Determining sample sizes in multistage samples requires variance components for each stage of selection. The relative sizes of the variance components in a cluster sample are dramatically affected by how much the clusters vary in size, by the type of sample design, and by the form of estimator used. Measures of the homogeneity of survey variables within clusters are related to the variance components and affect the numbers of sample units that should be selected at each stage to achieve the desired precision levels. Measures of homogeneity can be estimated using standard software for random-effects models but the model-based intracluster correlations may need to be transformed to be appropriate for use with the sample design. We illustrate these points and implications for sample size calculation for two-stage sample designs using a realistic population derived from household surveys and the decennial census in the U.S.
Effects of Cluster Sizes on Variance Components in Two-Stage Sampling
Valliant, R., Dever, J., & Kreuter, F. (2015). Effects of Cluster Sizes on Variance Components in Two-Stage Sampling. Journal of Official Statistics, 31(4), 763-782. https://doi.org/10.1515/JOS-2015-0044