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.

中文翻译：

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在农场实验中分析空间变化处理效果的新方法

摘要 随着对农场实验的兴趣日益浓厚，迫切需要开发严格的统计方法来分析这些实验。采用产量监测器和可变速率施肥机等先进技术，使农民和研究人员能够在一定范围内收集与空间信息相关的生物物理数据，从而使他们能够调查空间变异在制定最佳管理实践中的作用。一个相关的调查主题可能是：“最佳氮含量是多少，这些在整个领域有何不同/为什么不同”？尽管最近了解到适用于分析小区实验的传统统计方法不适合回答这些问题，仍然缺少一种统一的农场实验推理方法，这限制了该技术的采用。在本文中，我们提出了一种统一的方法来分析农场带状实验，以适应局部似然或地理加权回归的核心思想。我们提出了一个统计模型，该模型允许建模关系中的空间非平稳性，并估计控制这些关系的空间变化参数。实施这些模型的关键步骤是带宽选择，我们为与农场实验中产量监测数据建模相关的两个重要场景开发了带宽选择方法。引入了局部 t 分数用于推理目的，并且在分析农场实验的背景下描述了多重测试的相关问题。我们在本文中展示了如何调整局部 p 值来克服这个问题。为了说明我们提出的方法的适用性，我们分析了两个公开可用的数据集。创建图形显示以指导从业者就最佳管理实践做出明智的决定。