On the connectivity of row-column designs
Abstract
A procedure is described for investigating the causes of treatment disconnectivity of a row-column design in terms of constraints on the columns of the design matrix which are induced by the treatment allocation. It is shown that treatment disconnectivity is due to a partitioning of the treatments which is similar to the well-known but much simpler situation which arises with incomplete block designs. A process is described which identifies the partitions by deriving a basis of the kernel of the information matrix and then suitably reordering the rows and columns of the design. The consequent reallocation of treatments to produce a treatment connected design is discussed. Some implications for the pairwise disconnectivity of treatments and rows and for the pairwise disconnectivity of treatments and columns are considered. The results are illustrated by examples.
