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Keywords:

  • block design with nested rows and columns;
  • mixed model;
  • group divisible design;
  • C-design;
  • factorial experiment;
  • near-factorial experiment;
  • pesticide dose

Abstract

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.