Editing Cluster sampling (section)

==When clusters are of different sizes==

Without modifying the estimated parameter, cluster sampling is unbiased when the clusters are approximately the same size. In this case, the parameter is computed by combining all the selected clusters. When the clusters are of different sizes there are several options:

One method is to sample clusters and then survey all elements in that cluster. Another method is a two-stage method of sampling a fixed proportion of units (be it 5%  or 50%, or another number, depending on cost considerations) from within each of the selected clusters. Relying on the sample drawn from these options will yield an unbiased estimator. However, the sample size is no longer fixed upfront. This leads to a more complicated formula for the standard error of the estimator, as well as issues with the optics of the study plan (since the power analysis and the cost estimations often relate to a specific sample size).

A third possible solution is to use [[sampling (statistics)#Probability-proportional-to-size sampling|probability proportionate to size sampling]]. In this sampling plan, the probability of selecting a cluster is proportional to its size, so a large cluster has a greater probability of selection than a small cluster. The advantage here is that when clusters are selected with probability proportionate to size, the same number of interviews should be carried out in each sampled cluster so that each unit sampled has the same probability of selection.