Some block designs with nested rows and columns for research on pesticide dose limitation

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.

On a new approach to the analysis of variance for experiments with orthogonal block structure. III. Experiments in row-column designs

“…The presented results and conclusions regarding the basic contrasts coincide with the results of the analysis under the bottom stratum submodel presented by Kozłowska et al (2011). However, use of the direct analysis allowed the rejection of the general hypothesis (Table 9), which was not possible when stratum analyses were used.…”

“…Example 4. Kozłowska et al (2011) analyzed data from a plant protection experiment. The field experiment was carried out in Winna Góra at the Field Experiment Station of the Institute of Plant Protection -National Research Institute in Poznań, Poland.…”

Some notes on planning plant protection research in block designs with nested rows and columns

“…In plant protection research, a block design with nested rows and columns is frequently used (e.g. Kozłowska 2001, Kozłowska et al 2011, 2012, Łacka 2021, Łacka et al 2009b. A design is said to have nested rows and columns if the set of experimental units is partitioned into blocks and each block is further partitioned into rows and columns.…”