Block Designs

By: Aloke Dey

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Hardcover | 1 September 2010

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288 Pages

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25.3 x 16.6 x 2.2

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This book presents a systematic, rigorous and comprehensive account of the theory and applications of incomplete block designs. All major aspects of incomplete block designs are considered by consolidating vast amounts of material from the literature including the classical incomplete block designs, like the balanced incomplete block (BIB) and partially balanced incomplete block (PBIB) designs. Other developments like efficiency-balanced designs, nested designs, robust designs, C-designs and alpha designs are also discussed, along with more recent developments in incomplete block designs for special types of experiments, like biological assays, test-control experiments and diallel crosses, which are generally not covered in existing books. Results on the optimality aspects of various incomplete block designs are reviewed in a separate chapter, that also includes recent optimality results for test-control comparisons, parallel-line assays and diallel cross experiments.

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Preface	p. ix
Introduction	p. 1
Prologue	p. 1
Outline of the Book	p. 3
Analysis and Properties of Block Designs	p. 6
Introduction	p. 6
Intra-block Analysis	p. 7
Balancing in Block Designs	p. 18
Recovery of Inter-block Information	p. 26
Efficiency Factor	p. 38
Exercises	p. 42
Balanced Designs	p. 45
Introduction	p. 45
Some Properties of BIB Designs	p. 45
Analysis of BIB Designs	p. 56
Construction and Existence of BIB Designs	p. 60
BIB Designs Through Finite Geometries	p. 60
Method of Differences	p. 65
Some Other Constructions	p. 74
Existence of BIB Designs	p. 76
Some Generalizations of BIB designs	p. 77
Construction of Variance- and Efficiency-balanced Designs	p. 80
Nested BIB Designs	p. 83
Exercises	p. 87
Partially Balanced Designs	p. 91
Introduction	p. 91
Introducing PBIB Designs	p. 92
The Algebra of Association Matrices	p. 94
PBIB Designs with Two Associate Classes	p. 97
Group-divisible Designs	p. 98
Triangular Designs	p. 104
Latin Square Type Designs	p. 108
PBIB Designs Based on Partial Geometries	p. 110
Cyclic Designs with Two-associate Classes	p. 111
PBIB Designs with More Than Two Classes	p. 114
Rectangular Designs	p. 114
Generalized Right-angular Designs	p. 115
Designs Based on Factorial Association Schemes	p. 116
Designs Based on Group-divisible Family of Schemes	p. 117
The m-dimensional Triangular Designs	p. 117
Kronecker Product Designs	p. 118
Analysis of PBIB Designs	p. 119
Lattice Designs	p. 122
Cyclic Designs	p. 125
Linked Block Designs	p. 129
C-Designs	p. 130
Alpha Designs	p. 133
Exercises	p. 135
More Incomplete Block Designs	p. 138
Introduction	p. 138
Designs for Factorial Experiments	p. 139
Designs for Parallel Line Assays	p. 148
Introducing Bioassays	p. 148
Contrasts for Parallel Line Assays	p. 149
Block Designs for Parallel Line Assays	p. 154
Designs for Test-Control Comparisons	p. 165
Designs for Diallel Crosses	p. 171
Robust Incomplete Block Designs	p. 177
Robustness Against an Outlier	p. 177
Robustness Against Missing Data	p. 179
Trend-free Designs	p. 183
Exercises	p. 185
Optimality Aspects of Block Designs	p. 187
Introduction	p. 187
Optimality Criteria	p. 188
Optimality of Proper Block Designs	p. 197
Optimality of Symmetric Designs	p. 197
Optimality of Asymmetric Designs	p. 200
D-optimality of Some Incomplete Block Designs	p. 208
Optimal Designs for Test-Control Comparisons	p. 212
Optimal Designs for Parallel Line assays	p. 219
Optimal Designs for Diallel Crosses	p. 223
Exercises	p. 227
Appendix	p. 229
Some Results in Linear Algebra	p. 229
Some Aspects of Linear Models	p. 232
Finite Fields	p. 236
Finite Geometries	p. 240
References	p. 243
Index	p. 277
Table of Contents provided by Ingram. All Rights Reserved.

Incomplete Block Designs

At a Glance

Hardcover

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Defective items

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