Systematic sampling is a probability sampling method for obtaining a representative sample from a population. To use this method, researchers start at a random point and then select subjects at regular intervals of every n^{th} member of the population. Like other probability sampling methods, the researchers must identify their population of interest before sampling from it.

Researchers use systematic sampling because it is easier to perform than simple random sampling, which can be cumbersome with large populations. It’s a simpler process because only the initial selection is random, and then the fixed sampling interval expedites the rest of the process. Despite being a more straightforward procedure, systematic sampling can produce samples that faithfully represent the population.

Systematic sampling provides another benefit in that it does not require a complete population list in advance. Simple random sampling requires that list.

In this post, we’ll go into more depth about using systematic sampling with and without a population list! Then we’ll look at some of its potential drawbacks and how to minimize them.

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

## Systematic Sampling Using a Population List

When you have a list of your entire population, systematic sampling can closely approximate a simple random sample. The process involves taking your list and selecting every n^{th} person on the list. Imagine you’re sampling students in a school district and have a list of all students in that district. Simply start at a random point on the list and then pick every, say, 50^{th} student on it. Voila! You have a representative sample of students in the school district.

### List Considerations

When you use this form of systematic sampling, you must understand the order of your list.

Preferably, the list should be in a random or pseudo-random (e.g., alphabetical) order because systematic sampling will mimic simple random sampling. It can be ok if the list sorts population members in descending/ascending order by a characteristic. In this case, systematic sampling still tends to pick a representative sample because you’ll start at a random point and work your way through the full range of that characteristic as you progress through the list.

For example, in a company, you might sort a list by ascending years of experience. In this case, systematic sampling will start with the junior members of the company and work its way to those with more experience. However, it’s not necessary to sort by experience to obtain a representative sample.

Watch out for cycles or patterns in your list because they can cause systematic sampling to produce a biased, non-representative sample. For example, if you have a list that cycles through the ten departments in a company, then every 10^{th} or 20^{th} observation will be from the same department! You need to understand your list and be aware of any underlying patterns that might be present.

If your list has a problematic pattern, just re-sort the list to remove it! Then proceed with the systematic sampling. Statisticians consider alphabetical ordering to be acceptable for systematic sampling. For example, with the company that has ten departments, you can re-sort the list alphabetically, by years of experience, or randomly to remove the cyclical department pattern.

### Calculating the Sampling Interval

To use systematic sampling, you need to calculate your sampling interval.

Take the population size and divide it by your target sample size to calculate the sampling interval (n). Then pick every n^{th} person on your list.

Sampling Interval (n) = Population Size / Sample Size

For example, if the size of your population is 20,000 and you want to have a sample size of 500, then you need to pick every 20,000 / 500 = 40^{th} person on your list.

Before drawing the sample, researchers should randomly select the starting point on the list and choose the sampling interval. Making those determinations in advance helps avoid data manipulation!

## Systematic Sampling Without a List

Unlike simple random sampling and stratified sampling, you can use systematic sampling when you don’t have a complete list of the population. This method is a good option for populations that are difficult to document, such as the homeless, because a list won’t exist. The main requirement is that researchers know how to locate them, understand their habits, and can interact with them. While it’s not perfect in these cases, it’s a workable option, unlike other sampling methods that require a full list.

For example, you want to survey customers at a store but don’t have a complete list of all customers. Instead, you can use systematic sampling and administer the survey to every 20^{th} customer who exits the store. This method works because the customers leave randomly.

When you use systematic sampling in this manner, you must carefully understand the behavior of your population. For example, you might have different types of customers in the store at separate times. The store might have more retirees during daytime hours on weekdays, teenagers after school, and working people in the evening and on weekends. And, if you have multiple stores, you’ll need to sample the different locations.

Using systematic sampling without a list requires you to carefully plan your sampling protocol’s timing and locations. You’ll need to obtain all the subgroups in the correct proportions. That can take some work to figure out! However, if you don’t have a list of your population, you’ll need to use a method like systematic sampling to obtain a sample that reasonably represents the population.

In comparison, cluster sampling doesn’t require a list of the full population but does require a partial list. Convenience sampling also does not need a list but the results are minimally useful.

## Limitations of Systematic Sampling

Throughout this post, you’ve seen that systematic sampling provides the crucial benefits of simplicity, and it does not require a complete population list. However, it has several potential drawbacks.

### Cycles in the List

If you use a population list, systematic sampling can closely mirror simple random sampling. However, the quality of the sample ultimately depends on the lack of cycles in your list. The list can mess up the sample. Ultimately, using systematic sampling with a list is not quite as random as simple random sampling. Fortunately, there are simple precautions you can take to reduce this problem. For example, statisticians consider sorting lists alphabetically to be sufficiently random, and it can remove any cycles from it!

### Data Manipulation

Any time researchers devise a non-random system, it increases the potential for data manipulation, even if inadvertently. By allowing the researchers to choose both the starting point and the sampling interval in systematic sampling, the potential for manipulation exists. However, if the researchers make these decisions beforehand, it minimizes this risk.

## Reference

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

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