How does stratified sampling work? Guide & examples

Stratified sampling, or stratified random sampling, is a way researchers choose sample members. It’s based on a defined formula whenever there are defined subgroups, known as stratum/strata. 

This formula is:

Stratified random sampling = total sample size / entire population x population of stratum/strata

Stratified sampling is a common sampling method in research with subgroups (strata). Researchers use it when they need to understand a relationship between two strata.

In stratified sampling, researchers divide the population into homogeneous subgroups based on specific characteristics or attributes.

After creating the strata, researchers select a random sample from each stratum proportionate to its size or importance in the population. 

Step one: Define your sampling population and your strata. 

Step two: Put your sampling population in their stratum. 

Step three: Find your sampling size for that stratum. 

Step four: Take random samples from each stratum.

Examples of stratum subgroups for stratified sampling include:

• Gender

• Age

• Nationality

• Education level

• Any special subgrouping section participants are members of

Stratified sampling is the choice for probability sampling methods when the stratum members have different variable mean values.

To use stratified sampling as a research technique, you must be able to put every population member of your study into one subgrouping or stratum. Each subgroup should be mutually exclusive. 

If participants fit into multiple subgroups, don’t use stratified random sampling. 

When doing stratified random sampling, choose the characteristics that will divide up your subgroups or individual stratum. 

Since you can only place each study participant into one subgroup, your chosen classification must be precise and obvious. Grouping according to gender, age, or education is one way to ensure that members can only be in one subgroup. 

However, you can use multiple characteristics as a subgrouping if more than one needs to be part of the study. Just make sure your participants don’t fall into more than one. 

While you can only have participants in one subgroup, there are ways to stratify by multiple characteristics. To do this, you must multiply each characteristic by the number of strata. 

For example, if you're designating both age and gender, using three groups for gender and ten for age groups, you need to multiply them together, making 30 subgroups. 

This way, you designate your population sampling by age range and gender. 

An example would be males 10–19, females 30–39, or nonbinary 20–29.

Each age range would have a subset for the gender, so each participant will fulfil only one subgroup while the subgroup deals with two characteristics. Clever, huh?

Two forms of sampling exist inside stratified sampling: Proportional and disproportional. 

In proportionate sampling, the stratum sample size and the stratum's proportion to the population are equal. This means that a subgroup with a lesser percentage in the general population will have a lesser percentage in the sampling size.

For disproportionate sampling, the size of the strata sampling and the population representation is disproportionate. A researcher chooses this method when they want to highlight a minority or under-represented group. This keeps the subgroup's sample size from being too small to have a statistical conclusion.

Researchers can use certain strategies in stratified sampling to hone the project for mean and standard error and sample size allocation. This means the project or study is less fluid, rendering lower errors with a higher spectrum of the populace.

Mean and standard error

The difference between the sample mean and the population mean is the standard error of the mean or standard error. This lets the researcher know how much variance there would be if they redid the research study with new samples in that population. 

The standard error is inversely proportional to sample size, so there’s a smaller standard error with a larger sample size. The standard error of the mean is a part of inferential statistics and represents a dataset's standard deviation.

You can calculate confidence levels and test your hypothesis by using the standard error. A smaller standard error indicates that the sample mean or sample proportion is more precise and is more likely to be a good estimate of the true population mean or population proportion.

Sample size allocation

Sample size allocation is either proportionate or disproportionate. The population’s practicality, scale, and representative accuracy also determine this.

Proportionate allocation means that the sample size of the stratum is the same as the population size of the stratum. 

The equation nh = ( Nh / N ) * n applies to this sample size where:

• nh is the total size of the 'h' stratum sample

• Nh is the total size of the 'h' stratum population

• N is the total size of the population

• n is the total size of the sample

A sample size allocation calculator takes account of your parameters and lets you know how to allocate the population into your sample study.

The disproportionate sample size allocation means you must divide the population into exhaustive strata and disproportionately pick some aspects from that stratum. 

There are several advantages to using stratified random sampling as a research method. 

The main benefit is that the sample captures key characteristics of the population, much like a weighted average. With proportional sampling, the study results are proportional to the total population. 

Another benefit is that the study cost should be less because of the administrative ease of formed strata instead of varying and non-uniform subgroups. You lower the strata variability, resulting in more efficient estimates.

There are smaller estimation errors than in a simple random method and greater precision for the estimations. The bigger the strata differences, the more precise the study will be. 

When you divide the population into strata and take samples from each stratum, you drastically reduce the possibility of excluding a population group. This means you’re better representing a cross-section of the sample population.

Lastly, there can be survey execution efficiency with easier data collecting. When you’ve chosen the subgroups effectively, putting members into their groups is simple and precise. This creates a quicker turnaround for the study.

Like advantages, choosing a stratified random sampling method for a research project carries disadvantages. 

You can't use it in every situation because certain conditions must be in place. The biggest of these conditions is the subgrouping: No study member should be in more than one group. If you can classify a population member into more than one group, you can't use the stratified random sampling method.

Another disadvantage to this research method is that even with proper subgrouping, the population in that subgroup must be reasonably homogenous with the overall population. And if the subgroup members aren't incredibly similar, the sample study will not be useful to the researcher.

Lastly, the application of values to the strata needs to be accurate. You must ensure the groupings represent the population and the values of the strata are accurate. Without value accuracy, there can be bias in the results that lacks fairness to the overall population.

Stratified sampling is a research technique that fairly represents subgroups in a study’s sample population. It is an appropriate research method when predefined and exclusive subgroups are already available. 

An example would be age grouping, such as 10-19, 20-29, 30-39, etc. Using these subgroups, the researcher can collect data quicker and easier than other methods.

A variant of simple random sampling, stratified simple random sampling is where researchers randomly sample strata groups of the homogenous population. 

The results infer the qualities of the population by each stratum. Various factors, such as accuracy representation, practicality, and scale, will determine the sample size selected for random sampling.