Design-Based Versus Model-Based Approaches to Account for Spatial Heterogeneity.

Classical methods of controlling for heterogeneity in field experiments typically involve blocking schemes that restrict arrangement of treatments to more-or-less homogeneous units. Inferences from such experiments is based on randomization theory and may be said to be designed-based. In this approach, the large scale spatial heterogeneity is reduced through blocking small scale variation negated by randomization. In contrast, spatial analysis of designed trials is a model-based approach, where some model of a random field is incorporated into the analysis. However, in the case of designed experiments, this may represent a break between experimental planning and proposed inference. Care must be taken when choosing a spatial model to replaced a planned design. We present a series of simulations of lattice designs and compare the planned analysis with spatial models to illustrate methods of model selection for recovery of spatial information.