Block Design with Nested Rows and Columns for Research on Food Acceptability Limitation

Abstract

Block designs with nested rows and columns were introduced in Srivastava (1978) and more specifically defined in Singh and Dey (1979). We present properties of some partially balanced block designs with nested rows and columns. The designs are considered for near-factorial experiments, when there are a levels of experimental factor A and b levels of experimental factor B and there is one control treatment added. In this article we extend the theory of block designs with nested rows and columns described by \L acka and Kozłowska (2009) and Kozłowska et al. (2011). We carry out our consideration by the derived mixed linear model resulting from randomization of blocks, rows and columns. For this model of observations, some properties of estimation of treatment contrasts are discussed. We calculate the efficiency factors of estimation of treatment contrasts. We formulate theorems for some partially balanced block designs with nested rows and columns. Plant protection experiment on limitation of food acceptability for T. urticae is given to show how the obtained results can be applied.

Keywords:

• Block design with nested rows and columns
• Near-factorial experiments
• Optimal in the sense of majorization
• Tetranychus urticae

2000 Mathematics Subject Classification:

• 62K10

Acknowledgment

Project was partially financed by the National Science Center, contract 7350/B/P01/2011/40.