Elementary Statistics (1+1)

3.1.10.4 Multi-stage sampling or Cluster Sampling

Under this method, the random selection is made of primary, intermediate and final (or the ultimate) units from a given population or stratum. There are several stages in which the sampling process is carried out. At first, the first stage units are sampled by some suitable method, such as simple random sampling. Then, a sample of second stage units is selected from each of the selected first stage units, again by some suitable method which may be the same as or different from the method employed for the first stage units. Further stages may be added as required. The procedure may be illustrated as follows;

Suppose we want to take a sample of 5,000 households from the State of Tamil Nadu. At the first stage, the State may be divided into a number of districts and a few districts selected at random. At the second stage, each district may be subdivided into a number of villages and a sample of villages may be taken at random. At the third stage, a number of households may be selected from each of the villages selected at the second stage. To take another example suppose in a particular survey, we wish to take a sample of 10,000 students from Delhi University. We may take colleges—primary units—as the first stage, then draw departments as the second stage, and choose students as the third and last stage.

Merits. Multi-stage sampling introduces flexibility in the sampling method which is lacking in the other methods. It enables existing divisions and sub-divisions of the population to be used as units at various stges, and permits the field work to be concentrated and yet large area to be covered. Another advantage of the method is that subdivision into second stage units(i.e., the construction of the second stage frame) need be carried out for only those first stage units which are included in the sample. It is, therefore, particularly valuable in surveys of under-developed areas where no frame is generally sufficiently detailed and accurate for subdivision of the material into reasonably small sampling units.

Limitations. A multi-stage sample is  less accurate than a sample containing the same number of final stage units which have been selected by some suitable stage process.

We have discussed above the various random procedures in independent designs. In practice we often combine two or more of these methods into a single design.