# How stratified random sampling works, with examples (2023)

## What is stratified random sampling?

Stratified random sampling is a sampling method that divides a population into smaller subgroups called strata. In stratified random sampling, or stratification, strata are formed based on common attributes or characteristics of members, such as: B. Income or level of education. Stratified random sampling has numerous applications and benefits, such as: B. the study of population demography andLife expectancy.

Stratified random sampling is also known as proportional sampling or quota sampling.

### The central theses

• Stratified random sampling allows researchers to obtain a sample population that best represents the entire population studied.
• Sampling is a statistical inference made using a subset of a population.
• In stratified random sampling, the entire population is divided into homogeneous groups, called strata.
• Proportional stratified random sampling draws samples from groups stratified with respect to the population. With disproportionate sampling, the strata are not proportional to the occurrence of the population.
• Stratified random sampling differs from simple random sampling, which involves the random selection of data from an entire population so that each possible sample occurs with the same probability.

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## This is how stratified random sampling works

When conducting analysis or research on a group of entities with similar characteristics, a researcher may discover that thepopulationit is too big to complete the investigation about it. To save time and money, an analyst can take a more practical approach by selecting a small group of the population. The small group is denoted as asample size, which is a subset of the population that is used to represent the entire population. A sample can be selected from a population in several ways, one of which is the stratified random sampling method.

(Video) Sampling 03: Stratified Random Sampling

Stratified random sampling divides the entire population into homogeneous groups called strata (plural of stratum). Random samples are then taken from each layer.For example, imagine an academic researcher who wants to know how many MBA students were offered a job in 2021 within three months of graduation.

The researcher will soon discover that there were about 200,000 MBA graduates that year. He may decide to take a random sample of 50,000 graduates and conduct a survey. Even better, they could classify the population into strata and draw a random sample from the strata. To do this, they would create population groups based on gender, age group, race, country of nationality, and work experience. A random sample is drawn from each stratum in a number proportional to the size of the stratum in relation to the population. These strata subsets are then combined into a random sample.

Stratified sampling is used to highlight differences between groups in a population, as opposed to simple random sampling, which treats all members of a population as equals with the same probability of being sampled.

## Example of a stratified random sample

Suppose a research team wants to determine the grade point average (GPA) of college students in the United States. The research team struggles to collect data from all 21 million college students; You decide to draw a random sample from the population using 4000 students.

Now suppose the team looks at the different characteristics of the sample participants and asks if there are differences in the averages and majors of the students. Suppose you find that 560 students are majoring in English, 1,135 are majoring in science, 800 are majoring in computer science, 1,090 are majoring in engineering, and 415 are majoring in mathematics. The team wants to use a proportionally stratified random sample, where the stratification of the sample is proportional to the random sample in the population.

Suppose the team searches for thedemographic dataof college students in the US and find the percentage of what students study: 12% English, 28% Science, 24% Computer Science, 21% Engineering, and 15% Mathematics. Thus five strata are formed from the stratified random sample.

The team must then confirm that the population class is proportional to the sample class; However, you notice that the proportions are not the same. The team must then retest 4,000 students from the general population, randomly selecting 480 English, 1,120 science, 960 computer science, 840 engineering, and 600 math students.

With these groups, you have a proportionally stratified random sample of college students, providing a better representation of US college degrees. Researchers can then select specific strata, look at different types of studies conducted by US college students and look at different GPAs.

## Simple x Stratified Random Sampling

simple random samplesand stratified samples are statistical measures. A simple random sample is used to represent the entire data population.A stratified random sample divides the population into smaller groups, or strata, based on common characteristics. However, stratified sampling is more complicated, time-consuming, and potentially more expensive to perform than simplified random sampling.

(Video) Stratified Random Sampling

Simple random sampling is generally used when there is too little information available about the data population, when the data population has too many differences to separate it into different subsets, or when there is only one characteristic in the data population.

For example, a candy company might want to study the buying habits of its customers to determine the future of its product line. If there are 10,000 customers, you can select 100 of those customers as a random sample. You can then apply what you find from those 100 customers to the rest of your base.Unlike the stratification, 100 members are sampled purely at random, without taking into account their individual characteristics.

## Proportional and disproportionate stratification

Stratified random sampling ensures that each subgroup of a given population is adequately represented in the overall population sample of a research study. Stratification can be proportional or disproportionate. In a proportionally stratified method, the sample size of each stratum is proportional to the population size of the stratum. This type of stratified random sampling is generally a more accurate metric because it better represents the general population.

For example, if the researcher wants a sample of 50,000 graduates by age group, the proportional stratified random sample is obtained using this formula: (sample size/population size) × stratum size. The following table assumes a population size of 180,000 MBA graduates per year.

Article sources

Investopedia requires authors to use primary sources to support their work. This includes white papers, government data, original reports, and interviews with industry experts. If necessary, we also refer to original research from other well-known publishers. Visit our to learn more about the standards we follow to create accurate and unbiased content.editorial policy.

1. University of Arizona, College of Agriculture and Life Sciences. "Chapter 4: Stratified Random Sample," Page 1.

(Video) Stratified Sampling

2. Yale University, Department of Statistics and Data Science. "sampling.“

3. Just psychology. "This is how stratified random sampling works.“

## FAQs

### How stratified random sampling works, with examples? ›

But the most common type is probably proportional stratified random sampling, where a population divides into strata, and then the random sample is taken from each stratum in proportion to its size. For example, if the entire population is 60% female and 40% male, then the sample would be 60% female and 40% male.

What is stratified random sampling with example? ›

But the most common type is probably proportional stratified random sampling, where a population divides into strata, and then the random sample is taken from each stratum in proportion to its size. For example, if the entire population is 60% female and 40% male, then the sample would be 60% female and 40% male.

How does stratified random sampling work? ›

Stratified sampling is a method of random sampling where researchers first divide a population into smaller subgroups, or strata, based on shared characteristics of the members and then randomly select among these groups to form the final sample.

How do you solve stratified random sampling examples? ›

For example, if the researcher wanted a sample of 50,000 graduates using age range, the proportionate stratified random sample will be obtained using this formula: (sample size/population size) × stratum size. The table below assumes a population size of 180,000 MBA graduates per year.

How is a simple random sample different from a stratified random sample example? ›

A simple random sample is used to represent the entire data population and randomly selects individuals from the population without any other consideration. A stratified random sample, on the other hand, first divides the population into smaller groups, or strata, based on shared characteristics.

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