Incomplete block designs - Dey, Aloke (World Scientific, 2010)
Includes bibliographical references (pages 243-276) and index
1. Introduction. 1.1. Prologue. 1.2. Outline of the book -- 2. Analysis and properties of block designs. 2.1. Introduction. 2.2. Intra-block analysis. 2.3. Balancing in block designs. 2.4. Recovery of inter-block information. 2.5. Efficiency factor. 2.6. Exercises -- 3. Balanced designs. 3.1. Introduction. 3.2. Some properties of BIB designs. 3.3. Analysis of BIB designs. 3.4. Construction and existence of BIB designs. 3.5. Some generalizations of BIB designs. 3.6. Construction of variance- and efficiency-balanced designs. 3.7. Nested BIB designs. 3.8. Exercises -- 4. Partially balanced designs. 4.1. Introduction. 4.2. Introducing PBIB designs. 4.3. The algebra of association matrices. 4.4. PBIB designs with two associate classes. 4.5. PBIB designs with more than two classes. 4.6. Analysis of PBIB design. 4.7. Lattice designs. 4.8. Cyclic designs. 4.9. Linked block designs. 4.10. C-designs. 4.11. Alpha designs. 4.12. Exercises -- 5. More incomplete block designs. 5.1. Introduction. 5.2. Designs for factorial experiments. 5.3. Designs for parallel line assays. 5.4. Designs for test-control comparisons. 5.5. Designs for diallel crosses. 5.6. Robust incomplete block designs. 5.7. Exercises -- 6. Optimality aspects of block designs. 6.1. Introduction. 6.2. Optimality criteria. 6.3. Optimality of proper block design. 6.4. Optimal designs for test-control comparisons. 6.5. Optimal designs for parallel line assays. 6.6. Optimal designs for diallel crosses. 6.7. Exercises -- Appendix
"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"--Provided by publisher