Elementary Statstics

3.1.10.1 How to Select Stratified Random Sample?

Some of the issues involved in setting up stratified random sample are;

1. Base of Stratification

What characteristic should be used to subdivide the universe into different strata? As a general rule, strata are created on the basis of a variable known to be correlated with the variable of interest and for which information on each universe element is known. Strata should be constructed in a way which will minimize differences among sampling units within strata, and maximize difference among strata.

For example, if we are interested in studying the consumption pattern of the people of Delhi, the city of Delhi may be divided into various parts (such as zones or wards) and from each part a sample may be taken at random. Before deciding on stratification we must have knowledge of the traits of the population. Such knowledge may be based upon expert judgment, past data, preliminary observations from pilot studies, etc.

The purpose of stratification is to increase the efficiency of sampling by dividing a heterogeneous universe in such a way that (i) there is as great a homogeneity as possible within each stratum and (ii) a marked difference is possible between the strata.

2. Number of strata

How many strata should be constructed? The practical consideration limit the number of strata that is feasible, costs of adding more strata may soon outrun benefits. As a generalization more than six strata may be undersirable.

3. Sample size within strata

How many observations should be taken from each stratum? When deciding this question we can use either a proportional or a disproportional allocation. In proportional allocation, one samples each stratum in proportion to its relative weight. In disproportional allocation this is not the case. It may be pointed out that proportional allocation approach is simple and if all one knows about each stratum is the number of items in that stratum, the different strata are sampled at different rates. As a general rule when variability among observations within a stratum is high, one samples that stratum at a higher rate than for strata with less internal variation.