# Systematic sampling

Probability sampling type. Advantages and disadvantages of systematic sampling

## What is systematic sampling?

Systematic sampling is a type of probability sampling that **is based on listing an entire population, randomly choosing the first individual for the sample** and then, from an interval defined by the researcher, **selecting the rest of the individuals that will make up the sample.**

For example, suppose that we need to **extract a sample of ****10 people from a total population of 100** and the first individual selected for the sample is number 3. From this, through an interval of 4 decided by the researcher, they will be selected the next individuals to complete the sample, so that they will be numbers 7, 11, 15, etc.

## Steps for selecting a systematic sample

- Define the target population.

- Determine the desired sample size (
*n*).

- Identify the existing sampling frame or develop a sampling frame of the target population.

- Evaluate the sampling frame for lack of coverage, excessive coverage, multiple coverage, grouping, periodicity, and make adjustments when necessary. Ideally, the list will be in a random order with respect to the study variable or, better yet, ordered based on the variable of interest or its correlation, thus creating implicit stratification. Advantages and disadvantages of systematic sampling

- Determine the number of elements in the sample frame (
*N*).

- Calculate the sampling interval (
*i*) by dividing the number of items in the sampling frame (*N*) by the size of the specific sample (*n*). One should ignore the remainder and round or end to the nearest whole number. Rounding down and truncating can make the sample size larger than desired. If so, additional selections can be randomly removed. If the exact size is not known, or it is impractical to determine, a sampling fraction can be set.

- Randomly select a number,
*r*, from “1” using*i*.

- Select for the sample,
*r*,*r*+*i*,*r*+ 2i,*r*, + 3i, and so on, until the frame is exhausted.

On a technical level, systematic sampling does not create a truly random sample. Only the selection of the first systematic sampling item is a probability selection. Once the first element is selected, some of the elements will have a zero probability of selection.

Also, certain combination of items, such as items that are adjacent to each other in the sampling frame, may not be selected. Repeated systematic sampling can be used to address this problem.

## Advantages of systematic sampling

- It is extremely simple and convenient for researchers to create, conduct, and analyze samples.
- Since it is not necessary to list every member of the sample, systematic sampling is better for representing a population more quickly and easily. Advantages and disadvantages of systematic sampling
- The samples created are based on the selection of members free of favoritism.
- In the other sampling methods there are chances that the clusters created are highly biased, and this is not commonly the case in systematic sampling, since the members are at a fixed distance from each other.
- The risk factor involved in this sampling method is extremely minimal.
- In case there are several members of a population, systematic sampling can be beneficial due to the uniform distribution of the members that are selected to form a sample.

### Disadvantages

There is only one **disadvantage or inconvenience** when using this technique: **the order in which the selected population is placed may have a type of hidden periodicity** , which may coincide with the selected interval, causing a **biased sample.**

## Examples of systematic sampling

Suppose we have a population of 1000 individuals and we need to obtain a sample of 100 of them. To do this, **we will first divide the total population into 100 random fragments** of 10 individuals. Then we will select a random number between 1 and 10.

If the number obtained at random is 6, our sample will be defined from individual number 6 of the population. That is to say that from it intervals of 10 will be completed, that is: 6, 16, 26, 36, 46 until 996. Advantages and disadvantages of systematic sampling

In this way, **the sample of 100 individuals will be** made up through systematic sampling.