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# Cluster sampling

Cluster sampling is used when "natural" groupings are evident in the population. The total population is divided into groups or clusters. Elements within a cluster should be as heterogeneous as possible. But there should be homogeneity between clusters. Each cluster should be a small scale version of the total population. Each cluster must be mutually exclusive and collectively exhaustive. A random sampling technique is then used on any relevent clusters to choose which clusters to include in the study. In single-stage cluster sampling, all the elements from each of the selected clusters are used. In two-stage cluster sampling, a random sampling technique is applied to the elements from each of the selected clusters.

The main difference between cluster sampling and stratified sampling is that in cluster sampling the cluster is treated as the sampling unit so analysis is done on a population of clusters (at least in the first stage). In stratified sampling, the analysis is done on elements within strata. In stratified sampling, a random sample is drawn from each of the strata, whereas in cluster sampling only the selected clusters are studied. The main objective of cluster sampling is to reduce costs by increasing sampling effeciency (This contrasts with stratified sampling where the main objective is to increase precision.).

One version of cluster sampling is area sampling or geographical cluster sampling. Clusters consist of geographical areas. A geographically dispersed population can be expensive to survey. Greater economy than simple random sampling can be achieved by treating several respondents within a local area as a cluster. It is usually necessary to increase the total sample size to achieve equivalent precision in the estimators, but the savings in cost may make that feasible.

In some situations, cluster analysis is only appropriate when the clusters are approximately the same size. This can be achieved by combining clusters. If this is not possible, probability proportionate to size sampling is used. In this method, the probability of selecting an element in any given cluster varies inversely with the size of the cluster.

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