# Stratified Random Sampling: Definition, Method and Examples

## Stratified Random Sampling: Definition

Stratified random sampling is a type of probability sampling using which a research organization can branch off the entire population into multiple non-overlapping, homogeneous groups (strata) and randomly choose final members from the various strata for research which reduces cost and improves efficiency. Members in each of these groups should be distinct so that every member of all groups get equal opportunity to be selected using simple probability. This sampling method is also called “random quota sampling”.

Age, socioeconomic divisions, nationality, religion, educational achievements and other such classifications fall under stratified random sampling.

Let’s consider a situation where a research team is seeking opinions about religion amongst various age groups. Instead of collecting feedback from 326,044,985 U.S citizens, random samples of around 10000 can be selected for research. These 10000 citizens can be divided into strata according to age,i.e, groups of 18-29, 30-39, 40-49, 50-59, and 60 and above. Each stratum will have distinct members and number of members.

### 8 Steps to select a stratified random sample:

1. Define the target audience.
2. Recognize the stratification variable or variables and figure out the number of strata to be used. These stratification variables should be in line with the objective of the research. Every additional information decides the stratification variables. For instance, if the objective of research to understand all the subgroups, the variables will be related to the subgroups and all the information regarding these subgroups will impact the variables. Ideally, no more than 4-6 stratification variables and no more than 6 strata should be used in a sample because an increase in stratification variables will increase the chances of some variables canceling out the impact of other variables.
3. Use an already existent sampling frame or create a frame that’s inclusive of all the information of the stratification variable for all the elements in the target audience.
4. Make changes after evaluating the sampling frame on the basis of lack of coverage, over-coverage, or grouping.
5. Considering the entire population, each stratum should be unique and should cover each and every member of the population. Within the stratum, the differences should be minimum whereas each stratum should be extremely different from one another. Each element of the population should belong to just one stratum.
6. Assign a random, unique number to each element.
7. Figure out the size of each stratum according to your requirement. The numerical distribution amongst all the elements in all the strata will determine the type of sampling to be implemented. It can either be proportional or disproportional stratified sampling.
8. The researcher can then select random elements from each stratum to form the sample. Minimum one element must be chosen from each stratum so that there’s representation from every stratum but if two elements from each stratum are selected, to easily calculate the error margins of the calculation of collected data.

### Types of Stratified Random Sampling:

• #### Proportionate Stratified Random Sampling:

In this approach, each stratum sample size is directly proportional to the population size of the entire population of strata. That means each strata sample has the same sampling fraction.

 Proportionate Stratified Random Sampling Formula: nh = ( Nh / N ) * n

nh= Sample size for hth stratum

Nh= Population size for hth stratum

N = Size of entire population

n = Size of entire sample

If you have 4 strata with 500, 1000, 1500, 2000 respective sizes and the research organization selects ½ as sampling fraction. A researcher has to then select 250, 500, 750, 1000 members from the respective stratum.

 Stratum A B C D Population Size 500 1000 1500 2000 Sampling Fraction 1/2 1/2 1/2 1/2 Final Sampling Size Results 250 500 750 1000

Irrespective of the sample size of the population, the sampling fraction will remain uniform across all the strata.

• #### Disproportionate Stratified Random Sampling:

Sampling fraction is the primary differentiating factor between the proportionate and disproportionate stratified random sampling. In disproportionate sampling, each stratum will have a different sampling fraction.

The success of this sampling method depends on the researcher’s precision at fraction allocation. If the allotted fractions aren’t accurate, the results may be biased due to the overrepresented or underrepresented strata.

 Stratum A B C D Population Size 500 1000 1500 2000 Sampling Fraction 1/2 1/3 1/4 1/5 Final Sampling Size Results 250 333 375 400

### Stratified Random Sampling Examples:

Researchers and statisticians use stratified random sampling to analyze relationships between two or more strata. As the stratified random sampling involves multiple layers or strata, it’s crucial to calculate the strata before calculating the sample value.

Following is a classic stratified random sampling example:

Let’s say, 100 (Nh) students of a school having 1000 (N) students were asked questions about their favorite subject. It’s a fact that the students of the 8th grade will have different subject preferences than the students of the 9th grade. For the survey to deliver precise results, the ideal manner is to divide each grade into various strata.

Here’s a table of the number of students in each grade:

 Grade Number of students (n) 5 150 6 250 7 300 8 200 9 100

#### Calculate the sample of each grade using the stratified random sampling formula:

 Stratified Sample (n5) = 100 / 1000 * 150 = 15 Stratified Sample (n6) = 100 / 1000 * 250 = 25 Stratified Sample (n7) = 100 / 1000 * 300 = 30 Stratified Sample (n8) = 100 / 1000 * 200 = 20 Stratified Sample (n9) = 100 / 1000 * 100 = 10

### Advantages of Stratified Random Sampling:

• Better accuracy in results in comparison to other probability sampling methods such as cluster sampling, simple random sampling, and systematic sampling or non-probability methods such as convenience sampling. This accuracy will be dependent on the distinction of various strata, i.e., results will be highly accurate if all the strata are extremely different.
• Convenient to train a team to stratify a sample due to the exactness of the nature of this sampling technique.
• Due to statistical accuracy of this method, smaller sample sizes can also retrieve highly useful results for a researcher.
• This sampling technique covers maximum population as the researchers have complete charge over the strata division.