Efficient neighbour balanced block designs for correlated observations

Abstract

Neighbour balanced designs, permitting the estimation of direct and neighbour effects, are used when the treatment applied to one experimental plot may affect the response on neighbouring plots as well as the response on the plot to which it is applied. The allocation of treatments in these designs is such that every treatment occurs equally often with every other treatment as neighbours. Neighbour balanced block designs for observations correlated within a block have been investigated. The performance of a series of incomplete neighbour balanced design for autoregressive and nearest neighbour error correlation structure is studied when generalized least squares estimation is used. The efficiencies for direct and neighbour effects of the designs as compared to a neighbour balanced complete block design of Azais et al. (1993) under correlated error is computed and tabulated for some cases. It is observed that efficiency is quite high, in case of complete block designs for both AR(1) and NN correlation structures. In case of incomplete block designs, designs with AR(1) structure turns out to be more efficient. However, the efficiency of direct effects of treatments is more as compared to neighbour effects under both the structures.