# Multistage Sampling – A Guide, Applications, & Examples

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Multistage sampling, often referred to as multistage cluster sampling, is a methodology where samples are drawn from a vast population through progressively smaller units at various stages.

This technique is frequently employed when collecting data from large populations or widespread groups. This blog post delves into the intricacies of this sampling approach.

## Multistage Sampling – In a Nutshell

• Multistage sampling is a technique for collecting data from a large population.
• It involves using smaller and smaller groups as your sample at each stage of research.
• With this form of sampling, you can go from higher to lower-level clusters at each research stage.

## Definition: Multistage Sampling

This is a technique of getting a sample from a population by dividing it into smaller and smaller groups. It also involves taking samples of individuals from the most minor resulting 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
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## Step-by-step guide to multistage sampling

This technique features four primary stages. These are:

• ### Stage: Primary sampling units

This stage involves choosing a sampling frame by considering your population of interest. For instance, you can divide your population of interest into mutually exclusive and exhaustive clusters. Next, you must select some of the clusters to serve as your core sampling unit.

• ### Stage: Secondary sampling units

At this stage, you can choose a sampling frame of relevant separate sub-groups from related but different groups chosen in the first stage. 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 method.

• ### Stage: Repeat stage 2

You can repeat the second step if the sample size is still too large and you cannot afford to use it entirely.

• ### Stage: Ultimate sampling units

You can keep repeating the process of dividing the sampling units until you are satisfied. The end of the sampling process is where you have the ultimate sampling units. This unit represents the subjects from which you will collect data.

## When is multistage sampling used?

Multistage sampling is applicable when you have very large samples. For instance, it can be used in national surveys where the samples feature millions of units and collecting data from them may be extremely expensive. You can use multistage sampling when:

• You have a geographically dispersed population
• You have a large population that would cost a lot to study wholly
• You are conducting a national survey

## 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 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 schools 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.

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 or geographically dispersed population.
• It is more effective than simple random sampling when dealing with a large or dispersed population.
• 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 bias when selecting the sampling method 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.
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## FAQs

#### What is multistage sampling?

Multistage sampling is a technique where you break your study population into smaller and 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 diverse one.

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

This technique is cost-efficient, especially when dealing with a geographically diverse or large sample.

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

The four stages of multistage sampling are primary sampling units, secondary sampling units, repetition of stage three, and the ultimate sample stage.

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