Abstract Field scale experiments are seldom replicated due to size constraints and limitations of other resources. This presents a difficulty in performing statistical analysis and interpretation of the results collected. In this paper we will evaluate water and nutrient effluent data from two fields, one managed under controlled subsurface drainage (CSSD) compared with an adjacent field under conventional free subsurface drainage (FSSD). The purpose of this paper is to compare approaches for statistical analysis of unreplicated paired design drainage experiments. The methods tested include the paired watershed design, a before-after control-impact paired (BACIP) design, time-series, and analysis using a beta and a gamma distribution. The assumptions used in the paired watershed and BACIP designs require the data to follow a normal distribution with identically and independently distributed errors, while the beta and gamma distributions do not require the assumption of normality. Analysis of the data set using a normal distribution was found to be inappropriate due to the nature of the data set which violates the assumptions required for analysis of variance; whereas, the analysis of the data using a beta distribution was found to produce the most appropriate results. The time series approach mimicked the physical treatments applied to FSSD and CSSD fields and led to a significant effect of CSSD compared to FSSD. Future work should focus on confirming that the beta distribution or time series are the best approaches for statistical analysis of field scale unreplicated paired design drainage experiments.

中文翻译：

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非重复配对设计排水试验的统计分析选项

摘要 由于规模限制和其他资源的限制，田间规模的实验很少被复制。这给对收集的结果进行统计分析和解释带来了困难。在本文中，我们将评估来自两个油田的水和养分流出数据，一个在受控地下排水 (CSSD) 下管理，与相邻油田在常规自由地下排水 (FSSD) 下进行比较。本文的目的是比较非重复配对设计排水试验的统计分析方法。测试的方法包括配对分水岭设计、前后控制影响配对 (BACIP) 设计、时间序列以及使用 beta 和 gamma 分布的分析。成对流域和 BACIP 设计中使用的假设要求数据遵循具有相同且独立分布误差的正态分布，而 beta 和 gamma 分布不需要正态性假设。由于数据集的性质违反了方差分析所需的假设，因此发现使用正态分布分析数据集是不合适的；而使用 beta 分布的数据分析被发现会产生最合适的结果。时间序列方法模仿了应用于 FSSD 和 CSSD 领域的物理处理，并且与 FSSD 相比，CSSD 产生了显着的效果。