Efficient neighbour balanced block design with proportional neighbour effects

Neighbour balanced block (NBB) design, wherein the allocation of treatments is such that every treatment occurs, equally often with every other treatment as neighbour(s), is useful to have a more precise comparison of treatment effects when neighbour effect from the adjacent experimental units are suspected. Sometimes it may happen that the neighbour effects of treatments may be proportional to its direct effect. For example, in case of fungicide experiment, a heavier does is likely to have heavy neighbour effect (Gill, 1993). In this paper, block designs have been studied when neighbour effects may be postulated to be proportional to the direct effects of treatments. The advantage of this model lies in the fact that there are fewer parameters to be estimated. Information matrix has been derived for two-sided neighbour effect model under block design set up. A series of NBB designs given by Azais et. al. (1993) have been studied using proportional neighbour effect model for different values of the proportionality constant and their efficiencies have been worked out.