1 Introduction
2 Analysis and Properties of Block Designs
3 Intra-block Analysis
4 Balancing in Block Designs
5 Recovery of Inter-block Information
6 Efficiency Factor
7 Exercises
8 Balanced Designs
9 Some Properties of BIB Designs
10 Analysis of BIB Designs
11 Construction and Existence of BIB Designs
12 BIB Designs Through Finite Geometries
13 Method of Differences
14 Some Other Constructions
15 Existence of BIB Designs
16 Some Generalizations of BIB Designs
17 Construction of Variance- and Efficiency-balanced Designs
18 Nested BIB Designs
19 Exercises
20 Partially Balanced Designs
21 Introducing PBIB Designs
22 The Algebra of Association Matrices
23 PBIB Designs with Two Associate Classes
24 Group-divisible Designs
25 Triangular Designs
26 Latin Square Type Designs
27 PBIB Designs Based on Partial Geometries
28 Cyclic Designs with Two-associate Classes
29 PBIB Designs with More Than Two Classes
30 Rectangular Designs
31 Generalized Right-angular Designs
32 Designs Based on Factorial Association Schemes
33 Designs Based on Group-divisible Family of Schemes
34 The m-dimensional Triangular Designs
35 Kronecker Product Designs
36 Analysis of PBIB Designs
37 Lattice Designs
38 Cyclic Designs
39 Linked Block Designs
40 C-Designs
41 Alpha Designs
42 Exercises
43 More Incomplete Block Designs
44 Designs for Factorial Experiments
45 Designs for Parallel Line Assays
46 Introducing Bioassays
47 Contrasts for Parallel Line Assays
48 Block Designs for Parallel Line Assays
49 Designs for Test-Control Comparisons
50 Designs for Diallel Crosses
51 Robust Incomplete Block Designs
52 Robustness Against an Outlier
53 Robustness Against Missing Data
54 Trend-free Designs
55 Exercises
56 Optimality Aspects of Block Designs
57 Optimality Criteria
58 Optimality of Proper Block Designs
59 Optimality of Symmetric Designs
60 Optimality of Asymmetric Designs
61 D-optimality of Some Incomplete Block Designs
62 Optimal Designs for Test-Control Comparisons
63 Optimal Designs for Parallel Line Assays
64 Optimal Designs for Diallel Crosses
65 Exercises
66 Appendix
67 Some Results in Linear Algebra
68 Some Aspects of Linear Models
69 Finite Fields
70 Finite Geometries
Incomplete Block Designs 1st Edition by Aloke Dey ISBN 9814322687 978-9814322683
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ISBN 10: 9814322687
ISBN 13: 978-9814322683
Author: Aloke Dey
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 — 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 results for test-control comparisons, parallel-line assays and diallel cross experiments.
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Tags: Aloke Dey, Incomplete Block