## Systematic Random Sampling

Lucas is a new manager at the local movie theater. The owner of the movie theater wants to find out how the customers feel about the new renovations they've done at the theater. Lucas can't ask every customer that comes in how they feel, especially when the movie theater gets busiest on Friday and Saturday nights.

In this lesson, you will learn about systematic random sampling and how to use it when collecting data.

## What Is Systematic Random Sampling?

**Systematic random sampling** is the random sampling method that requires selecting samples based on a system of intervals in a numbered population. For example, Lucas can give a survey to every fourth customer that comes in to the movie theater. The fact that Lucas is giving the survey to every fourth customer is what makes the sampling systematic because there is an interval system. Likewise, this is a random sample because Lucas cannot control what type of customer comes through the movie theater.

Additionally, remember that systematic random sampling must still ensure that all outcomes are given equal chance of getting selected in the sample. Therefore, Lucas cannot only select every fourth customer that comes through the door during the evenings or on the weekends. He must select every fourth customer every time the theater is open.

Lucas must also ensure that by choosing every fourth customer he does not include any sort of pattern in the selection. We will talk about this more when discussing the pros and cons of systematic random sampling.

Now that you understand the definition of systematic random sampling, you can learn when and how to use systematic random sampling.

## How to Use Systematic Random Sampling

Let's discuss when and how to use systematic random sampling. Lucas's boss wants to send his employees to a weeklong training session that is out of town. Due to limited funding, Lucas's boss, Alex, cannot send all of his employees; he must choose a group to go to the training. Alex owns 12 movie theaters and employs 200 people. He has 12 managers out of the 200 employees. Alex can use systematic random sampling to select the group of employees that will attend the training.

Alex can follow these steps to create a group from systematic random sampling:

- Create a list of employees
- Select a beginning number
- Select an interval
- Gather a list of employees based on the interval number

First, Alex will need to create a list of his employees. Then, he will need to randomly decide which number to start his selection process. For this, Alex uses a random number generator to select which employee he will begin with. The random number generator produces the number 34. Now Alex needs to create an interval. First, he needs to decide how many employees he wants to send to the training. After reviewing his budget, Alex decides he can afford to send 20 employees to the training. To find the interval he needs, Alex can divide the total number of employees he has (the population size) by the number of employees he wants to send to the training (the sample size), like this:

200 / 20 = 10

This would make his interval 10, meaning that every 10th person after the 34th person would be selected until he had a total of 20 people.

Therefore, the following people would be selected:

34, 44, 54, 64, 74, 84, 94, 104, 114, 124, 134, 144, 154, 164, 174, 184, 194, 14, 24, 35

The numbers 14, 24, and 35 are included here because in order to select 20 people, Alex will have to continue selecting every 10th person, even if that means starting back at the beginning of the list. The number 35 is included because the 34th person has already been selected at this point.

What if the interval number happened to be a fraction? What if Alex decided he wanted to select 23 people to go to the training?

He would still use this method:

200 / 23 = 8.69565â€¦.

Obviously, you cannot select .69565â€¦.. of a person. To compensate for this, Alex will need to pick every 8th person then every 9th person and continue to rotate this pattern until he has 23 people.

Alex would end up with the following people:

34, 42, 51, 59, 68, 76, 85, 93, 102, 110, 119, 127, 136, 144, 153, 161, 170, 178, 187, 195, 4, 12, 21

## When to Use Systematic Sampling

It is best to use systematic random sampling only if the population is homogeneous, or of the same subgroup. For example, if Alex's list contains employees from a competitive movie theater, then obviously he won't want to use a random selection because he may accidentally select an employee from the wrong theater.

Also, you will need to be careful when using systematic random sampling in case your original list and interval create a pattern. For example, let's say that each movie theater sent in the list of employees by age. The oldest employee was at the top and the youngest employee at the bottom. If every movie theater employed roughly eight or nine people, this means that there is a potential that all of the youngest employees would be selected for training. Make sure that your list is fully randomized before beginning the interval and selection process.

## Why Use Systematic Random Sampling?

Now that you understand how to use systematic sampling, let's discuss the advantages of this method:

Systematic random sampling is simple to use. It doesn't require you to put in 200 names in a bag or use a random generator to create a sample. It works really well for larger populations. By creating a system, it helps the researcher select the sample quickly and efficiently. It also makes the sample unbiased by using the system to select the sample. It also guarantees that the population will be evenly sampled by using an interval to select the sample rather than a blind system. The biggest problem with systematic random sampling is the possibility of a pattern in the interval selection.

## Lesson Summary

Lucas needed a way to gather information from his customers without collecting biased information and without having to ask each customer that comes through the door. To do this, Lucas decided to use **systematic random sampling**, the random sampling method that requires selecting samples based on a system of intervals in a numbered population. When using systematic random sampling, remember that all outcomes in a given population must still have equal probability of getting selected.

Follow these steps to create a group from systematic random sampling:

- Create a list
- Select a beginning number
- Select an interval (population size / sample size)
- Gather a list based on the interval number

Remember, the best times to use systematic random sampling is when you have a homogeneous population. The advantages of systematic random sampling are:

The disadvantages are:

- Can be biased if it creates a pattern

Overall, systematic random sampling is a great way to produce an unbiased sample, specifically for large, homogeneous populations.

## Learning Outcomes

After you have finished with this lesson, you should be able to:

- Define systematic random sampling
- Recall when it is appropriate to use this method
- Describe the steps involved in creating a group from systematic random sampling
- Explain the advantages and disadvantages of this sampling method