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.
