Stratified and cluster sampling

Definition taught in Studies, data, and evidence, part of Data analysis

Type	Definition
Taught in	Studies, data, and evidence
Part	Data analysis
Worked examples	1

In stratified sampling the population is split into subgroups called strata, and a simple random sample is drawn from each, usually of size nN_s/N for a stratum of size N_s. In cluster sampling the population is split into many small clusters, a few clusters are chosen at random, and every unit in each chosen cluster is measured, or a simple random sample is taken within it.

Examples

Sampling ten villages

Worked example from Studies, data, and evidence

A population lives in 10 small villages: 5 eastern villages of 50 people and 5 western villages of 100 people, so N=750. A sample of n=100 is wanted.

Question. How would a stratified sample and a cluster sample be drawn?

Solution. Stratify by east and west, of sizes 250 and 500. The eastern share is 100\times250/750=33.3, so take a simple random sample of 33 eastern villagers and 67 western ones. That will almost certainly reach every village, which is fair and representative but means a lot of travel.

For a cluster sample, make each eastern village a cluster of 50, and split each western village into two clusters of 50, giving 15 clusters. Choosing 2 clusters at random and measuring everyone in them gives the 100 observations with at most two villages visited, but most of the variety between villages is never seen. A middle course chooses 4 clusters and takes a random half of each, 4\times25=100, at the cost of visiting up to four villages. Stratifying into east and west first and then clustering within each would guarantee both regions appear.

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Taught in Studies, data, and evidence, where the derivation and examples are.
All 6 questions on Studies, data, and evidence

Examples

Sampling ten villages

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