Stratified Sampling

What is Stratified Sampling?

Stratified sampling, also known as stratified random sampling or proportional random sampling, is a method of sampling that requires that all samples need to be grouped in accordance to some parameters, and choosing samples from each such group instead of taking randomly from the entire population. In this, the entire population is divided into various groups of similar attributes and amongst them, few samples are being chosen, whereas in the simple random sampling all the members of a population have a chance of being selected for sampling.

Stratified Sampling Formula

As the division of sub-groups or strata, and a total sample is taken to represent the entire population depends upon the researcher, there is no specific formula for Stratified Random Sampling. But, the formula mentioned below is used widely.

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For eg:
Source: Stratified Sampling (wallstreetmojo.com)

Types of Stratified Random Sampling

They are of two types – Proportionate and Disproportionate.

• Proportionate: The purpose of the stratified sampling is that from every group, few samples are being chosen for the final selection. In the proportionate sampling, the predetermined sample base is proportionate of all the groups created. For example, if 5 groups have been created of varied sample sizes such as 10, 30, 20, 100, 60, and 80. The researcher has decided to choose 10 % of the total population size, i.e., 300. In this case, 10 of each sample group would be chosen as total samples to be researched. So, the numbers would be 1,3,2,10,6, and 8 and the total would be 30 samples. This method is quite prevalent and famous for its application.
• Disproportionate: Here, we do not take proportionate samples from each sub-group and could choose any method to arrive at the pre-determined sample size. If we take the above-mentioned example, we could take any number from any group such as 5,5,5,4,3,8 to get a total sample size of 30 as we can clearly see that the samples chosen by various groups are disproportionate in relation to the respective sub-group size.

Examples of Stratified Random Sampling Formula(with Excel Template)

Example #1

Let’s assume a research team is doing a survey for an FMCG company about the taste and preferences of people in food choices. The team decided to take 3 major categories; men, women, and children. The total number of persons required for the data set is close to 1 million in numbers. How could Stratified Random Sampling help researchers in gathering the required data with the use of less time and resources?

 Solution

It is quite difficult to talk to one million people and take their opinion; rather, its quite easy and time-saving to create various groups, select a few amongst them, and take opinions from them as these data segregation would be representative of the entire population.
So, it’s better to segregate the entire data-set into three broad categories; Men, Women, and Children. Then take samples from these categories and frame an opinion on the responses received from the persons chosen under the said categories. Now, we can assume that the opinion received from the samples of different categories would be equal to the total population.

Thus, its application helps in saving resources, whether time or money.

Example #2

A research team is expecting to derive a sample of an organization about the retirement benefits taken by the employees. The entity employs 800 employees of diverse age groups, and the researchers planned to take a sample size of 10% or 80 persons from this organization. Find out the number of samples taken by each group or strata as per stratified random sampling.

 Solution

The following steps are required to arrive at stratified random sampling.

• First of all, we will segregate the entire population into a small group or strata. Here we have dissected the entire population of 800 employees in accordance with the age group they belong to. So, we have a table ready from the age group of 21 to 71.

Age Group	Population
21-30	150
31-40	200
41-50	250
51-60	120
61-70	80

• Now we will assign the number of employees belonging to that particular age group. So, we have posted numbers like 150, 200, 250, and so on.
• Then, find out the number of samples to be taken from the entire population. The question has already been mentioned to take up 10% or 80 samples from the total population.

Total Population & Total Sample Size

• Total Population = 800
• Total Sample Size = 80

Calculation of Sample Size

• =80/800*150

Sample Size will be –

• Sample Size = 15

The same procedure will be followed by the age group of 61 – 70.

The stratified sampling process has given us the number of samples from each sub-group or strata, which is reflective of the entire population.

Example #3

 A group of students has been given a project to find out the sample size of 1200 students studying in the different streams of majors. You need to find out the samples from each stratum or sub-group mentioned below by applying the stratified random sampling formula.

 Solution

Use the below-given data:

Student Majors	Population
English Major	200
Science Majors	260
Computer Science Majors	190
Engineering Majors	380
Math Majors	170

Calculation of Total Population

• = 200+260+190+380+170
• Total Population  =1200

Calculation of Sample Size

• =120/1200*200

Sample Size will be –

• Sample Size = 20

Similarly, we can calculate the sample size for the remaining population as shown below,

Relevance and Uses

• Auditor, generally Certified Public Accountant (CPA), use this formula at large for vouching and verification purposes in auditingPurposes In AuditingThe primary purpose of an audit is to conduct an independent and unbiased verification of all financial and non-financial material information to ensure that it is in line with what the management has reported.read more the company’s accounts. This formula fits well for their criteria as various groups or sub-groups are could be created on the basis of amounts involved, and the sample size also gets reduced.
• Portfolio managersPortfolio ManagersA Portfolio Manager is an executive responsible for making investment decisions & handle investment portfolios for fulfilling the client’s investment-related objectives. Also, he/she works towards maximizing the benefits & minimizing the potential risks for clients. read more widely apply the random stratified sampling to replicate various indexes such as the bond index or equity index to create a portfolio that provides a similar return in comparison to bonds.
• One of the greatest advantages of stratified random sampling is its capacity to select a sample of dissimilar characteristics by creating sub-groups and providing a sample from each stratum that is representative of the entire sample size. The formula becomes most useful when the features of the sub-groups tend to be diverse, and thus the answer varies a lot if general sampling is performed instead of or random stratified sampling.

Recommended Articles

This has been a guide to Stratified Sampling Formula. Here we discuss the formula for calculation of sample size along with practical examples and a downloadable excel sheet. You can learn more from the following articles –

• Sampling Distribution Definition
• Systematic Sampling
• Calculate Sampling Error
• Standard Error
• Mean Examples