Combinatorial mathematicians and statisticians have made a wide range of contributions to the development of block designs, and this book brings together much of that work. The designs developed for a specific problem are used in a variety of different settings. Applications include controlled sampling, randomized response, validation and valuation studies, intercropping experiments, brand cross-effect designs, lotto and tournaments.
The intra- and inter- block, nonparametric and covariance analysis are discussed for general block designs, and the concepts of connectedness, orthogonality, and all types of balances in designs are carefully summarized. Readers are also introduced to the designs currently playing a prominent role in the field: alpha designs, trend-free designs, balanced treatment-control designs, nearest neighbor designs, and nested designs.
This book provides the important background results required by researchers in block designs and related areas and prepares them for more complex research on the subject.
Contents:
- Linear Estimation and Tests for Linear Hypotheses
- General Analysis of Block Designs
- Randomized Block Designs
- Balanced Incomplete Block Designs — Analysis and Combinatorics
- Balanced Incomplete Block Designs — Applications
- t-Designs
- Linked Block Designs: Partially Balanced Incomplete Block Designs
- Lattice Designs: Miscellaneous Designs
Readership: Statisticians, combinatorial mathematicians and social scientists.
