# Stratified Sampling

Definition: The Stratified Sampling is a sampling technique wherein the population is sub-divided into homogeneous groups, called as ‘strata’, from which the samples are selected on a random basis.

The strata are formed on the basis of the member’s shared attributes and characteristics. These are mutually exclusive as every item of the population is assigned to a single stratum. The items should be selected from every stratum such that each element has the chance of being selected in a sample, with a probability close to 0.

The stratified sampling is used when the investigator wants to study or compare the specific subgroups within the population. In simple random sampling, the researcher is not sure that the subgroup which he wants to observe is represented by the sample selected or not.  Thus, there is more statistical precision in stratified sampling technique than the simple random sampling. This is also because the sampling error, i.e. the variability in the subgroups is smaller than that of the population.

### Types of Stratified Sampling

1. Proportionate Stratified Sampling: In this method, the elements from each stratum is selected in proportion to the size of the strata. Hence, there is a same sampling fraction between the strata.

For example, if the population is to be divided into five strata with respective sizes 10, 15, 20, 20, 35 percent of the population and the sample of 1000 is to be drawn, then the proportional sample will be obtained as follows:

Stratum-1: 1000 (0.10) = 100 items
Stratum-2: 1000 (0.15) = 150 items
Stratum-3: 1000 (0.20) = 200 items
|Stratum-4: 1000 (0.20) = 200 items
Startum-5: 1000 (0.35) = 350 items
On adding the items drawn from each stratum we get the total sample size as 1000.

This method is useful only when there are no significant variations between strata.

2. Disproportionate Stratified sampling: Under this sampling plan, there are different sampling fractions for different strata. These fractions are decided by the researcher on the basis of the pursued research objective.

Thus, the investigator can adopt either of the type of stratified sampling provided the sampling fractions allocated, in case of the disproportionate method, to each stratum is appropriate, otherwise, the stratum will either be over-representative or under-representative thereby yielding the skewed results.

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