Power analysis based on spatial effects mixed models: A tool for comparing design and analysis strategies in the presence of spatial variability

Spatial variability among experimental units is known to exist in many designed experiments. Agronomic field trials are a particularly well-known example, but there are others. Historically, spatial variability has been dealt with in one of two ways: either though design, by blocking to account for spatial effects, or though analysis, by nearest neighbor adjustment. More recently, mixed models with spatial covariance structures such as those used in geostatistics have been proposed. These mixed model procedures have tempted some to conclude-to the dismay of many consulting statisticians-that design principles may be bypassed, since spatial covariance models can recover any lost information. Although design principles clearly should not be ignored, spatial procedures do raise questions. Are traditional notions of appropriate design affected? If so, how? How do spatial effects mixed models compare to conventional analysis of variance used in conjunction with blocked designs? This article presents mixed model methods to assess power and precision of proposed designs in the presence of spatial variability and to compare competing design and analysis strategies. The main conclusion is that, if anything, spatial models reinforce the need for sound design principles, particularly the use of incomplete block designs.