We identify three major components of spatial variation in plot errors from field experiments and extend the two-dimensional spatial procedures of Cullis and Gleeson (1991) to account for them. The components are nonstationary, large-scale (global) variation across the field, stationary variation within the trial (natural variation or local trend), and extraneous variation that is often induced by experimental procedures and is predominantly aligned with rows and columns. We present a strategy for identifying a model for the plot errors that uses a trellis plot of residuals, a perspective plot of the sample variogram and, where possible, likelihood ratio tests to identify which components are present. We demonstrate the strategy using two illustrative examples. We conclude that although there is no one model that adequately fits all field experiments, the separable autoregressive model is dominant. However, there is often additional identifiable variation present.

Key Words
Spatial analysis; REML; Field experiments; Variogram.

Arthur R. Gilmour is Senior Research Scientist, Orange Agricultural Institute, Forest Road, Orange, NSW 2800, Australia. Brian R. Cullis is Principal Research Scientist, NSW Agriculture, Agricultural Research Institute, Wagga Wagga, NSW 2650, Australia. Arunas P. Verbyla is Senior Lecturer, Department of Statistics, University of Adelaide, Adelaide, SA 5005, Australia.