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Even though the sample population is selected beforehand, systematic sampling is still considered random if the periodic interval is determined beforehand and the starting point is random. This interval, called the sampling interval, is calculated by dividing the population size by the desired sample size.

## How Systematic Sampling Works

Since simple random sampling from a population can be ineffective and time consuming, statisticians resort to other methods, such as systematic sampling. Choosing a sample size using a systematic approach can be done quickly. Once a fixed starting point has been identified, a constant interval is selected to facilitate the selection of participants. When you are sampling, be sure to represent the population fairly. Systematic sampling is a symmetric process in which the researcher chooses samples after a specifically defined interval. Systematic sampling is popular with researchers and analysts due to its simplicity.

## How to carry out systematic sampling

Within systematic sampling, as with other sampling methods, a target population must be selected before selecting participants. A population can be identified based on any number of desired characteristics that suit the purpose of the study being conducted. Some selection criteria may include age, gender, race, location, level of education, and / or profession.

## Examples of systematic sampling

As a hypothetical example of systematic sampling, suppose that in a population of 10,000 people, a statistician selects every 100 people for sampling. Sampling intervals can also be systematic, such as choosing a new sample to draw every 12 hours.

As another example, if you wanted to select a random group of 1,000 people from a population of 50,000 using systematic sampling, all potential participants should be placed on a list and a starting point would be selected.

Once the list is formed, every 50 people on the list (starting the count at the selected starting point) would be chosen as a participant, since 50,000 / 1,000 = 50. For example, if the selected starting point was 20, it would be chosen to the 70th person on the list followed by the 120th, and so on. Once the end of the list is reached and if additional participants are required, the count is repeated to the top of the list to end the count.

## Systematic sampling versus cluster sampling

In the case of cluster sampling, the population is divided into clusters, while systematic sampling uses fixed intervals from the largest population to create the sample. Systematic sampling selects a random starting point from the population, and then a sample is taken at regular fixed intervals from the population according to its size. Cluster sampling, on the other hand, divides the population into clusters and then takes a simple random sample from each cluster.

Cluster sampling is considered less accurate than other sampling methods. It's a two-step sampling procedure. It can be used when it is difficult to complete a list of the entire population. For example, it might be difficult to build the entire customer population of a grocery store to interview. However, a person could create a random subset of stores, which is the first step in the process. This is a simple manual process that can save time and money.

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

These are the steps to form a systematic sample:

Define the interval for this sample. This will be the standard distance between the elements.

The sample interval must be 10, the result of dividing 5000 (N = population size) and 500 (n = sample size). Systematic sampling formula for the interval (i) = N / n = 5000/500 = 10

Select the members that fit the criteria, which in this case will be 1 in 10 people.

Randomly choose the initial member (r) of the sample and add the interval to the random number to continue adding members in the sample. r, r + i, r + 2i, etc. will be the sample items.

## What are the types of systematic sampling?

#### Systematic random sampling:

As a researcher, select a random starting point between 1 and the sampling interval. Here are the example steps to set up a systematic random sample:

First, calculate and set the sampling interval. (The number of items in the population divided by the number of items required for the sample.)

Pick a random starting point between 1 and the sampling interval.

Finally, repeat the sampling interval to choose later items.

#### Systematic linear sampling:

Linear systematic sampling is a systematic sampling method in which samples are not repeated at the end and "n" units are selected to be part of a sample that has "N" population units. It follows a linear path and then stops at the end of a particular town.

This sampling interval or jump (k) = N (total population units) / n (sample size)

###### How is a linear systematic sample selected?

Organize the entire population in a classified sequence.

Select sample size (n)

Calculation of the sampling interval (k) = N / n

Select a random number between 1 and k (including k)

Add the sampling interval (k) to the random number chosen to add the next member to a sample, and repeat this procedure to add the remaining members of the sample. In case k is not an integer, you can select the integer closest to N / n.

#### Systematic circular sampling:

In systematic circular sampling, a sample starts over from the same point once more after finishing; hence the name. For example, if N = 7 and n = 2, k = 3.5. There are two likely ways to form a sample:

If we consider k = 3, the samples will be - ad, be, ca, db and ec.

If we consider k = 4, the samples will be: ae, ba, cb, dc and ed.

###### How is a circular systematic sample selected?

Calculate the sampling interval (k) = N / n. (If N = 11 and n = 2, then k is taken as 5 and not as 6)

Start randomly between 1 and N

Create samples by omitting k units at a time until you select members from the entire population.

In the case of this method, there will be N number of samples, as opposed to k samples in the linear systematic sampling method.

It is extremely simple and convenient for researchers to create, run, and analyze samples. Since it is not necessary to number each member of a sample, it is better to represent a population in a faster and easier way. The samples created are based on precision in the selection of members and are free of favoritism. The risk factor involved in this sampling method is extremely minimal. In case there are several members of a population, this sampling technique can be beneficial due to the uniform distribution of members to form a sample. It is less time consuming as it requires a selection of the sample size and the identification of the starting point for this sample, which must be continued at regular intervals to form a sample.

## When to use systematic sampling?

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

Here are other scenarios of when to use systematic sampling:

Hassle-free implementation: Since systematic sampling relies on defined sampling intervals to decide the sample, it is easy for researchers and statisticians to manage samples with more respondents. This is because the time invested in sample creation is minimal and the cost invested is also restricted due to the periodic nature of systematic sampling.

Absence of data pattern: there are specific data that do not have an established arrangement. These data can be analyzed in an unbiased way, using systematic sampling.

Low risk of data manipulation in research: It is very productive when researching a broad topic, especially when there is a negligible risk of data manipulation.

## Bibliographic References

Sharon L. Lohr. Muestreo. Diseño y análisis. Ed Thompson. 2000
Pérez L. César. Muestreo Estadístico. Ed. Pearson Prentice Hall.2005
Sheaffer R. , Mendehall W. y Lyman R. Elementos de Muestreo. Ed. Thomson. 2007
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