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# 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:

Imagine you would like to interview schools that 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

rev. 05-Aug-2019

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