Block V Block
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Incomplete Block Designs
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.
Engineering Metrology and Measurements
Author: EduGorilla Prep Experts
language: en
Publisher: EduGorilla Publication
Release Date: 2024-09-03
EduGorilla Publication is a trusted name in the education sector, committed to empowering learners with high-quality study materials and resources. Specializing in competitive exams and academic support, EduGorilla provides comprehensive and well-structured content tailored to meet the needs of students across various streams and levels.
Block Designs: A Randomization Approach
Author: Tadeusz Calinski
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
In most of the literature on block designs, when considering the analysis of experimental results, it is assumed that the expected value of the response of an experimental unit is the sum of three separate components, a general mean parameter, a parameter measuring the effect of the treatment applied and a parameter measuring the effect of the block in which the experimental unit is located. In addition, it is usually assumed that the responses are uncorrelated, with the same variance. Adding to this the assumption of normal distribution of the responses, one obtains the so-called "normal-theory model" on which the usual analysis of variance is based. Referring to it, Scheffe (1959, p. 105) writes that "there is nothing in the 'normal-theory model' of the two-way layout . . . that reflects the increased accuracy possible by good blocking. " Moreover, according to him, such a model "is inappropriate to those randomized-blocks experiments where the 'errors' are caused mainly by differences among the experimental units rather than measurement errors. " In view of this opinion, he has devoted one of the chapters of his book (Chapter 9) to randomization models, being convinced that "an understanding of the nature of the error distribution generated by the physical act of randomization should be part of our knowledge of the basic theory of the analysis of variance.