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Some block designs with nested rows and columns for research on pesticide dose limitation
Author(s) -
Kozłowska Maria,
Łacka Agnieszka,
Krawczyk Roman,
Kozłowski Radosław J.
Publication year - 2011
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/env.1070
Subject(s) - factorial experiment , fractional factorial design , block (permutation group theory) , design of experiments , row and column spaces , row , mathematics , factorial , statistics , computer science , combinatorics , programming language , mathematical analysis
In 1979, Singh and Dey defined a block design with nested rows and columns (NRC for short). In this paper we take the view, common among statisticians, that the principles for the planning of factorial experiments and near‐factorial experiments in NRC designs are not the same. A group divisible NRC design for a factorial experiment is considered. Some constructions of the designs are given. Necessary and sufficient conditions are formulated and proven for a group‐divisible NRC design to be a C ‐design. For near‐factorial experiments, when there are a levels of experimental factor A and b levels of experimental factor B and one control treatment is added, we propose a method for constructing NRC designs. A plant protection experiment on limitation of pesticide dose is described in order to show how the results can be applied. Copyright © 2010 John Wiley & Sons, Ltd.