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Multistage sampling is a complex form of cluster sampling. Using all the sample elements in all the selected clusters may be prohibitively expensive or not necessary. Under these circumstances, multistage cluster sampling becomes useful. Instead of using all the elements contained in the selected clusters, the researcher randomly selects elements from each cluster. Constructing the clusters is the first stage. Deciding what elements within the cluster to use, is the second stage. The technique is used frequently when a complete list of all members of the population does not exist.
Probability-proportional-to-size sampling is a type of multistage cluster sampling. In this method, the probability of selecting an element in any given cluster varies inversely with the size of the cluster.
Although cluster sampling and stratified sampling bear some superficial similarities, they are substantially different. In stratified sampling, a random sample is drawn from all the strata, where in cluster sampling only the selected clusters are studied, either in single stage or multi stage.
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