Simple random sampling (SRS) is a probability sampling method where researchers randomly choose participants from a population. All population members have an equal probability of being selected. This method tends to produce representative, unbiased samples.

For example, if you randomly select 1000 people from a town with a population of 100,000 residents, each person has a 1000/100000 = 0.01 probability. That’s a simple calculation requiring no additional knowledge about the population’s composition. Hence, simple random sampling.

Simple random sampling helps ensure that the sample mirrors the population. The process proportionately samples from larger subpopulations more frequently than smaller subpopulations.

Suppose the town contains subpopulation A with 40,000 people and subpopulation B with 10,000. Using SRS with a probability of 0.01, the process will tend to enlist 400 from subpopulation A and 100 from B. Hence, the process tends to produce a proportionate representation in the sample that reflects the entire population. You don’t need to know the details about the subpopulations for this process to work!

## How to Use Simple Random Sampling

Performing simple random sampling requires that you have a complete list of all population members and the ability to contact and involve them in your study.

To perform simple random sampling, do the following:

- Define the population.
- Create a list of all population members.
- Assign random numbers to each member.
- Use a random number generator to select participants until you reach your target sample size.

Alternatively, if the population is not too large, you can use a lottery system for drawing the sample. Place all the names in a hat and randomly draw your sample. For large populations, researchers typically use computers to select participants randomly from a database.

## Example of Simple Random Sampling

Imagine we are studying the town with 100,000 residents. We want to perform simple random sampling to obtain a sample size of 1000. We first need to define the population. We’ll define it as residents of the town who pay township taxes and are at least 18 years old.

Next, we need to create a complete list of residents who meet those criteria. Perhaps we’ll work with the township tax office to make the list. We’ll add all eligible residents to our list.

Finally, we need to select participants randomly from the list. We can use a computer program to do that. Alternatively, we can print out names on slips of paper and draw them from a basket. We keep drawing from the list until we have 1000 names.

## Benefits of Simple Random Sampling

Many statisticians consider simple random sampling to be the gold standard for producing representative samples. Because it is entirely random, it minimizes the potential for researchers biasing the results, even if unintentionally. As you’ll read, there are alternative sampling methods that provide concessions to real-world sampling difficulties. Unfortunately, the alternatives can unwittingly produce a biased sample.

Procedurally, SRS is the simplest method for obtaining an unbiased sample. While the researchers need a list of the entire population, they don’t need other information about that population, its subpopulations, and its features.

Conversely, other more complex forms of sampling require researchers to understand the population’s characteristics. Then, using that knowledge and a lot of preplanning, they divide the population into strata or clusters and perform other procedures before sampling. With SRS, you just randomly draw from the list until you have enough subjects.

Because simple random sampling tends to produce unbiased samples that mirror the population, it’s excellent for analysts who need to use a sample to infer the properties of a population (i.e., inferential statistics). In a study, having a representative sample improves both its internal and external validity. After simple random sampling, you can use statistical hypothesis tests to use the sample to draw conclusions about the population.

For more information about inferential statistics, read my articles about Populations, Parameters, and Samples in Inferential Statistics and Descriptive versus Inferential Statistics.

## Drawbacks of Simple Random Sampling

Even though there are great benefits to using this method, simple random sampling has some significant drawbacks.

### Population List

First and foremost, this method can be quite cumbersome and require ample resources for large populations. You’ll need a list of all population members, which can be a tremendous hurdle by itself. If that list doesn’t exist, you might need to expend considerable resources to create it. An incomplete list can bias your results. Only a complete list allows the researchers to have an equal probability of selecting all population members.

### Logistics

Then you’ll need to contact and interact with everyone you randomly select. Depending on the nature of your study, that process can be pretty expensive and time-consuming if your participants span a wide geographic range, particularly when you need a large sample size.

### Insufficient Representation of Subpopulations

Despite being entirely random, simple random sampling can miss important subpopulations and features in the population. For example, in our town with 100,000 residents, imagine that we’re particularly interested in surveying those who are at least 90 years old. You plan to obtain a sample size of 1000, which is 1 out of 100 residents. However, there are only 50 people in town who are older than 90. Your sample might not include anyone in this vital group! If it does, it’ll be a tiny number that doesn’t provide a clear picture of this subgroup.

Simple random sampling can fail to provide precise data about particular subgroups and differences between subgroups. Other sampling methods can ensure sufficient numbers from small subgroups that produce a clear picture and increase the ability to compare subgroups.

## Simple Random Sampling vs. Other Methods

Because you need a list of the entire population, simple random sampling is most feasible when working with a relatively small population that is already defined. For example, if you’re surveying a company and can easily obtain a list of employees from Human Resources, SRS isn’t too difficult. Large populations can require extensive amounts of time and resources just to create the complete list. Simple random sampling is a great option when you don’t know much about your population other than its membership.

However, other sampling methods can be more efficient when creating the population list is difficult, your population is large and dispersed, or you need to guarantee sufficient data for specific subpopulations. Alternative methods can reduce the need for a complete list and reduce the logistical headaches of a geographically extensive study.

For example, a national opinion poll company might consider an alternative method to assess differences between subpopulations, such as gender, race, and age.

These other methods frequently require you to have a greater understanding of your population than SRS requires. Consider the following alternatives to simple random sampling that can also obtain representative samples:

- Systematic sampling: Uses a random starting point but then samples at a fixed interval. Does not require a complete population list.
- Stratified sampling: Divides the population into dissimilar strata. Ensures that the sample includes specific subpopulations and facilitates comparisons between them.
- Cluster sampling: Divides the population into clusters that mirror the entire population. Then you randomly select from a subset of clusters. Reduces the need for a complete list of the population and eases logistics issues.

For a contrast to representative sampling methods, learn about convenience sampling, which tends to produce biased samples.

## Reference

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

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