ENBIS-11 in Coimbra

4 – 8 September 2011 Abstract submission: 1 January – 25 June 2011

Experimental Design: BIBD and PBIBD applications and links

6 September 2011, 11:15 – 11:45

Abstract

Submitted by
Teresa Oliveira
Authors
Teresa A. Oliveira and Amilcar Oliveira
Affiliation
Center of Statistics and Applications, University of Lisbon (CEAUL); DCeT-Universidade Aberta
Abstract
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. Block designs are used to control such sources since the main purpose of forming blocks is to maintain the homogeneity within blocks. The simplest block design is the Randomized Complete Block (RCB). When the number of varieties in an experiment increases, incomplete block designs with smaller block sizes can be adopted. Balanced Incomplete Block (BIB) and Partially Balanced Incomplete Block Designs (PBIBD) designs are two important types of such designs. A Balanced Incomplete Block Design (BIBD) 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. In some incomplete designs it is not possible to define a balance but there is still the possibility for the design to be partially balanced. BIBD and PBIBD have applications in areas as diverse as Agriculture, Industry, Genetics, Biology, Education Sciences and Cryptography. Thanks to their optimal properties these designs present also extremely relevant links, highlighted in Pure and Applied Mathematics. In our work we illustrate some applications and links considering BIBD and PBIBD.
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