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# Systematic Sampling: Types, Benefits and Disadvantages

• Sangita Kalita
• Jun 23, 2022

“Sampling, statisticians have told us, is a much more effective way of getting a good census.”

-Rob Lowe

In statistics, a predetermined number of observations can be extracted from a larger population. This is called sampling. There are many sampling techniques adopted by researchers and statisticians and the type of sampling depends upon the analysis to be performed. When it seems time consuming to obtain data from every member of the population, then sampling techniques are employed.

Systematic sampling is one of the most effective sampling techniques. You will learn more about systematic sampling in this blog.

## What is Systematic Sampling?

In probability sampling, each member of the group is selected at regular intervals to be a part of the sample. Systematic sampling is an implementation of probability sampling. In systematic sampling, researchers use statistical methods to choose the desired population on whom they want to research. The sampling interval can be calculated by division of the entire population by required sample size.

From a target population, desired elements can be chosen by researchers by selecting a random starting point. After that, sample members are chosen after a sample interval, which is fixed.

For example, if a school wants to form a systematic sample of 500 students for a volunteer event from a population of 5000 students, then they can select every 10th student from the entire student population to build a systematic sample.

Also Read | Stratified Random Sampling: Everything you need to know

### Systematic Sampling vs Cluster Sampling

Both systematic sampling and cluster sampling are types of probability sampling. The main difference between systematic sampling and cluster sampling is noticed in the way they pull the sample points from the elements of the population included in the sample.

#### Systematic Sampling

1. Fixed intervals from the larger population are used to create samples in systematic sampling.

1. A random starting point is selected from the population in systematic sampling. Then the sample is taken from the fixed intervals of the population. It is dependent on size.

1. It is a precise method and used for highly detailed research.

#### Cluster Sampling

1. In cluster sampling, the population is divided into clusters.

1. A simple random sample is selected from each cluster.

1. Cluster sampling is considered to be less precise than other methods of sampling. It is a two step procedure and is a cost saving method which can be used when compiling a list of the entire population becomes difficult.

Also Read | What is Sampling Distribution and its Types in Statistics?

## Overview of Systematic Sampling

### Uses of Systematic Sampling

Systematic sampling in statistics is a very useful technique for researchers as well as for organizations. The main uses of systematic sampling are given below.

1. #### Budget restrictions

Systematic sampling is a better choice than simple random sampling in conditions where there are budget restrictions. This helps in uncomplicated study and helps the researchers to accomplish their goals.

1. #### Uncomplicated implementation

Systematic sampling is dependent on sampling intervals. Therefore, even if the initial population is quite large, it becomes easy for statisticians and researchers to manage the sample. Less time is required to create the sample and is quite low budget due to the periodic nature of the sampling.

1. #### Absence of data pattern

If there is no particular arrangement of the data, analysis can be done in an unbiased manner. Systematic sampling can be used in such cases and is quite a useful tool.

If the sample is broad, the risk of data manipulation is also low. Systematic sampling can be used in such cases.

### Systematic Sampling with and without Population List

1. #### With population list

The order in which the population is listed should be considered to ensure that one gets a valid sample.

Systematic sampling is carried out smoothly if the population is in ascending or descending order since it will include members from both the top and bottom end of the population. For example, if a population is sorted by age, then the sample will consists of members from the entire age spectrum

If the population is ordered cyclically or periodically, then the resultant sample will not be representative.

For example, in periodic lists, if the population consists of alternating men and women, and if one has to choose after an interval of 10 members, then the sample will consist only of men or only of women.

In cyclic lists, if the population consists of 1000 hospitals divided into departments and sorted by age, then the sample will consist of the same age demographic since the age of the required member of every department will be similar.

1. #### Without population list

The population can be randomized like in simple random sampling if one does not have access to a population list.

### Steps of forming sample without population list using Systematic Sampling

The steps that one should follow in order to form a systematic sample are given below.

1. Development of a well defined structural audience is important to begin working on the other aspects of sampling. Therefore, this is the first step that one should implement.

1. Deciding on the ideal size of the sample is the next step. This means that from the entire population, the ideal sample size on which the research will be carried out is chosen.

1. Every member of the sample is assigned a number in this step.

1. The next step is deciding on the interval of the sample. The interval is considered to be the standard distance between the elements of the sample. This can be one by using the formula given below.

Systematic Sampling Formula for interval, i = N/n = Size of population/Size of sample

For example, if the size of population is 5000 and the size of sample is 500, then the sample interval can be found out by using the formula.

i = 5000/500 = 10

Therefore, the sample interval is 10.

1. The members that fit the criteria are selected. In the above example, the sample interval is 10, so 1 in 10 individuals are selected.

1. Then, the starting member of the sample is selected at random. Then the interval is added to the random number. This helps in the addition of new members to the sample.

If r is taken as the starting member and i is the sample interval, then the series will follow the pattern given below.

r, r+i, r+2i, ….

## Types of Systematic Sampling

Types of Systematic Sampling

There are three types of systematic sampling. Information about these types are given below.

1. ### Systematic Random Sampling

In systematic random sampling, samples are selected at a particular preset interval. The steps to set up a systematic random sampling are given below.

• The sampling interval is fixed and calculated. This can be done by dividing the number of elements in the population by the number of elements required for the sample.
• A random sampling point between 1 and the sampling interval is chosen.
• The sampling interval is repeated to choose the next elements.

1. ### Linear Systematic Sampling

In linear systematic sampling, the samples are not repeated at the end. 'n' units are selected to be in the sample which has 'N' population units. Instead of choosing randomly, a researcher can use the help of skip logic to select the units.

Skip interval = total population units / sample size

k = N/n

Then the sample follows a linear pathway. It stops at the end of a specific population. The steps to set up linear systematic sampling are given below.

• The entire population is arranged in a classified sequence.
• The sample size (n) is selected.
• The sampling interval (k) is calculated by N/n.
• A random number is chosen between 1 to k. k is also included.
• k is added to the chosen random number. This is done to add the next member to the sample. The procedure is repeated to add the remaining members of the sample.
• In case the value of k is not an integer, then the next nearest integer can be chosen.

1. ### Circular Systematic Sampling

In circular systematic sampling, the ending point of a sample constitutes a new beginning. The steps to set up circular systematic sampling are given below.

• Sampling interval (k) is calculated by N/n.
• A random starting point is selected between 1 to N.
• Samples are created by skipping through k units every time members of the population are selected.
• There will be N number of samples in this type of sampling, instead of k number of samples like in linear systematic sampling.
• If N=7 and n=2, then k is taken as 3 and not 4.

Also Read | Different Types of Sampling Techniques

### Difference between Circular Systematic Sampling and Linear Systematic Sampling

There are many differences between circular systematic sampling and linear systematic sampling. They are given below.

#### Circular systematic sampling

1. Total samples created are equal to the total population, N.

1. Once the entire population is over, then it restarts from the ending point.

1. The elements are arranged in a circular manner before selection.

1. For example, let's take a case where N=7, n=2 and k=3.

Let the elements of the population be a, b, c, d, e.

Then the samples will be ad, be, ca, db and ec.

#### Linear systematic sampling

1. Total samples created are equal to the sampling interval, k.

1. The ending and starting point of this type of sampling is distinct.

1. The elements are arranged in a linear manner before selection.

Also Read | What are the Applications of Statistical Techniques?

Systematic Sampling is used by many researchers and analysts since it is very simple and has many advantages over the other techniques of sampling. The advantages of systematic sampling are given below.

1. Systematic sampling is convenient and simple to use and researchers can use it to create and analyze samples.

1. Numbering of each member in a sample is not required, therefore it is fast and simple.

1. The samples are created by precise member selection, therefore it is free from biasness.

1. There are other methods of probability sampling like stratified sampling and cluster sampling and non probability methods like convenience sampling. These methods are flawed because there are chances of favoritism dusing choosing of samples. In systematic sampling, the members are kept at a fixed distance from one another, preventing favoritism.

1. There is minimal risk involved in systematic sampling.

1. In the presence of diverse members in a sample, this type of sampling is beneficial since the members of samples are evenly distributed.

The disadvantages of systematic sampling are given below.

1. The organization of the list which is used during the sampling interval is very crucial. If the list is organized in a cyclic pattern that matches with the sample interval, then the selected sample may be biased.

1. The size of people needs to be known during systematic sampling. If the number of elements in the population are not known, then systematic sampling will not work.

1. A natural amount of randomness needs to be exhibited by the population. Otherwise, there is a risk of choosing similar elements. Then, the purpose of systematic sampling is diminished.

Also Read | Non-Parametric Statistics: Types, Tests, and Examples

Simple random sampling of the population is considered to be time consuming and inefficient. Therefore, systematic sampling is preferred by analysts and researchers because of its simplicity and accuracy. It is easy to understand and simple to conduct.

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