In a balanced design, researchers allocate the same number of units across all treatment groups. It has been believed as a rule of thumb among some researchers in agriculture. Sometimes, an unbalanced design outperforms a balanced design. Given a specific parameter of interest, researchers can design an experiment by unevenly distributing experimental units to increase statistical information about the parameter of interest. An additional way of improving an experiment is an adaptive design (e.g., spending the total sample size in multiple steps). It is helpful to have some knowledge about the parameter of interest to design an experiment. In the initial phase of an experiment, a researcher may spend a portion of the total sample size to learn about the parameter of interest. In the later phase, the remaining portion of the sample size can be distributed in order to gain more information about the parameter of interest. Though such ideas have existed in statistical literature, they have not been applied broadly in agricultural studies. In this article, we used simulations to demonstrate the superiority of the experimental designs over the balanced designs under three practical situations: comparing two groups, studying a dose-response relationship with right-censored data, and studying a synergetic effect of two treatments. The simulations showed that an objective-specific design provides smaller error in parameter estimation and higher statistical power in hypothesis testing when compared to a balanced design. We also conducted an adaptive experimental design applied to a dose-response study with right-censored data to quantify the effect of ethanol on weed control. Retrospective simulations supported the benefit of this adaptive design as well. All researchers face different practical situations, and appropriate experimental designs will help utilize available resources efficiently.

中文翻译：

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统计实验设计在杂草管理中改进统计推断的应用。

在平衡设计中，研究人员在所有治疗组中分配相同数量的单位。它被认为是一些农业研究人员的经验法则。有时，不平衡的设计胜过平衡的设计。给定感兴趣的特定参数，研究人员可以通过不均匀分布实验单元来设计实验，以增加有关感兴趣参数的统计信息。另一种改进实验的方法是适应性设计（例如，在多个步骤中花费总样本量）。对感兴趣的参数有所了解有助于设计实验。在实验的初始阶段，研究人员可能会花费总样本量的一部分来了解感兴趣的参数。在后期阶段，可以分布样本量的剩余部分以获得有关感兴趣参数的更多信息。虽然这些想法在统计文献中已经存在，但它们并没有在农业研究中得到广泛应用。在本文中，我们使用模拟来证明实验设计在以下三种实际情况下优于平衡设计：比较两组，研究具有右删失数据的剂量反应关系，以及研究两种治疗的协同效应。模拟表明，与平衡设计相比，特定于目标的设计在参数估计中提供了更小的误差和更高的假设检验统计功效。我们还进行了适应性实验设计，该设计适用于具有右删失数据的剂量反应研究，以量化乙醇对杂草控制的影响。回顾性模拟也支持这种自适应设计的好处。所有研究人员都面临不同的实际情况，适当的实验设计将有助于有效利用可用资源。