Probability Sampling - Cluster sampling

A cluster sample is a probability sample in which each sampling unit is a collection, or cluster, of elements. Cluster sampling is less costly than simple or stratified random sampling if the cost of obtaining a frame that lists all population elements is very high or if the cost of obtaining observations increases as the distance separating the elements increases.

A cluster sample is obtained by selecting clusters from the population on the basis of simple random sampling. The sample comprises a census of each random cluster selected. For example, a cluster may be some thing like a village or a school, a state. So you decide all the elementary schools in Newyork State are clusters. You want 20 schools selected. You can use simple or systematic random sampling to select the schools, then every school selected becomes a cluster. If you interest is to interview teachers on thei opinion of some new program which has been introduced, then all the teachers in a cluster must be interviewed. Though very economical cluster sampling is very susceptible to sampling bias. Like for the above case, you are likely to get similar responses from teachers in one school due to the fact that they interact with one another.

In Cluster Sampling, two (or more) stage sampling of clusters of people.
Most commonly used method
Stage 1: Select sample of clusters from sampling frame of all clusters
Stage 2: Select sample of people from within each selected cluster
Probability that any member picked = Prob (Cluster picked) * Prob (Person picked from cluster)

Cluster sampling is an effective design for obtaining a specified amount of information at minimum cost under the following conditions:
1. A good frame listing population elements either is not available or is very costly to obtain, while a frame listing clusters is easily obtained.
2. The cost of obtaining observations increases as the distance separating the elements increases.
The first task in cluster sampling is to specify appropriate clusters. Elements within a cluster are often physically close together and hence tend to have similar characteristics. Stated another way, the measurement on one element in a cluster may be highly correlated with the measurement on another.
In cluster sampling each sampling unit is a group, or cluster, of elements. Cluster sampling may provide maximum information at minimum cost when a frame listing population elements is not available or when the cost of obtaining observations increasing distance between elements.

Scheme of Cluster Random Sampling

*. Blue circle show us selected sample

Summary
Cluster Sampling
• Example: A primary application is area sampling, where clusters are city blocks or other well-defined areas.
• The population is first divided into separate groups of elements called clusters. Each cluster is a representative small-scale version of the population (i.e. heterogeneous group).
• All elements within each sampled (chosen) cluster form the sample.
• Advantage: The close proximity of elements can be cost effective (i.e. many sample observations can be obtained in a short time).
• Disadvantage: This method generally requires a larger total sample size than simple or stratified random sampling.


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