Texts and Readings in Mathematics

This book presents a systematic, rigorous and comprehensive account of the theory and applications of incomplete block designs. An attempt has been made to cover all major aspects of incomplete block designs by consolidating vast amounts of material from the literature. The classical incomplete block designs, like the balanced incomplete block (BIB) designs and partially balanced incomplete block (PBIB) designs are covered at length. Some other developments like efficiency-balanced designs, nested designs, robust designs, C-designs and Alpha designs are also discussed. 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 the existing books, are given adequate coverage. Results on the optimality aspects of various incomplete block designs are reviewed in a separate chapter, which includes major results on optimal block designs as also many recent results on the optimality of incomplete block designs for test-control comparisons, parallel line assays and diallel cross experiments.

Numerous examples illustrating the results are included and there are a number of exercises at the end of each of the chapters. There is also a fairly exhaustive bibliography. The book meets the requirements of the students at the master´s level in statistics and there are some portions of the book which may be found useful for research students and consulting statisticians. 1. Introduction
2. Analysis and Properties of Block Designs
3. Balanced Designs
4. Partially Balanced Designs
5. More Incomplete Block Designs
6. Optimality Aspects of Block Designs
Appendix
A.1 Some Results in Linear Algebra
A.2 Some Aspects of Linear Models
A.3 Finite Fields
A.4 Finite Geometries References
Index