Planning of factorial experiments with one control treatment in a block design with nested rows and columns for environmental research

摘要

We presented principles for the planning of factorial experiments concerned with protection of the environment, carried out on heterogeneous experimental material or, for example, in the case of non-uniform or, particularly, low levels of disease or pest infection. A block design with nested rows and columns (NRC) is proposed. We supposed that there are a levels of experimental factor A and b levels of experimental factor B. Hence ab experimental combinations and one control treatment are applied to experimental units. We assumed a mixed linear model resulting from randomization of blocks, rows and columns. We proposed stratum analysis and obtained the efficiency factors of estimation of treatment contrasts in the strata. We described a NRC design having certain properties. We considered type S designs, designs possessing C-property and presented constructions of type S NRC designs and NRC designs possessing C-property. A necessary and sufficient condition is obtained for a type S NRC design to be design possessing C-property.