Author(s):
Oliveira, Teresa 
Date: 2010
Persistent ID: http://hdl.handle.net/10400.2/1716
Origin: Repositório Aberto da Universidade Aberta
Subject(s): BIBD; Experimental design; BIBD with repeated blocks
Document details
BIB designs with repeated blocks: review and perspectives
Description
Experimental Design plays an important role on establishing an interface between Applied Mathematics and statistical applications in several fields, like Agriculture, Industry, Genetics,Biology and Education Sciences. The goal of any Experimental Design is to obtain the maximum amount of information for a given experimental effort, to allow comparisons between varieties and to control for sources of random variability. Randomized block designs are used to control for these sources. A Balanced Incomplete Block Design (BIB Design) is a randomized block design with number of varieties greater than the block size and with all pairs of varieties occurring equally often along the blocks. The Fisher related information of a balanced block design will remain invariant whether or not the design has repeated blocks. This fact can be used theoretically to build a large number of non-isomorphic designs for the same set of design parameters, which could be used for many different purposes both in experimentations and surveys from finite populations. The original and most important method on the construction of BIB Designs with repeated blocks (BIBDR) is due to Hedayat and Li (1979): the trade-off method. Since then, many authors and researchers have been paying particular attention to the construction of BIBDR, but still some unsolved problems remain. This issue will be briefly reviewed and new results on the existence and construction of BIBDR, as well as several unsolved problems for further research will be presented.
Experimental Design plays an important role on establishing an interface between Applied Mathematics and statistical applications in several fields, like Agriculture, Industry, Genetics,Biology and Education Sciences. The goal of any Experimental Design is to obtain the maximum amount of information for a given experimental effort, to allow comparisons between varieties and to control for sources of random variability. Randomized block designs are used to control for these sources. A Balanced Incomplete Block Design (BIB Design) is a randomized block design with number of varieties greater than the block size and with all pairs of varieties occurring equally often along the blocks. The Fisher related information of a balanced block design will remain invariant whether or not the design has repeated blocks. This fact can be used theoretically to build a large number of non-isomorphic designs for the same set of design parameters, which could be used for many different purposes both in experimentations and surveys from finite populations. The original and most important method on the construction of BIB Designs with repeated blocks (BIBDR) is due to Hedayat and Li (1979): the trade-off method. Since then, many authors and researchers have been paying particular attention to the construction of BIBDR, but still some unsolved problems remain. This issue will be briefly reviewed and new results on the existence and construction of BIBDR, as well as several unsolved problems for further research will be presented.
Document Type
Article
Language English
Language English
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