Novel approach to the analysis of spatially-varying treatment effects in on-farm experiments

Abstract With increasing interest in on-farm experiments, there is a pressing need to develop rigorous statistical methods for analysing these experiments. The adoption of advanced technologies such as yield monitors and variable-rate fertilizer applicators has enabled farmers and researchers to collect biophysical data linked to spatial information at a scale which allows them to investigate the role of spatial variability in the development of optimum management practices. A relevant topic for investigation could be: “what are the optimum rates of nitrogen and how/why do these differ across the field”? Although it has been recently understood that traditional statistical methods that are appropriate for analysing small-plot experiments are inappropriate for answering these questions, a unifying approach to inference for on-farm experiments is still missing and this limits the adoption of the technique. In this paper we propose a unifying approach to the analysis of on-farm strip experiments adapting the core ideas of local likelihood or geographically weighted regression. We propose a statistical model that allows spatial nonstationarity in modelled relationships and estimates spatially-varying parameters governing these relationships. A crucial step is bandwidth selection in implementing these models, and we develop bandwidth selection methods for two important scenarios relevant to the modelling of yield monitor data in on-farm experiments. Local t-scores have been introduced for inferential purposes and the associated problem of multiple testing has been described in the context of analysing on-farm experiments. We demonstrate in this paper how local p-values can be adjusted to overcome this problem. To illustrate the applicability of our proposed method, we analysed two publicly available datasets. Graphical displays are created to guide practitioners to make informed decisions on optimal management practices.