# Stratified Random Sampling

This sampling procedure may be summarized as follows:

(1) The universe to be sampled is divided (or stratified) into groups that are that are mutually exclusive and include al items in the universe.
(2) As simple random sample is then chosen independently from each group of stratum.

The process of stratified random sampling differs from simple random sampling in that, with the latter sample items are chosen at random from the entire Universe. In stratified random sampling, the sample is designed so that a separate random sample is chosen from each stratum. In simple random sampling the distribution of the sample among strata is left entirely to chance.

An example of Stratified Random Sampling:

Suppose a researcher wishes to study retail sales of a product such as Wheaties in a universe of 100,000 grocery stores. The researchers might first subdivide this universe into three strata, based on store size, as illustrated below:

Store Size Stratum Numbers of Stores
% of stores

Large stores 20,000
20

Medium stores 30,000
30

Small Stores 50,000
50

Total 100,000
100

Then, by random sampling independently within each of the three strata, the researcher could guarantee to desired sample allocation of stores within each size group instead of leaving their representation to chance.

For instance, suppose it were desirable to have a total sample of 120 stores, split equally among the three size strata, that is, 40 stores from each stratum. With the stratification scheme shown, the researcher would simply choose 40 stores at random from each stratum. Without, stratification simple random sampling from the métier universe would be expected to yield about 24 large stores (20 percent of 120); about 36 medium stores (30 percent of 120); and about 60 small stores (50 percent of 120).

Reason for Stratified random sampling: There are two reasons for using stratified random sampling instead of simple random or other types of sampling. One reason is that marketers often want information about the components parts of the universe. Stratified random sampling is also used to increase the precision of sampling estimates.

Obtaining Information about parts of the Universe:

Researchers are often interested in obtaining data about the component strata making up a universe. For example, one might want to know the average Wheaties sales in ‘large’, ‘medium’, and ‘small’ stores. In such a case, separate sampling from within each of these strata would be called for. The results might then be used to plan different promotional activities for each store-size stratum.

Greater Precision through Stratification: Suppose a researcher wishes to estimate monthly Wheaties sales per store in the previously mentioned universe of 100,000 grocery stores.

A small random sample from this universe would tend to yield a sample mean with a large sampling error. The reason is the high store-to-store variation in Wheaties sales, occasioned by a few stores having much larger sales than the others. The presence or absence (by chance) in the sample of a few very large stores could impact significantly on the sample mean value obtained via simple random sampling.

Now suppose there were information that made it possible to subdivide this store universe into three strata, A,B,C, as indicated. A relatively small sample taken within each stratum would provide a good estimate of the mean of that stratum because of the similarity of the items included in that stratum The estimated means of these strata could then be weighted together so as to provide an estimate of the mean of the entire universe.

If, as in this instance, the variable being studied varies little among items in the same stratum, but a great deal among strata, this stratification procedure will ordinarily provide a better estimate of the mean than would be obtained by using simple random sampling. Under these circumstances, stratified random sampling will be more statistically efficient than simple random sampling. That is, stratified random sampling will provide greater precision (a smaller standard error of the mean) than a simple random sample of the same total size.