To use stratified sampling, we divide the population into relatively homogeneous groups, called strata. Then we use one of two approaches. Either we select at random from each stratum a specified number of elements corresponding to the proportion of that stratum in the population as whole or we draw an equal number of elements from each stratum and give weight to the results according to the stratum’s proportion of total population. With either approach, stratified sampling guarantees that every element in the population has a chance of being selected.
Stratified sampling is appropriate when the population is already divided into groups of different sizes and we wish to acknowledge this fact. Suppose that a physician’s patients are divided into four groups according to age.
Age group
|
Percentage of total
|
Birth—19 years
|
30
|
20—39
|
40
|
40—59
|
20
|
60 years and older
|
10
|
The physician wants to find out how many hours his patients sleep. To obtain an estimate of this characteristic of the population, he could take a random sample from each of the four age groups and give weight to the sample according to the percentage of patients in that group. This would be an example of a stratified sample.
Cluster Sampling
In cluster sampling, we divide the population into groups, or clusters, and then select a random sample of these clusters. We assume that these individual clusters are representative of the population as a whole. If a market research team is attempting to determine by sampling the average number of television sets per household in a large city, they could use a city map to divide the territory into blocks and then choose a certain number of blocks (clusters) for interviewing. Every household in each of these blocks would be interviewed. A well-designed cluster sampling procedure can produce a more precise sample at considerable less cost than of simple random sampling.
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