What is Systematic Sampling?

Systematic sampling is like dealing cards at family game night…

Say you, your spouse, and two other family members decide to play a game of Spades. The rules require you to distribute the cards to each of the four players evenly. You could spread the pile around on the table (facedown) and let everyone grab whichever 13 cards they want. However, most people use a systematic approach. They pass the cards out, one at a time, going in a circle. If you use this approach, each player holds every fourth card from the deck. Your hand is a systematic sample of the 52 card population.

In statistics, it is often difficult to measure every single person, tree, animal, rock — or whatever it is you care about. A complete count of the entire population of anything is called a census. If you wanted to know the average height of a U.S. citizen, you might be tempted to think you need to measure every American and take the average. However, the central limit theorem tells us that after you measure a few thousand people, the average won’t change very much as you move forward. It’s the same principle that applies to cooking — You don’t have to eat a whole pot of soup to know if it’s too salty. Just a sample will give you the information you need. If you want to know the average height in America, measuring a sample of the population will get you close.

But a sample has to be unbiased to be useful. Otherwise, the average of the sample only represents the sample itself and not the rest of the population. A biased estimate doesn’t tell you much about the rest of the population. Therefore, samples must be randomly chosen from the population. That is why statisticians use sampling techniques like systematic sampling to ensure the conclusions from the sample can be extrapolated to the rest of the population.

To complete a systematic sampling of a population, you first need to order the population in some way. It could be a line or a list. For example, the transportation security administration (TSA) officer at the airport might systematically sample passengers in line at airport security checkpoints for additional screening. Or, you might conduct a survey using the phone book as a population list.

Next, you must choose a sampling interval. The most common method is dividing the population size by the desired sample size. Let’s say you have a budget for a 500 person sample to learn how long the average child brushes their teeth in your state. You acquire a list of names of every child in your state, which totals 500,000 kids. Dividing 500,000 by 500 gives you a sample interval of 1,000. When you choose your sample, you will pick every 1,000th name on the list.

Finally, you need a random starting point. If you simply start with the first name on the list, there may be some room for bias. Therefore, you will randomly select a number that will serve as the first member of your sample. Perhaps you just throw some dice and use the face values. For instance, if you roll a 4, 3, and 1, your first member is number 431 on the list. The next member of your sample will be number 1,431, then 2,431, and so on until you reach the end of the list. Once you have your sample, you can collect the data you need to complete the study.

While systematic sampling generates a randomly selected set of members, the process is not purely random. Some people have a problem with that. To minimize bias, a randomly selected sample is more desirable.

With simple random sampling, there is no structure to the way that members of the sample are selected. They might be chosen by picking names out of a hat, or by using a computer program to pick members from a list using a random number generator. With this type of sampling, every member of the population has an equal probability of being selected.

However, a simple random sample tends to pick more members that are close together than people assume. Other sampling methods ensure that the selection is spread across the population. Imagine a bag filled with 90 red marbles and 10 blue marbles. If you randomly draw 10 marbles from that bag, you will get a selection of only red marbles about a third of the time.

The simple random sample will under-represent the minority within the population. Because of this fact, you need a larger sample if you want to represent the population better. Other sampling methods, such as systematic sampling, can do a better job of ensuring that the sample is spread across the population with a smaller sample. That smaller sample size implies a lower cost of conducting the research.

Systematic sampling spreads the members across the population by using a set interval. But unless the population is organized in terms of some characteristic, it can still lead to misrepresentation.

Stratified sampling solves this problem directly. With this method of sampling, the population is first divided into groups called strata. For example, you might create groupings by gender. If your population is 50 percent male and 50 percent female, you have two equal strata.

Next, you proportionally assign your sample size to each group. In this case, half of your sample will be men and half women. Then, you sample each strata to get the number of members you need. In this case, if you had a target sample size of 100, you would assign 50 to each strata. If you had a population of 90 percent red marbles and 10 percent blue marbles, you would assign 10 to the blue grouping to ensure that 10 percent of your sample was blue.

Finally, you select your members using a simple random, cluster, or systematic sampling method within each stratum. Pooling the results gives you an unbiased estimate of the entire population. But, stratified sampling has the additional benefit of providing data specific to each group for further study.

Cluster sampling is a little different than systematic sampling and stratified sampling. The idea is to minimize research costs by choosing members that are close together. For example, you might include all of the houses on a randomly selected street in your dataset. This process reduces the effort to locate and travel to the individuals, therefore reducing the cost of data collection.

To conduct a cluster sample, you start by separating the population into clusters. Perhaps a population of 100,000 can be grouped into 100-member sets. Then, you randomly select which clusters to include. If your target sample is 500 people, you would choose five clusters and include everyone from that set in your sample.

Cluster sampling can be combined with characteristics of other sampling methods to reduce bias. For instance, you might use stratified sampling to break a state into counties. Then, you could select every sixth street listed on the county map (systematic sampling). Finally, you could include every person living on that street in the sample (cluster sampling).

Many researchers use systematic sampling due to the simplicity of the process, combined with the reduced size of the sample that is required.

The systematic approach allows researchers to show that their methods are unbiased. For instance, an officer at the airport security checkpoint might select every 32nd passenger for additional screening. The systematic approach, in theory, can assure the public — or the courts — that people who are chosen are not victims of racial profiling or some other bias.

Systematic sampling is a reliable technique for many occasions. However, it can be biased if the population is ordered in a way that matches the sampling interval.

That can occur intentionally or coincidentally. For instance, if the sampling interval is 20, an unscrupulous researcher could place members with the desired quality at every 20th place in the line or on the list.

Alternatively, if a list is ordered by some characteristic that happens to have groupings the same size as the interval, it could create a biased sample despite the researcher’s best intentions. For example, an organization might be divided into 20-member teams, with a team leader listed first. In this case, the systematic sampling method could choose only team leaders, which may not represent the rest of the organization.