Block Designs with Neighbour Effects

Abstract: Experiments in agriculture, horticulture, and forestry often show neighbour effects, that is the response on a given plot is affected by the treatments on neighbouring plot as well as by the treatment applied to that plot. When treatments are varieties, neighbour effects may be caused by differences in height, root vigor, or germination date, especially on small plots. As a result, the estimate of treatment differences may deviate because of this interference from neighbouring units. Neighbour-balanced designs ensure that no treatment is unduly disadvantaged by its neighbours. The allocation of treatments in these designs is such that every treatment occurs equally often with every other treatment as neighbours. Some aspects of block designs with neighbour effects have been presented considering the designs in linear blocks. Some methods of obtaining neighbour balanced block designs that are balanced and partially variance balanced for estimating the contrast pertaining to direct and neighbour effects have been described.