Statistical opportunities for analyzing spatial and temporal heterogeneity of field soils

Abstract

Statistical techniques for analyzing data in the agricultural sciences have traditionally followed the pioneering efforts of R.A. Fisher who assumed that observations in the field were independent and identically distributed. Such techniques, proven useful in the past and still being used today for comparing the merits of different management practices or different treatments, are presently giving way to additional methods that are based upon observations being spatially or temporally correlated. It is physically more sensible to expect soil attributes to be correlated when they are measured at adjacent points in space or time. Spatially repetitious patterns of soil attributes for physical and biological processes occurring at distances of a few molecules to those of kilometers are also expected. Opportunities to use geostatistics, time series analyses, state-space models, spectral analyses of variance, lagged regression models and other alternative techniques for analyzing multidimensional random fields are available to enhance the understanding of agro-ecosystems. Approaches to modeling and fitting data using stochastic partial differential equations and scaling techniques also help reveal the underlying processes occurring in field soils. Inclusion of these alternatives in the development of an agro-ecological technology leads to improved sampling designs to better entire management units, rather than ascertaining the impact of particular, sometimes arbitrary treatments applied to a set of small plots using analysis of variance methods.