Probability Sampling - Two Stage Cluster Sampling

The concept of cluster sampling can be extended to two stage sampling by taking a simple random sampling of elements from each sampled cluster. Two satege cluster sampling is advantageous when one wishes to have sample elements in geographic proximity because of travel cost. Two stage cluster sampling eliminates the need to sample all elements in each sampled cluster. Thus the cost of sampling can often be reduced with little loss of information.

Two stage cluster sampling is an extension of the concept of cluster sampling. A cluster often contain too many elements to obtain a measurement on each, or it contains elements so nearly alike that measurement of only a few elements provides information on an entire cluster. When either situation occurs, the researcher can select a probability sample of clusters and then take a probability sample of elements within each cluster. The result is a two stage cluster sample.

A two stage cluster sample is obtained by first selecting a probability sample of clusters and then selecting a probability sample of elements from each sample cluster.

A certain similarity between cluster sampling and stratified random sampling. Think of a population being divided into nonoverlapped groups of elements. If these groups are considered to be a strata, then a simple random sample is selected from each group. If these groups are considered to be clusters, then a simple random sample of groups is selected, and the sampled groups are then subsampled. Stratified random sampling provides estimators with small variance when there is little variation among elements within each group. Cluster sampling does well when the elements within each group are highly variable, and all groups are quite similar to one another.

The advantages of two stage cluster sampling over other designs are same as cluster sampling.
First, a frame listing all elements in the population, may be impossible or costly to obtain, whereas to obtain a list of all clusters may be easy.
Second, the cost of obtaining data may be inflated by travel cost if the sampled elements are spread over a large geographic area.

How to draw a two stage random sample
The first problem in selecting a two stage cluster sample is the choice of appropriate clusters. Two conditions are desirable:
1. Geographic proximity of elements within a cluster
2. Cluster sizes that are convenient to administer

The selection of appropriate clusters also depends on whether we want to sample a few clusters and many elements from each or many clusters and few elements from each. The choice is based on costs.
-. Large clusters tend to possess heterogeneous elements, and hence a large sample is required from each in order to acquire accurate estimates of population parameters.
-. Small clusters frequently frequently contain homogenous elements, in which case accurate information on the characteristics of a cluster can be obtained by selecting a small sample from each cluster.

To select sample:
First, obtain a frame listing all clusters in the population
Second, draw a simple random sample of clusters
Third, we obtain frames that list all elements in each of the sampled clusters
Fourth, we select a simple random sample of elements from each of these frames


Source:
-. Richard L. Scheaffer, William Mendenhall, Lyman Ott; Elementary Survey Sampling, 4-th, PWS-Kent Publishing Company, 1990, Boston
-. Mugo Fridah W, Sampling in Research
-. SamplingBigSlides.pdf