## What is Stratified Sampling?

Stratified sampling is a method of obtaining a representative sample from a population that researchers have divided into relatively similar subpopulations (strata). Researchers use stratified sampling to ensure specific subgroups are present in their sample. It also helps them obtain precise estimates of each group’s characteristics. Many surveys use this method to understand differences between subpopulations better. Stratified sampling is also known as stratified random sampling.

The stratified sampling process starts with researchers dividing a diverse population into relatively homogeneous groups called strata, the plural of stratum. Then, they draw a random sample from each group (stratum) and combine them to form their complete representative sample. Learn more about representative samples. When researchers use non-random selection to choose subjects from the strata, it is known as Quota Sampling.

Strata are subpopulations whose members are relatively similar to each other compared to the broader population. Researchers can create strata based on income, gender, and race, among many other possibilities. For example, if your research question requires you to compare outcomes between income levels, you might base the strata on income. All members of the population should be in only one stratum.

For background information about using samples to draw conclusions about populations, read my posts about Populations, Parameters, and Samples in Inferential Statistics and Descriptive versus Inferential Statistics.

Learn more about Types of Sampling Methods in Research.

## When to Use Stratified Sampling

Stratified sampling is beneficial in cases where the population has diverse subgroups, and researchers want to be sure that the sample includes all of them. Simple random sampling and systematic sampling might not adequately capture all these groups, particularly those that are relatively rare. Use this method when you suspect that the group means are different, and the goal of your study is to understand these differences.

Before using stratified sampling, you must divide the population into mutually exclusive groups that collectively capture all individuals in the population. These strata can be predefined census and demographic variables, such as gender, race, location, etc. And they can include strata that the researchers devise based on the needs of their study. Consequently, stratified samples place more burden on the researchers by requiring them to obtain all this information and assigning individuals into each category. In some cases, the necessary information might not be available.

Stratified sampling produces more precise group estimates by placing similar individuals into the groups. Consequently, you must understand the grouping scheme that increases the homogeneity of the groups relative to the entire population. The weighted averages of these groups have less variability than the regular mean from a simple random sample. In other words, this methodology can produce better group estimates in the right circumstances and when you have the necessary information.

## Advantages of Stratified Sampling

Many surveys use stratified sampling because it provides vital benefits.

### Precise Estimates for subgroups

When members of the subpopulations are relatively homogeneous relative to the entire population, stratified sampling can produce more precise estimates of those subgroups than simple random sampling. In this case, the strata have lower standard deviations than the entire population. The strata are the subpopulations in the study.

This increased precision for the strata can be crucial when a study needs to assess group characteristics. Additionally, the precision gives your analyses greater statistical power for detecting differences between groups. For example, a standardized testing company might want to evaluate how testing scores vary by household income or geographic region, such as urban versus rural.

**Related post**: Sample Statistics are Always Wrong (to Some Extent)!

### Efficiency in Conducting the Survey

Stratified sampling can reduce survey costs and simplify data collection. In many cases, dividing the entire population into strata provides benefits to the survey administrators. Studies can become less expensive and more practical when the researchers divide a large population into smaller groups containing similar members. These benefits occur when specific skills, expertise, or personnel can more efficiently sample a particular stratum. For example, you might use different people to survey rural versus urban areas.

### Ensures Representation of all Groups of Interest

By explicitly incorporating the strata into the sampling methodology, you ensure that the sample represents all groups. When you have smaller groups in your study, simple random sampling can miss some of them by chance. Stratified sampling helps retain the complete variety of the population in the sample.

In contrast, convenience sampling does not tend to produce representative samples. These samples are easier to gather but the results are minimally useful.

## Disadvantages of Stratified Sampling

Stratified sampling imposes several significant burdens on the researchers.

First, they must devise a scheme for their strata so that every member of the population fits into one, and only one, stratum. These strata must collectively contain all members of the population.

Second, the researchers must then have sufficient information to assign subjects to the correct strata.

Unfortunately, that can involve a lot of planning and information gathering!

Additionally, stratified sampling produces benefits only when the researchers can form subgroups that are relatively homogeneous relative to the entire population. If researchers cannot create appropriate strata or the members of a stratum are not reasonably similar, the stratified sample will be ineffective.

Finally, the feasibility of performing stratified sampling depends on your strata to some degree. Some groups are easy to identify and assign members, such a gender, graduation status, etc. However, other strata can be more complex, such as ethnicity and religion.

## Example of Stratified Sampling

Stratified sampling involves multiple steps. First, break down the population into strata. From each stratum, use simple random sampling to draw a sample. This process ensures that you obtain observations for all strata.

For example, imagine we’re assessing standardized testing and our research requires us to compare test scores by income. We can use income levels for our strata. Students from households with similar incomes should be relatively similar compared to the overall state population.

While we want a random sample for unbiased estimates overall, we also want to obtain precise estimates for each income level in our population. Using simple random sampling, income levels with a small number of students and random chance could conspire to provide small sample sizes for some income levels. These smaller sample sizes produce relatively imprecise estimates for them.

To avoid this problem, we’ll use stratified sampling. Our sampling plan might dictate that we select 100 students from each income level using simple random sampling. Of course, this plan presupposes that we know the household income level for each student, which might be problematic.

The benefit of stratified sampling is that you obtain reasonably precise estimates for all subgroups related to your research question. The drawback is that analyzing these datasets is more complicated. When you use stratified random sampling, you can’t simply take the overall sample average and use it for the general population because you know that the smaller strata are overrepresented. You need to use a weighted average technique.

## Proportionate vs. Disproportionate Stratified Sampling

When using stratified sampling, you’ll need to decide whether your strata will be proportionate or disproportionate. Here are the pros and cons of both techniques. Match your research goals to the correct method.

### Proportionate sampling

In proportionate stratified sampling, the sample size of each stratum is proportional to its share in the population. For example, if the rural subgroup comprises 40 percent of the population you’re studying, your sampling process will ensure it makes up 40% of the sample.

Use proportionate sampling when you want to ensure that the sample represents all groups of interest and you’re focusing on obtaining a good estimate for the overall population.

Groups with lower representation will also have smaller numbers in a proportionate sample. In turn, these smaller sample sizes will produce less precise sample estimates. Consequently, proportionate stratified sampling yields less precise estimates of smaller groups than disproportionate sampling, but it gives better overall population estimates.

To calculate the sample size for each stratum, take its population share and multiply that by the total sample size for your study. For example, if the rural group is 40% of the overall population and your full sample size will be 200, you need 0.40 X 200 = 80 rural observations.

### Disproportionate sampling

Disproportionate stratified sampling does not retain the proportions of the strata in the population. Use this method when you need to obtain precise estimates of each group and the differences between them. However, it sacrifices some precision in the estimate of the whole population.

This process is an excellent choice when you need to study underrepresented groups in a population. In a proportionate sample, you’re likely to have too few observations to draw meaningful conclusions about these smaller groups. A disproportionate sample ensures that you have an adequate number for analyzing even the smallest groups in a population.

Using this method, the researchers can evenly divide the total sample size between the subgroups or use different proportions that make sense for their study.

Alternatively, they can use a disproportionate stratified sampling approach that adjusts the size of the strata by the variability within the strata. The researchers will collect more samples from the strata with greater variability to reduce sampling error. This method requires knowledge during the planning stages about the variability in each stratum.

### Example of Proportionate vs. Disproportionate Stratified Sampling

Suppose researchers want to assess opinions and see how they differ by generation. The relative frequency table below shows the population share of each generation. In choosing their stratified sampling method, the critical question they need to consider is whether they are focusing on the estimate for the entire population or the subgroups.

Generation (US) |
Percentage |
Proportionate |
Disproportionate |

Pre-Boomer | 7.6% | 228 | 500 |

Baby Boomers (1946 – 1964) | 21.8% | 654 | 500 |

Generation X (1965 – 1980) | 19.9% | 597 | 500 |

Millennials (1981 – 1996) | 22.0% | 660 | 500 |

Generation Z (1997 – 2012) | 20.3% | 609 | 500 |

Post Generation Z | 8.4% | 252 | 500 |

Total |
3000 | 3000 |

Generation data from Brookings

If their goal is to produce the most precise estimate for the overall population while ensuring that they include all generations in the sample, they should use proportionate stratified sampling. This method ensures that the sample will adequately represent even the Pre-Boomers with a share of only 7.6%. The table displays the sizes of proportionate groups if the researchers have a budget for 3000 surveys (Stratum population share * total sample size = stratum sample size).

However, if their goal is to really understand each group’s mean response and the differences between them with the most precision, they should use a disproportionate stratified sample. However, the estimate for the entire population will be less precise than the proportionate sample. The table displays a disproportionate approach that divides the sample size evenly between the generations.

Cluster sampling is another method that divides a population into subgroups to obtain a representative sample. However, its goals and methods are strikingly different. For more information, read my article about Cluster Sampling.

## Reference

Sampling in Developmental Science: Situations, Shortcomings, Solutions, and Standards (nih.gov)

Runesu says

Quite understandable. Life made simple

SARTYAKI MANNA says

why disproportionate stratified sample is used to estimate each group’s mean response and the differences between them with the most precision?

Jim Frost says

Hi Sartyaki,

This is true based on how hypothesis tests work. Suppose you are testing the mean difference between two groups. The test is most efficient (has the most power) when the two groups have the same sample size. For example, if you have n = 200, then the test is most powerful when you have 100 in one group and 100 in the other group. They don’t have to be equal, but you’ll get the most precise estimate of the difference when they’re equal. Unequal group sizes are valid, but it reduces the power of the test and lessens the precision of the estimate (wider CI).

So, that comes into play when you’re drawing a sample from a population. For simplicity, imagine that we have two strata in our sample. One strata accounts for 90% of the population while the other strata covers the remaining 10%. Now, if we wanted a total n = 200 and we draw a proportionate sample, given the proportions of the strata in the population, we’d end up with 180 for one strata and 20 for the other. We can estimate the difference between the means, but because the sample sizes are fairly unequal, we’ll be fairly far from the most precise estimate possible. The CI will be wider.

However, if we devise a disproportionate stratified sampling design so that we end up with 100 for strata 1 and 100 for strata 2, we now can obtain the most precise estimate possible give our n = 200.

I hope that helps explain it!