# Stratified Random Sample: Example & Definition

Lesson Transcript
Instructor
Yolanda Williams

Yolanda has taught college Psychology and Ethics, and has a doctorate of philosophy in counselor education and supervision.

Expert Contributor
Kathryn Boddie

Kathryn has taught high school or university mathematics for over 10 years. She has a Ph.D. in Applied Mathematics from the University of Wisconsin-Milwaukee, an M.S. in Mathematics from Florida State University, and a B.S. in Mathematics from the University of Wisconsin-Madison.

Researchers often use samples in their research and they can select a sample using a variety of methods. Learn about the stratified random sample by reviewing its definition and examples. Explore the process to produce a stratified random sample and understand this type of sample's advantages and disadvantages. Updated: 08/30/2021

## What is a Stratified Random Sample?

A stratified random sample is a population sample that requires the population to be divided into smaller groups, called 'strata'. Random samples can be taken from each stratum, or group.

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## Example of a Stratified Random Sample

Suppose that you were a researcher interested in studying the income of American college graduates one year after graduation. The population that you are interested in is American college graduates. A population consists of all members of a defined group who possess specific characteristics that you are interested in studying.

You find out that each year there are over 1,750,000 people graduating from college, which means that your population size is almost two million! It's impossible for your research team to collect data from every member of your population, so you decide to collect data from a sample, which is a subset of the population that is used to represent the whole population. You and your research team decide that you want to take a sample of 3,000 American college graduates.

How do you choose your sample? You could choose a random sample, in which each member of the population has the same chances of being selected for the sample.

Assume you chose a random sample of 3,000 college grads. You look at the demographics of your sample participants and find that 2,034 are Caucasian, 832 are African-American, and 134 are Asian-American. You start to wonder if there are any differences in income one year after graduation between the different racial subgroups. You also wonder if the demographics of your sample are truly representative of the demographics of American college graduates. One way of examining these questions is by using a stratified random sample.

Suppose that instead of conducting a random sample, you decide to use a stratified random sample. You look up the demographics of American college graduates and find that 51% of American college graduates are Caucasian, 22% are African-American, 9% are Asian, 8% are Native American, 5% are Hispanic, 3% are Pacific Islander, and 2% are multiracial. You divide your population into strata based off the participant's racial demographics. Here you have seven strata, one for each of the seven racial categories. Using this information, you can conduct either a proportional stratified sample or a disproportional stratified sample.

In a proportional stratified sample, the size of each stratum in the sample is proportionate to the size of the stratum in the population. In a disproportional stratified sample, the size of each stratum is not proportional to its size in the population.

Let's assume that you have decided to conduct a proportional stratified sample. Your next step is to ensure that the proportion of the strata in the population is the same as the proportion in the sample. This means that 51% of your sample needs to be Caucasian (since 51% of the population is Caucasian), 22% should be African-American, 9% Asian, 8% Native American, 5% Hispanic, 3% Pacific Islander, and 2% multiracial. By calculating the proportions, you determine that the racial demographics of your 3,000 study participants should include:

• (3,000 x 0.51) = 1,530 Caucasians
• (3,000 x 0.22) = 660 African-Americans
• (3,000 x 0.09) = 270 Asians
• (3,000 x 0.08) = 240 Native Americans
• (3,000 x 0.05) = 150 Hispanics
• (3,000 x 0.03) = 90 Pacific Islanders
• (3,000 x 0.02) = 60 multiracial

You can see that the demographics of the stratified random sample are very different than those of the random sample.

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## Using a Stratified Random Sample with Different Strata

Suppose that, just as in the lesson, you wish to study the income of American college graduates one year after graduation. The demographics are as follows: 51% of American college graduates are Caucasian, 22% are African-American, 9% are Asian, 8% are Native American, 5% are Hispanic, 3% are Pacific Islander, and 2% are multiracial. Suppose also that in looking up the demographics, you find that 52% of American college graduates are female and 48% are male and the racial distribution across the genders is equal to the racial distribution overall (so 9% of the females are Asian and 9% of the males are Asian, etc). In each example below, state how many individuals should be selected in each strata if you want to survey a total of 5000 college graduates.

## Examples

• strata defined by race/nationality
• strata defined by gender
• strata defined by both gender and race/nationality

## Solutions

• We would want the demographics of our sample of 5000 graduates to match the demographics of the overall population of graduates. So, we would need (5000 x 0.51) = 2550 Caucasians, (5000 x 0.22) = 1100 African-Americans, (5000 x 0.09) = 450 Asians, (5000 x 0.08) = 400 Native Americans, (5000 x 0.05) = 250 Hispanics, (5000 x 0.03) = 150 Pacific Islanders, and (5000 x 0.02) = 100 multiracial.
• We want the gender representation in our sample to match the gender distribution of the overall population of graduates. So, we would need (5000 x 0.52) = 2600 female graduates and (5000 x 0.48) = 2400 male graduates.
• We want both the racial and gender demographics of our sample to match that of the overall population of graduates. From the second example, we know we want 2600 females and 2400 males. For the females, we want (2600 x 0.51) = 1326 female Caucasians, (2600 x 0.22) = 572 female African-Americans, (2600 x 0.09) = 234 female Asians, (2600 x 0.08) = 208 female Native Americans, (2600 x 0.05) = 130 female Hispanics, (2600 x 0.03) = 78 female Pacific Islanders and (2600 x 0.02) = 52 females who are multiracial. For the males, we want (2400 x 0.51) = 1224 male Caucasians, (2400 x 0.22) = 528 male African-Americans, (2400 x 0.09) = 216 male Asians, (2400 x 0.08) = 192 male Native Americans, (2400 x 0.05) = 120 male Hispanics, (2400 x 0.03) = 72 male Pacific Islanders and (2400 x 0.02) = 48 males who are multiracial.

## Discussion

In your examination of the income of college graduates a year after graduation, you want to see the effects of gender and race on income. Which strata above would you choose to give the most accurate representation?

## Guide to Discusssion

The best strata to choose would likely be the third option - dividing by both gender and race - so that comparisons can be made based on gender, race, or both.

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