Combining Standard Block Analyses With Spatial Analyses Under a Random Effects Model

Spatial trends are often a significant source of variability in field trials. Since trends vary from block to block, they should be estimated as random effects. In this paper we propose to consider spatial covariates as post hoc random effects within the context of the experiment design. We demonstrate that making use of the spatial information leads to more efficient estimation of treatment effects. The models considered for spatial effects include block effects which are part of the experiment design, random gradients, regression trends, nearest neighbor analysis and smoothing. The analyses are applied to an example, which exhibits quite different results for the different methods. Since computations are tedious, programs for the various statistical procedures are presented.