# What is Stratified Random Sampling?

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Definition:

Stratified random sampling creates a sample of a population where the proportionality of the subgroups to the population is mirrored in the sample.

## 🤔 Understanding a stratified random sample

Stratified random sampling is a probability sampling technique that creates a sample with subgroups that reflect the proportional make-up of the overall population. A population can often be divided into strata (subgroups) according to specific features, such as grouping people into different age brackets. Individual subjects can then be randomly selected from each stratum to ensure that each stratum is represented in the sample in the same proportion that they exist in the original population. So, if 50% of your original population is 50-65 years old, then 50% of your sample will be as well. Stratified random sampling is used in a variety of fields, including marketing, science, statistics, and investing.

Example

Say a researcher wanted to track the performance of start-up companies and their founders. One thing to look at might be how these companies performed, based on the age, education level, nationality, or gender of the founders. To study this, the researcher would look at a stratified random sample, representing founders based on these characteristics in proportion to how many people in each group founded start-up companies in a given timeframe.

## Takeaway

Stratified random sampling is like a scale model...

A scale model of an airplane is a replica of the life-sized airplane in that the model maintains the precise physical relationships between its parts. On the model, the ratio of the wingspan to the body length is the same as a real airplane. The dimensions are proportional, even though it's tiny. A stratified random sample is a sample of a larger population that maintains the ratios of specific subgroups within the population.

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## What is stratified random sampling?

Sampling is a statistical technique that takes a representative sample size from a target population to study the characteristics of the overall population. Viewing a smaller sample of a population is more accessible than considering an entire population. There are many different sampling designs.

Stratified random sampling (aka proportionate stratified random sampling) is a type of probability sampling where you divide an entire population into different subgroups (strata). Then you randomly select individual subjects from within each subgroup (stratum) to create an accurate mini-sample that is proportional to the overall population.

Stratified random sampling is a sampling technique portfolio managers commonly use to create an investment portfolio that replicates a stock or bond index without having to buy all of the stocks or bonds in the index. A portfolio manager can select assets for an index-tracking portfolio so that it copies the structure of the index with fewer assets.

Indexes can be divided into subgroups using one or more characteristics, such as market capitalization or industry. A portfolio manager might use the market capitalization of the assets in an index to create a stratified sample. Each of the assets selected for the portfolio would be in proportion in market capitalization to those in the index.

## How does stratified random sampling work?

Stratified random sampling is a method of sampling that ensures the ratio of each subgroup (stratum) to the entire population size is the same as the ratio of its sample counterpart stratum to the sample population size.

First, you divide the population into strata based upon a particular characteristic. Then you randomly select individuals from each stratum relative to the percentage that each group exists in the total population.

Say we have a giant bag of 1,000 gummy bears of assorted flavors, and we want to divide the giant bag into 10 smaller bags of 100 gummy bears each, with each smaller bag containing the exact ratio of flavors that the giant bag has.

1. We count the number of orange, lemon, lime, and raspberry gummy bears, as shown in column 1.
2. We figure the ratio of each flavor to the total population, as shown in column 2.
3. We select gummy bears of each flavor for our smaller bag of 100 in the same ratio as the flavor in the giant bag of 1000, as shown in column 3.

In this example, we would randomly select 10 orange gummy bears from the original 100 possible choices to create that stratum of our sample. Then we would randomly select 20 lemon ones, and so on, to create our stratified random sample of 100 gummies.

## What is the difference between stratified random sampling and simple random sampling?

Simple random sampling is a sampling method where every member of the population has an equal chance of being selected. The population is not broken into subpopulations before the random sample is selected.

If you have 100 people in a population size and you want a random sample size of 10% of the population, you could put 100 names in a hat, pull out 10 names, and create a simple random sample of 10% of the population. A random sample is easier to create than a stratified random sample, but it may not tell you much about the characteristics of the population.

If you want a more precise representation of the overall population, you could use stratified random sampling instead. You could divide the population into subgroups by a similar attribute such as age, race, gender, income level, etc. This would give a sample that more accurately represents the characteristics of the overall population.

Say we want to study a population by its age. If the original population has 40% of under-25-years-olds, 50% of 25–70-years-olds, and 10% over-70-year-olds, we could pick four people who were under 25, five people who were over 25, and one person over 70. We would have a sample population of 10 people with age subgroups that accurately represent the ratio of age ranges in the target population of 100 people.

## What is the difference between stratified random sampling and cluster random sampling?

Cluster sampling randomly selects some groups out of a population. It may leave out other groups, and the groups it chooses may not accurately represent the whole population.

For example, suppose you wanted to survey a neighborhood’s residents about their political affiliations but didn't have a lot of time. You could divide the neighborhood into streets and randomly select a few of the streets (clusters) to perform your survey.

Compared to stratified random sampling, cluster sampling is not as precise and leaves room for error. It can leave out some clusters and can't replicate any specific diversity, such as income levels, in the neighborhood.

If you wanted to create a more accurate survey that accounted for income levels as an attribute, to compare whether the survey answers varied — relative to income level in that neighborhood — you would have to pick your samples differently, which would take more time.

Suppose the neighborhood you want to survey has eight different streets, and you were able to acquire data on the income levels of each of the households on each street. You may decide to divide each street into subgroups of income levels under \$50K per year and income levels of over \$50K.

You would then quantify how many households on each street fell into each of these two subgroups (under \$50K and over \$50K). Then you'd choose a random sampling from each street that represented the ratio of the households with incomes over and under \$50K.

## What is the difference between proportionate and disproportionate stratified random sampling?

Proportionate stratified random sampling (aka stratified random sampling) gives you a sample of the population that accurately portrays the correct ratio of subpopulations. The fraction of the whole population that each stratum represents is the same as the fraction it represents in the sample population.

Disproportionate stratified random sampling ignores the ratios of the subgroups represented in the population. The sample population contains different strata that do not represent the same ratio of the subgroups to the whole population. Disproportionate stratified random sampling can create skewed results that don't represent the actual population.

## What are the advantages and disadvantages of stratified random sampling?

Compared to simple random sampling (pulling a name out of a hat) and random cluster sampling (choosing some of the subgroups), stratified random sampling has some advantages and disadvantages.

Pros

• More accurate representation of a population
• More precise than simple random sampling
• Less time consuming than studying an entire population

Cons

• Requires defining characteristics to create subgroups
• Mathematically more complex than simple random or cluster sampling methods
• More time consuming than simple random or cluster sampling methods
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