Stratified Sampling

Sometimes subpopulations within your entire population vary considerably.  In this case, it is advantageous to divide your sample into subpopulations called "strata" and then perform simple random sampling within each stratum.  This is stratified sampling.

The primary advantage of stratified sampling over simple random sampling is it improves accuracy of estimation if you select a relevant stratification variable.

In general, the size of the sample in each stratum is taken in proportion to the size of the stratum.

Example:

If we use the same example demonstrated in simple random sampling, suppose each of the schools referenced contract with different vendors to bring food to their cafeteria. We would expect opinions about cafeteria food to vary widely from school to school.  Therefore, it makes sense to create school strata to sample from.  Suppose the schools are as follows:

School 1: 1050 students
School 2: 565 students
School 3: 1554 students
School 4: 306 students

Total students: 1050 + 565 + 1554 + 306 = 3475 students

The administrator wishes to take a sample of 150 students. 

Step 1:
The first step is to find the total number of students (3475 above) and calculate the percent of students in each stratum.

School 1:  1050 / 3475 = .30
School 2:  565 / 3475 = .16
School 3:  1554 / 3475 = .45
School 4:  306 / 3475 = .09

Step 2:
Next, to select a sample in proportion to the size of each stratum (in this case school), the following number of students should be randomly selected:

School 1:  150 x .30 = 45
School 2:  150 x .16 = 24
School 3:  150 x .45 ~ 67
School 4:  150 x .09 ~ 14

This tells us that our sample of 150 students should be comprised of:

• 45 students randomly selected from School 1
• 24 students randomly selected from School 2
• 67 students randomly selected from School 3
• 14 students randomly selected from School 4

For more information about simple random sampling, stratified sampling, or other sampling methods, please consult a sample design textbook.

 

Return to Probability Sampling

 

 

rev. 15-Jul-2006