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.

农场实验可以为农民提供有关其各自领域更有效的农作物管理的信息。诸如产量监测和可变利率应用技术之类的精确农业技术的发展使农民能够进行农场试验。包括实验设计和统计分析方法在内的研究框架极大地影响了实验的精度。常规的统计方法（例如，普通最小二乘回归）可能不适用于农场实验，因为它们无法准确地说明特定响应变量（例如，产量数据）中潜在的空间变化。通过在日本三个麦田进行的假设性模拟研究，探索了实验设计和统计方法对I型错误率和估计准确性的影响。建立了各向同性和各向异性的空间线性混合模型，用于与普通最小二乘回归模型进行比较。重复的设计不足以单独降低I型错误的风险和估计偏差。有时需要将重复设计和各向异性模型结合起来以提高实验的精度。应该执行模型选择以确定是否需要各向异性模型来分析任何特定领域。各向异性模型比其他模型具有更大的标准误差，尤其是当估计值具有较大偏差时。