Efficient row-column designs with multiple units per cell balanced for special effects

Abstract

Generalized Row-Column (GRC) designs are defined as designs with v treatments in p rows and q columns such that the intersection of each row and column (cell) consists of k experimental units. In GRC designs, since there are more than one number of units in a cell, it is likely that the treatment applied to one experimental unit may affect the response of the neighbouring unit in the same cell if the units are placed linearly adjacent giving rise to spatial effects. The study in presence of spatial effects from neighbouring units requires construction of an arrangement in which the neighbouring units have to appear in a predetermined pattern. Here, series of GRC designs balanced for these spatial effects have been developed. The information matrices for estimating the contrasts pertaining to direct effect and spatial effect have been derived. The designs developed ensure that within a cell every treatment has every other treatment appearing as neighbour a constant number of times. A list of efficient designs has been prepared. Further, in order to give a readymade solution to the experimenters, a SAS macro has been developed that generates the layout of the designs with parameter v (prime), p = v, q = v-1, k = s (3 ≤ s ≤ v-1).