# Multistage Sampling – A Guide, Applications, & Examples

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In research, sometimes it is not precise enough to just sample participants for a study randomly from an entire population. In order to represent each group equally and still keep the sample as small as possible, methodologies like stratified sampling or cluster sampling might be helpful. The following article will explain a technique to narrow down your group of participants, multistage sampling.

## Multistage Sampling – In a Nutshell

In multistage sampling, the population is divided into groups, the clusters, which can be separated into even smaller groups before the participants are sampled from them.

## Definition: Multistage Sampling

Multistage sampling, often referred to as multistage cluster sampling, is a technique of getting a sample from a population by dividing it into smaller and smaller groups. This technique is frequently employed when collecting data from large populations or widespread groups.

Example

Assume you want to estimate the average income of households in your country with over 50 million households. Instead of collecting data from 50 million samples, you can take a simple random sample of a few states, like 20 states. Then, from each stage, you can take a small random sample of fifteen provinces. Then, from each province, you can take a sample of 50 households. So, your resulting sample will be:

• 20 states * 15 provinces * 50 households = 15,000 households

## Step-by-step guide

This technique features four primary stages. These are:

• ### Stage 1: Primary sampling units (PSU)

The primary stage involves choosing a sampling frame by considering your population of interest. These can be geographical areas or institutions as well as other entities depending on the study. The PSUs should make sure to accurately represent the entire population and be practical in the face of the study’s resources and objections. For example, you can divide your population of interest into mutually exclusive and exhaustive clusters.

• ### Stage 2: Secondary sampling units (SSU)

At this stage, you can form subgroups from the clusters chosen in the first stage. These SSUs are selected within the primary sampling units and are either sampled randomly or with any other sampling method of the researcher’s choice. If your PSUs are geographical areas, you should also watch the population density and thus form smaller SSUs in densely populated areas.

Note that you can end the sampling process at this stage. If you choose to conclude at this stage, then you will have adopted the double-stage or two-stage sampling technique.

• ### Stage 3: Repeat stage 2

You can repeat the second step until you find the ideal sample size, and you cannot afford to use it entirely. Keep in mind that it is best to stick with one sampling method throughout the whole process to avoid introducing bias.

• ### Stage 4: Ultimate sampling units (USU)

The end of the sampling process is where you have the ultimate sampling units. These units consist of the subjects from which you will collect data and thus has to be manageable and accessible for the researcher, as well as unbiased to ensure validity.

## Example of multistage sampling

The following example explains how each stage of multistage sampling works.

You want to study the average performances of schools in a specific stage.

Stage 1: The first stage of multistage sampling will include listing all school districts within the study state. Each school district will become a cluster.

Next, you categorize the districts by area, like urban, rural, and sub-rural districts. The key is to make sure that all the areas are represented in your study sample. Finally, you can list the school districts in each category and then pick five random school districts using the simple random sampling technique.

So, if you had three categories and pick five schools from each, your primary sample unit will be 15 schools.

Stage 2: In the second stage, you will list all the schools within the school districts you selected.

Next, narrow down the number into a number you can afford to visit and research. You can choose ten schools from the 15 school districts you chose at the first stage of multistage sampling.

So, if you have ten schools from each of the 15 school districts, your secondary sample unit will be 150 schools.

Stage 3: At this stage, you can divide your secondary sample unit further by grouping the sample into registered students. From each school, you can choose 50 students using systematic sampling. So, from 150 schools, you will have 7,500 students.

Stage 4: If you do not see the need to divide the sampling units further, your ultimate sampling unit will be 7,500 students.

## Applications for multistage sampling

Multistage sampling is applicable when you have large populations. While it is a very useful technique in research, it is not always the best and easiest option. The following list will show you, when it is profitable or even necessary to use multistage sampling.

• You have a large population that would cost a lot to study wholly, like a national survey.
• You have a geographically dispersed population and cannot reach every individual.
• Your study is expensive, and you cannot have a large sample size.
• You want to study behavior or opinions of people in different areas to compare them.

Multistage sampling has its pros and cons. Below is a summary of the advantages and disadvantages of multistage sampling:

Pro

• You do not have to begin with a sampling frame for your chosen population.
• It is relatively cheap when you have a large-scale survey or geographically dispersed population.
• It is more effective than simple random sampling when dealing with a large or dispersed population.
• It does not need a complete list of the entire population, which is often difficult to get, and thus simplifies the sampling process.
• It is flexible and allows you to use different sampling methods between the stages.

Cons

• You may fail to achieve some statistical inference if you do not have a large enough sample size.
• You are prone to sampling bias when selecting the sampling technique at each stage.
• You may encounter unrepresentative samples, as you may end up not including a large section of the population in your sample.

## Single-stage vs Multistage sampling

• Single-stage sampling involves dividing a population into simple units and then picking a sample directly by collecting data from all individuals in the units.
• In contrast, multistage sampling involves dividing the population into smaller and smaller units at different stages to create a sample. For instance, it takes into account hierarchical groupings to create an easy-to-handle sample.
• Also, single-stage sampling usually begins with a sampling frame while multistage sampling does not require a sampling frame at the start.
• Single-stage and multistage sampling also have a few things in common. For instance, you can use similar sampling methods (probability and non-probability methods) in both.

## Types of multistage sampling

Multistage sampling is typically used as a form of cluster sampling, then also called multistage cluster sampling. In this case, the researcher divides the population into clusters and might even divide each cluster into smaller groups before sampling participants from those.

There is, however, a second type, called multistage random sampling, where the researcher creates subgroups randomly. A cluster is always formed with intention, while these subgroups are just coincidentally picked.

Example

For example, you study the time students invest in preparing for exams.

In multistage cluster sampling, you would select one university or school from each state in the first stage. In the second stage, you would select maybe ten boys and ten girls from each grade, defining your sample.

In multistage random sampling, you would just pick a random number of schools across the country and blindly select the number of students you want as participants from each of them.

In both cases, you first select a number of universities or schools and then select participants among the students. In the first case, however, it is a systematic approach to gain representativeness among the country, whereas the second one only decides about their participants on a whim.

## FAQs

#### What is multistage sampling?

Multistage sampling is a technique where you break your study population into smaller groups at each stage to develop a final study sample.

#### When should you use multistage sampling?

You can use multistage sampling if you have a large population or a geographically dispersed one.

#### What are the benefits of multistage sampling?

This technique is cost-efficient, especially when dealing with a geographically dispersed or large sample. Furthermore, it is a flexible but still very reliable method to get representative samples.

#### What are the four stages of multistage sampling?

The four stages of multistage sampling are forming primary sampling units, secondary sampling units, the repetition of stage two until you are satisfied with the sample size, and the ultimate sample stage, where you select your participants.

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