# Stratified Random Sampling

Stratified Random Sampling is a probabilistic sampling technique. It is also known as Stratified sampling

It is employed when the population has identifiable strata (singular: stratum) or layers/ groups.

Example: A class having both boys and girls has two strata: one of the boys, and the other of the girls.

Please note that the strata should be independent and mutually exclusive. That is, members of one stratum should belong only to that stratum- they should not be members of another stratum at the same time.

Requirements:

1. The population should have distinct, identifiable strata.

2. The relative proportions of each stratum in the population must be known.

3. The sum of all strata should equal the population size/ total. (Which implies that the strata should be independent and mutually exclusive)

4. The strata should not be too thin (only a few members), or too many (some say the number should not exceed 6).

5. The required sample size should be known.

6. The size of the population should be known.

Procedure (Example):

Let’s assume that we require a sample of 50 students from a co-ed class (having both boys and girls) of 200 students. It turns out that there are 120 girls and 80 boys in that class.

The relative proportions of boys and girls, therefore, are:

Girls: 120/ 200 = 0.60 (or 60%);

Boys: 80/ 200 = 0.40 (or 40%).

In order to be representative, the sample must consist of 60% girls and 40% boys.

So, exactly how many girls and boys do we need to have in the sample?

Let’s apply the relative proportions of boys and girls to the sample size to find out:

50 x 0.60 = 30 Girls { 50 is the sample size; 0.60 is the relative proportion of girls in the class}

and 50 x 0.40 = 20 Boys {50 is the sample size; 0.40 is the relative proportion of boys in the class}.

The big question now is: “How does one select 30 girls and 20 boys from the class?”

The simple answer is, “By using any one of the (other) probabilistic sampling methods (simple random sampling/ systematic random sampling) we have discussed so far.”

An alternate method to arrive at the same numbers is given in Wikipedia.

Here, instead of calculating the relative proportions, we simply use the following formula:

Number required from Stratum = Size of stratum x (Sample size/ Total Population)

Applying it to our example, we get:

Number of Boys required = 80 x (50/ 200)    = 20;

Number of girls required = 120 x (50/ 200)   = 30

This technique is useful when the population has distinct, independent sections (strata).

One needs to know many details about the population in advance, some (or many) of which may not be easily available.

This technique is not suitable when there are numerous strata, especially if some are very large; and some very small (the resultant sample will not be “representative”).

Summary:

Stratified Random Sampling is a Probabilistic sampling technique.

It is suitable for sampling populations having discrete, independent strata.

After obtaining the relative proportions of the strata, the actual sampling is performed using Simple random sampling or Systematic random sampling.

It is not suitable when the population has numerous strata of extreme sizes, or their relative proportions are unknown.