On-farm experiments can provide farmers with information on more efficient crop management in their own fields. Developments in precision agricultural technologies, such as yield monitoring and variable-rate application technology, allow farmers to implement on-farm experiments. Research frameworks including the experimental design and the statistical analysis method strongly influences the precision of the experiment. Conventional statistical approaches (e.g., ordinary least squares regression) may not be appropriate for on-farm experiments because they are not capable of accurately accounting for the underlying spatial variation in a particular response variable (e.g., yield data). The effects of experimental designs and statistical approaches on type I error rates and estimation accuracy were explored through a simulation study hypothetically conducted on experiments in three wheat fields in Japan. Isotropic and anisotropic spatial linear mixed models were established for comparison with ordinary least squares regression models. The repeated designs were not sufficient to reduce both the risk of a type I error and the estimation bias on their own. A combination of a repeated design and an anisotropic model is sometimes required to improve the precision of the experiments. Model selection should be performed to determine whether the anisotropic model is required for analysis of any specific field. The anisotropic model had larger standard errors than the other models, especially when the estimates had large biases. This finding highlights an advantage of anisotropic models since they enable experimenters to cautiously consider the reliability of the estimates when they have a large bias.

翻译：农业实验可以向农民提供关于自己田间更有效作物管理的信息; 精确农业技术的发展,如产量监测和可变率应用技术等精确农业技术的发展,使农民能够实施农场实验; 研究框架,包括实验设计和统计分析方法,对实验的精确性产生了强烈的影响; 常规统计方法(例如,普通最不平方回归)可能不适合农业实验,因为它们无法准确计算特定反应变量(例如,产量数据)中潜在的空间差异; 实验设计和统计方法对第一类误差率和估计准确性的影响,通过假设在日本三个小麦田进行实验的模拟研究进行了探讨; 建立了同普通最低平方回归模型进行比较的实验框架(例如,普通最不平方回归),这些重复的设计不足以减少一类误差的风险和对本身的偏差估计; 反复设计和反向型模型有时需要提高实验的精确性。 应进行模型选择,以确定在日本三个小麦田间进行实验时是否具有亚地差率模型的优势,特别是从任何特定田间分析的大规模模型。