Guide to systematic sampling

It's often impractical to conduct a study on a large population due to the cost involved, lack of time, or other resource or population issues. To enable the research to happen and to draw conclusions, researchers can survey a population sample. One method they can use to do this is called systematic sampling.

For the correct type of population, this is a simple and effective way to get a representative sample of a population.

In statistical analysis, researchers can use various methods to select samples. One of these methods is systematic sampling, which entails choosing every nth item after a random start. This approach results in a systematic selection of elements since each subsequent item is picked at a regular and predetermined interval.

Systematic sampling is particularly advantageous when the sample population is large and well-organized.

Systematic vs. standard sampling

Standard sampling is also known as simple random sampling. This method is entirely random, with each person in the sample population having an equal chance of being selected. Systematic sampling provides a simpler way of generating a representative sample from an evenly distributed population.

Systematic vs. stratified sampling

When the data is heterogeneous, stratified sampling can help to organize it better. Stratified sampling involves dividing the population into distinct subgroups or strata based on certain characteristics important to the study. 

If a school, for example, wants to measure the performance of all grades, it might first break the students up by grade level and then gather samples from each grade to represent the whole school. Systematic sampling may lead to the overrepresentation of one grade compared to others.

These two methods aren't mutually exclusive. The students could be stratified by grade and then systematically sampled from each grade.

Systematic vs. cluster sampling

Cluster sampling involves dividing the population into groups and selecting the entire groups to be part of the sample. These groups should be representative of the entire population. For instance, a school might choose to select specific classes from a particular grade to assess the academic performance of that grade. This differs from systematic sampling, where students would be picked individually. 

Similarly, the methods can be combined. The population can be clustered, and then the clusters can be chosen systematically.

Systematic sampling uses several methods. The first thing to understand is the difference between linear and circular sampling, as their difference impacts the other choices you make in the sampling process.

Linear systematic sampling

This type of sampling treats the population as a line, selecting every fixed nth interval sample until the end is reached and then stopping.

Circular systematic sampling

This type of sampling treats the population like a circle. Once it reaches the end, it loops back around and selects every nth sample until the desired number of samples is reached. This type of sampling is also known as radial systematic sampling or equidistant angular sampling.

The most basic type of systematic sampling involves selecting a value for n, randomly selecting from the first n items, and then selecting every nth item afterward. For example, let's say n is 10. A random number between 1 and 10 will be chosen. If the number turns out to be 8, the 8th item would be the first sample, then the 18th, 28th, 38th, and so on.

When using circular systematic sampling, the first sample doesn't need to come from the first n samples. For example, given a population of 5,000, you can choose the first sample randomly from anywhere in that range. If the random number is 4,995, the 4,995th item would be the first sample. 

Because circular sampling is used, moving 10 forward would loop around to the 5th item. Next would come the 15th, 25th, and so on.

If the data allows for it, you can modify the above methods of systematic sampling by shuffling the data before beginning the sampling process. Depending on how you arrange the data, this method might produce a more representative sample of the population and remove any bias in the default ordering.

Systematic sampling is a useful method in several situations. Researchers find its simplicity especially useful when they need to sample from a large population with high sampling costs. This simplicity also makes it an ideal choice when researchers must perform the sampling task quickly.

To help you better understand when you should and shouldn’t use systematic sampling, we've assembled a set of pros and cons for the method.

Advantages of using systematic sampling

Efficient

Systematic sampling requires less time and resources to obtain a sample than many other methods. This allows researchers to get the samples they need in a cost-effective way and under greater time constraints than might otherwise be possible.

Less variability

Systematic sampling often results in less variability than other sampling methods. When the data are relatively homogeneous, the nature of the sampling ensures an even representation of the population.

Easy to implement

Systematic sampling is easy to use and doesn't require specialized knowledge or software or a complete list of the population to be surveyed. This increases accessibility to the method and can reduce the chance of error.

Disadvantages of using systematic sampling

Biased samples

There are several instances where systematic sampling won't provide a representative sample of the population. If the data is periodic in nature, the sampling interval may align with that period, leave some important items out, and introduce bias to your results. Similarly, a sample interval that's too large could also skip over important data.

Limited flexibility

Systematic sampling can be less flexible than other sampling methods. It relies heavily on a homogeneous and evenly distributed population, which may be an issue with populations with underlying patterns or characteristics. To achieve more precise control over sample selection, researchers should employ other methods.

Sampling frame

Systematic sampling relies on a sampling frame, which may not always be available or complete. The sampling frame lists all people or items available for sampling. For certain research types, this is impractical.

In the examples given so far, we've given you the basics of creating a systematic sample. Let's now take a more detailed look at how the process works. 

You can break down the development of the sample into five steps, including:

1. Define the population

Decide what type of population will best meet the needs of your research question.

2. Determine the sample size

Then, determine the desired sample size. You should pick a sample size that's large enough to provide a representative population sample but not so large as to become cost-prohibitive or otherwise impractical. 

You can calculate the ideal sample size from the required level of precision and confidence interval. 

3. Define the sampling interval

With the sample size determined, it's time to calculate the sampling interval. This is the value of n in the examples we've given previously.

For linear sampling, this number is a function of the sample size and the population size. To calculate it, divide the total population size by the sample size. For example, a population size of 1,000 and a sample size of 100 would give a sampling interval of 10. Because it loops around, circular sampling allows you to choose a larger interval if you'd like.

4. Select the first unit at random

Next, select the first unit in the sample at random. You can use several of the methods we mentioned to accomplish this. The method you choose will depend on personal preference and the structure of the data. When choosing a method, consider how bias may impact the selection and try to account for it.

5. Select subsequent units

After selecting the first unit, select the remaining units in the sample systematically by selecting every nth unit in the population, where n is the sampling interval. For example, if the sampling interval is 15, the first item would be 15, and subsequent items would be 30, 45, 60, etc. 

When using linear sampling, you stop when you reach the end of the data. For circular sampling, loop around and continue until you get the required number of samples. 

Let's close out by looking at some examples of how systematic sampling might be used by researchers operating in different fields. This will help you understand how it may apply to your research situation.

Education

A researcher wants to survey students at a large university on their opinions of the campus dining services. They get a list of all enrolled students and choose a random starting point. From there, they select every tenth student on the list to participate in the survey.

Marketing

A company decides to conduct a customer satisfaction survey to improve its products. They generate a list of all customers who purchased in the past month and choose a random starting point. From there, they select every fifth customer on the list to participate in the survey.

Healthcare

A researcher wants to study how common a particular illness is in a large city. They divide the city into regions and obtain a list of all households in each region. From there, they choose a random starting point in each region and select every tenth household on the list to participate in the study.