24 Row-column designs

Abstract

This chapter focuses on row-column designs. It discusses the application of row-column designs as designs for estimation of treatment effects in face of two crossed nuisance factors. Row-column design refers to an experimental situation where there is two well-identified grouping or blocking factors, usually referred to as “row and column (classifications).” These are designed to eliminate heterogeneity in the experimental material or units in two clearly stated directions, viz., along the directions of rows and columns, assuming that the units have been displayed in the form of a rectangle. In a row-column design, the sources of information on the treatment contrasts are the within cell observational contrasts and the tetra-differences among the cell means. These along with the contrasts formed of the row totals and the column totals comprise all observational contrasts. Therefore, while analyzing the data, to extract information on the treatment contrasts, one need to concentrate only on the within cell observational contrasts and the tetra-differences. The data is then analyzed with a Gauss–Markov set-up with the treatment effects as the only parameters in the model.