Spatial heterogeneity in terms of trends or periodicity in blocks may affect the outcome of experiments, especially in agricultural experiments. The conventional randomized allocation of treatments to plots in a block may result in lesser precision. It has been commonly found that the experimental units which are neighbouring to each other within a block are correlated, or there may be existing significant trends even within small block. Use of some methods of local control, called spatial or nearest neighbour (NN) methods for analyzing the observations in the presence of significant trends in adjacent plots of field data, help in increasing precision. Other approaches to guard the effects from neighbouring plots in experimental designs leads to construction of useful optimal neighbour balanced block designs which are not only efficient under standard intra-block incomplete block design type analysis but also provide protection against the effects of correlated observations or potentially unknown trends which are highly correlated with plot positions within blocks (Keifer and Wynn, 1981, Cheng, 1983; Stroup and Mulitze, 1991; Jackroux, 1998 etc). Neighbour balanced designs are designs, wherein the allocation of treatments is such that every treatment occurs equally often with every other treatment as immediate neighbours. All Ordered Neighbour design (AONBD) are those designs where allocation of treatments is done such a way that neighbor balance is obtained at every order of neighbor, given immediate neighbor is first order.
School of Mathematical Sciences
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