Researchers often turn to block randomization to increase the precision of their inference or due to practical considerations, such as in multi-site trials. However, if the number of treatments under consideration is large it might not be practical or even feasible to assign all treatments within each block. We develop novel inference results under the finite-population design-based framework for a natural alternative to the complete block design that does not require reducing the number of treatment arms, the balanced incomplete block design (BIBD). This includes deriving the properties of two estimators for BIBDs and proposing conservative variance estimators. To assist practitioners in understanding the trade-offs of using BIBDs over other designs, the precisions of resulting estimators are compared to standard estimators for the complete block design, the cluster-randomized design, and the completely randomized design. Simulations and a data illustration demonstrate the strengths and weaknesses of using BIBDs. This work highlights BIBDs as practical and currently underutilized designs.

翻译：研究者常采用区组随机化以提高推断精度或出于实际考虑（如多中心试验）。然而，若待考察的处理数量较多，在每个区组内分配所有处理可能不切实际甚至不可行。本文在有限总体设计基的框架下，针对一种无需减少处理组数量的完全区组设计替代方案——平衡不完全区组设计（BIBD），提出了新的推断结论。这包括推导BIBD两种估计量的性质，并提出保守的方差估计量。为帮助实践者理解BIBD相对于其他设计的权衡，我们将所得估计量的精度与完全区组设计、整群随机化设计及完全随机化设计的标准估计量进行比较。模拟实验与数据示例揭示了使用BIBD的优势与局限。本研究强调BIBD是一种实用且当前未得到充分利用的设计方案。