Clusters form the basis of a number of research study designs including survey and experimental studies. Cluster-based designs can be less costly but also less efficient than individual-based designs due to correlation between individuals within the same cluster. Their design typically relies on ad hoc choices of correlation parameters, and is insensitive to variations in cluster design. This article examines how to efficiently design clusters where they are geographically defined by demarcating areas incorporating individuals and households or other units. Using geostatistical models for spatial autocorrelation, we generate approximations to within cluster average covariance in order to estimate the effective sample size given particular cluster design parameters. We show how the number of enumerated locations, cluster area, proportion sampled, and sampling method affect the efficiency of the design and consider the optimization problem of choosing the most efficient design subject to budgetary constraints. We also consider how the parameters from these approximations can be interpreted simply in terms of ‘real-world’ quantities and used in design analysis.

集群构成了许多研究设计的基础，包括调查和实验研究。由于同一集群中个体之间的相关性，基于集群的设计可能比基于个体的设计成本更低，但效率也更低。他们的设计通常依赖于临时相关参数的选择，并且对集群设计的变化不敏感。本文研究了如何有效地设计集群，在这些集群中，集群是通过划分包含个人和家庭或其他单位的区域来在地理上定义的。使用空间自相关的地统计模型，我们生成集群内平均协方差的近似值，以便在给定特定集群设计参数的情况下估计有效样本量。我们展示了枚举位置的数量、集群区域、采样比例和采样方法如何影响设计的效率，并考虑了在预算约束下选择最有效设计的优化问题。