# Systematic Sampling: Definition, Examples and Types

## What is systematic sampling?

Systematic sampling is a statistical method that researchers use to zero down on the desired population they want to research. Researchers calculate the sampling interval by dividing the entire population size by the desired sample size. Systematic sampling is an extended implementation of probability sampling in which each member of the group is selected at regular periods to form a sample.

### Systematic sampling definition

Systematic sampling is defined as a probability sampling method where the researcher chooses elements from a target population by selecting a random starting point and selects sample members after a fixed ‘sampling interval.’

For example, in school, while selecting the captain of a sports team, most of our coaches asked us to call out numbers such as 1-5 (1-n) and the students with a random number decided by the coach. For instance, three would be called out to be the captains of different teams. It is a non-stressful selection process for both the coach and the players. There’s an equal opportunity for every member of a population to be selected using this sampling technique.

### What are the steps to form a sample using the systematic sampling technique?

Here are the steps to form a systematic sample:

Step one: Develop a defined structural audience to start working on the sampling aspect.

Step two: As a researcher, figure out the ideal size of the sample, i.e., how many people from the entire population to choose to be a part of the sample.

Step three: Once you decide the sample size, assign a number to every member of the sample.

Step four: Define the interval of this sample. This will be the standard distance between the elements.

For example, the sample interval should be 10, which is the result of the division of 5000 (N= size of the population) and 500 (n=size of the sample).

 Systematic Sampling Formula for interval (i) = N/n = 5000/500 = 10

Step five: Select the members who fit the criteria which in this case will be 1 in 10 individuals.

Step six: Randomly choose the starting member (r) of the sample and add the interval to the random number to keep adding members in the sample. r, r+i, r+2i, etc. will be the elements of the sample.

### How systematic sampling works

When you are sampling, ensure you represent the population fairly. Systematic sampling is a symmetrical process where the researcher chooses the samples after a specifically defined interval. Sampling like this leaves the researcher no room for bias regarding choosing the sample. To understand how systematic sampling exactly works, take the example of the gym class where the instructor asks the students to line up and asks every third person to step out of the line. Here, the instructor has no influence over choosing the samples and can accurately represent the class.

#### Systematic sampling example

For instance, if a local NGO is seeking to form a systematic sample of 500 volunteers from a population of 5000, they can select every 10th person in the population to build a sample systematically.

### What are the types of systematic sampling?

Here are the types of systematic sampling:

1. Systematic random sampling
2. Linear systematic sampling
3. Circular systematic sampling

Let’s take a closer look at these sampling techniques.

#### Systematic random sampling:

Systematic random sampling is a method to select samples at a particular preset interval. As a researcher, select a random starting point between 1 and the sampling interval. Below are the example steps to set up a systematic random sample:

1. First, calculate and fix the sampling interval. (The number of elements in the population divided by the number of elements needed for the sample.)
2. Choose a random starting point between 1 and the sampling interval.
3. Lastly, repeat the sampling interval to choose subsequent elements.

#### Linear systematic sampling:

Linear systematic sampling is a systematic sampling method where samples aren’t repeated at the end and ‘n’ units are selected to be a part of a sample having ‘N’ population units. Rather than selecting these ‘n’ units of a sample randomly, a researcher can apply a skip logic to select these. It follows a linear path and then stops at the end of a particular population.

This sampling or skip interval (k) = N (total population units)/n (sample size) How is a Linear systematic sample selected?

• Arrange the entire population in a classified sequence.
• Select the sample size (n)
• Calculate sampling interval (k) = N/n
• Select a random number between 1 to k (including k)
• Add the sampling interval (k) to the chosen random number to add the next member to a sample and repeat this procedure to add remaining members of the sample.
• In case k isn’t an integer, you can select the closest integer to N/n.

#### Circular systematic sampling:

In circular systematic sampling, a sample starts again from the same point once again after ending; thus, the name. For example, if N = 7 and n = 2, k=3.5. There are two probable ways to form sample: 1. If we consider k=3, the samples will be – ad, be, ca, db and ec.
2. If we consider k=4, the samples will be – ae, ba, cb, dc and ed.

How is a circular systematic sample selected?

• Calculate sampling interval (k) = N/n. (If N = 11 and n = 2, then k is taken as 5 and not 6)
• Start randomly between 1 to N
• Create samples by skipping through k units every time until you select members of the entire population.
• In the case of this method, there will be N number of samples, unlike k samples in the linear systematic sampling method.

### Difference between linear systematic sampling and circular systematic sampling:

Here is the difference between linear systematic sampling and circular systematic sampling.

 Linear Systematic Sampling Circular Systematic Sampling Create samples = k (sampling interval) Create samples = N (total population) The start and endpoints of this sample are distinct. It restarts from the start point once the entire population is considered. All sample units should be arranged in a linear manner prior to selection. Elements will be arranged in a circular manner.

### What are the advantages ofsystematic sampling?

Here are the advantages of systematic sampling.

• It’s extremely simple and convenient for the researchers to create, conduct, analyze samples.
• As there’s no need to number each member of a sample, it is better for representing a population in a faster and simpler manner.
• The samples created are based on precision in member selection and free from favoritism.
• In the other methods of probability sampling methods such as cluster sampling and stratified sampling or non-probability methods such as convenience sampling, there are chances of the clusters created to be highly biased which is avoided in systematic sampling as the members are at a fixed distance from one another.
• The factor of risk involved in this sampling method is extremely minimal.
• In case there are diverse members of a population, this sampling technique can be beneficial because of the even distribution of members to form a sample.

Other probability sampling techniques like cluster sampling and stratified random sampling can be very unorganized and challenging due to which researchers and statisticians have turned to methods like systematic sampling or simple random sampling for better sampling results. It consumes the least time as it requires a selection of sample size and identification of the starting point for this sample, which needs to be continued at regular intervals to form a sample.

### When to use systematic sampling?

Let’s take an example where you want to form a sample of 500 individuals out of a population of 5000; you’d have to number every person in the population.

Once the numbering is done, the researcher can select a number randomly, for instance, 5. The 5th individual will be the first to be a part of the systematic sample. After that, the 10th member will be added into the sample, so on and so forth (15th, 25th, 35, 45th, and members till 4995).

Here are 4 other situations of when to use Systematic Sampling:

1. Budget restrictions: In comparison to other sampling methods like simple random sampling, this sampling technique is more suitable for conditions where there are budget restrictions and also the extremely uncomplicated accomplishment of the study.
2. Uncomplicated implementation: As systematic sampling depends on the defined sampling intervals to decide the sample, it becomes simple for the researchers and statisticians to manage samples with more respondents. This is because the time invested in creating samples is minimal, and the cost spent is also restricted due to the periodic nature of systematic sampling.
3. Absence of data pattern: There are specific data that don’t have an arrangement in place. This data can be analyzed in an unbiased manner, using systematic sampling.
4. Low risk of data manipulation in research: It is highly productive while researching a broad subject, especially when there’s a negligible risk of data manipulation.

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