What Is Probability Sampling? | Types & Examples

Probability sampling is a sampling method that involves randomly selecting a sample, or a part of the population that you want to research. It is also sometimes called random sampling.

To qualify as being random, each research unit (e.g., person, business, or organisation in your population) must have an equal chance of being selected. This is usually done through a random selection process, like a drawing, to minimise the risk of selection bias.

Be sure to name or number your target population to ensure accurate randomisation (random assignment).

Types of probability sampling

There are four commonly used types of probability sampling designs:

Simple random sampling

Simple random sampling gathers a random selection from the entire population, where each unit has an equal chance of selection. This is the most common way to select a random sample.

To compile a list of the units in your research population, consider using a random number generator. There are several free ones available online, such as random.org, calculator.net, and randomnumbergenerator.org.

Example: Simple random sampling
You are researching the political views of a municipality of 4,000 inhabitants. You have access to a list with all 4,000 people, anonymised for privacy reasons. You have established that you need a sample of 100 people for your research.

Writing down the names of all 4,000 inhabitants by hand to randomly draw 100 of them would be impractical and time-consuming, as well as questionable for ethical reasons. Instead, you decide to use a random number generator to draw a simple random sample.

If the first number generated by the program is 1735, this means that resident #1735 on your list should be selected to be part of the sample. You continue by matching each number with the respective resident on the list.

Stratified sampling

Stratified sampling collects a random selection of a sample from within certain strata, or subgroups within the population. Each subgroup is separated from the others on the basis of a common characteristic, such as gender, race, or religion. This way, you can ensure that all subgroups of a given population are adequately represented within your sample population.

For example, if you are dividing a student population by college majors, Engineering, Linguistics, and Physical Education students are three different strata within that population.

To split your population into different subgroups, first choose which characteristic you would like to divide them by. Then you can select your sample from each subgroup. You can do this in one of two ways:

  • By selecting an equal number of units from each subgroup
  • By selecting units from each subgroup equal to their proportion in the total population
Example: Stratified sampling
You are investigating why young people choose to play basketball. You want to know if children from urban areas are more likely to play than children from rural areas. As you look at a list of all the youth players in your state, you notice that there are 32,000 children from urban areas and 8,000 children from rural areas.

If you take a simple random sample, children from urban areas will have a far greater chance of being selected, so the best way of getting a representative sample is to take a stratified sample.

First, you divide the population into your strata: one for children from urban areas and one for children from rural areas. Then, you take a simple random sample from each subgroup. You can use one of two options:

  • Select 100 urban and 100 rural, i.e., an equal number of units
  • Select 80 urban and 20 rural, which gives you a representative sample of 100 people

Then, you can continue with your data collection (e.g., ask them to fill in a questionnaire). If you choose an equal number of units, keep in mind that you need to weigh the results in order to draw conclusions for the population as a whole. In this case, since children from urban areas form 80% of the population, you will have to weigh their results 4 times more than those of the children from rural areas.

Systematic sampling

Systematic sampling draws a random sample from the target population by selecting units at regular intervals starting from a random point. This method is useful in situations where records of your target population already exist, such as records of an agency’s clients, enrollment lists of university students, or a company’s employment records. Any of these can be used as a sampling frame.

To start your systematic sample, you first need to divide your sampling frame into a number of segments, called intervals. You calculate these by dividing your population size by the desired sample size.

Then, from the first interval, you select one unit using simple random sampling. The selection of the next units from other intervals depends upon the position of the unit selected in the first interval.

The selection of a unit within the first interval is random, but the selection of units from the next intervals depends on the first selection you made. For this reason, systematic sampling design is sometimes viewed as a mixed design.

Let’s refer back to our example about the political views of the municipality of 4,000 inhabitants. You can also draw a sample of 100 people using systematic sampling. To do so, follow these steps:

  1. Determine your interval: 4,000 / 100 = 40. This means that you must select 1 inhabitant from every 40 in the record.
  2. Using simple random sampling (e.g. a random number generator), you select 1 inhabitant.
  3. Let’s say you select the 11th person on the list. In every subsequent interval, you need to select the 11th person in that interval, until you have a sample of 100 people.
For this to work, you must be completely sure that there is no hidden pattern or hierarchical order in the sampling frame, as this can bias your results.

For example, suppose you have a list of all the employees in an organisation divided by department. If each department list is also organised by seniority (starting with the most senior person and ending with the most recent hire), you run the risk of only selecting the more senior or junior employees, depending on what number you set as your interval.

Cluster sampling

Cluster sampling is the process of dividing the target population into groups, called clusters. A randomly selected subsection of these groups then forms your sample. Cluster sampling is an efficient approach when you want to study large, geographically dispersed populations. It usually involves existing groups that are similar to each other in some way (e.g., classes in a school).

There are two types of cluster sampling:

  • Single (or one-stage) cluster sampling, when you divide the entire population into clusters
  • Multistage cluster sampling, when you divide the cluster further into more clusters, in order to narrow down the sample size
Example: Single-stage cluster sampling
You are researching the perceptions of sixth-form students about higher education. It is not feasible to get a list of all sixth-form students in your region, but you are able to access your city’s data following required privacy protocols.

Clusters are pre-existing groups, so each sixth-form college is a cluster, and you assign a number to each one of them. Then, you use simple random sampling to further select clusters. How many clusters you select will depend on the sample size that you need.

Next, you contact the headteacher of each selected college and ask them to collaborate with you by disseminating your questionnaire to their students.

Multi-stage sampling is a more complex form of cluster sampling, in which smaller groups are successively selected from larger populations to form the sample population used in your study.

Example: Multi-stage sampling
You are investigating workplace-related stress in an ed-tech company. You want to draw a sample of employees to survey. In the organisational chart, you see that the company consists of 9 departments, and each department consists of 2 to 4 units, resulting in 17 different units in total.

First, you take a simple random sample of departments. Then, again using simple random sampling, you select a number of units. Based on the size of the population (i.e., how many employees work at the company) and your desired sample size, you establish that you need to include 3 units in your sample.

Once you have made your selection, you ask every employee working in the selected units to fill in your questionnaire.

In stratified sampling, you divide your population in groups (strata) that share a common characteristic and then select some members from every group for your sample. In cluster sampling, you use pre-existing groups to divide your population into clusters and then include all members from randomly selected clusters for your sample.

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Examples of probability sampling methods

There are a few methods you can use to draw a random sample. Here are a few examples:

Fishbowl draw

You are investigating the use of a popular portable e‐reader device among library and information science students and its effects on individual reading practices. You write the names of 25 students on pieces of paper, put them in a jar, and then, without looking, randomly select three students to be interviewed for your research.

All students have equal chances of being selected and no other consideration (such as personal preference) can influence this selection. This method is suitable when your total population is small, so writing the names or numbers of each unit on a piece of paper is feasible.

Random number generator

Suppose you are researching what people think about road safety in a specific residential area. You make a list of all the suburbs and assign a number to each one of them. Then, using an online random number generator, you select four numbers, corresponding to four suburbs, and focus on them.

This works best when you already have a list with the total population and you can easily assign every individual a number.

RAND function in Microsoft Excel

If your data are in a spreadsheet, you can also use the random number function (RAND) in Microsoft Excel to select a random sample.

Suppose you have a list of 4,000 people and you need a sample of 300. By typing in the formula =RAND() and then pressing enter, you can have Excel assign a random number to each name on the list. For this to work, make sure there are no blank rows.

This video explains how to use the RAND function.

Probability vs. non-probability sampling

Depending on the goals of your research study, there are two sampling methods you can use:

  • Probability sampling: Sampling method that ensures that each unit in the study population has an equal chance of being selected
  • Non-probability sampling: Sampling method that uses a non-random sample from the population you want to research, based on specific criteria, such as convenience

Probability sampling

In quantitative research, it is important that your sample is representative of your target population. This allows you to make strong statistical inferences based on the collected data. Having a sufficiently large random probability sample is the best guarantee that the sample will be representative and the results are generalisable.

Non-probability sampling

Non-probability sampling designs are used in both quantitative and qualitative research when the number of units in the population is either unknown or impossible to individually identify. It is also used when you want to apply the results only to a certain subsection or organisation rather than the general public.

Example: Non-probability sampling
You are investigating the coping mechanisms of employees dealing with workplace stress. You want to conduct expert interviews with organisational psychologists to get their viewpoint on the topic.

You are unlikely to be able to compile a list of every practising organisational psychologist in the country, but you could compile a list with all the experts in your area and select a few to interview.

A good rule of thumb is to conduct interviews until you have reached a saturation point, when you no longer hear new responses to your questions.

Advantages and disadvantages of probability sampling

It’s important to be aware of the advantages and disadvantages of probability sampling, as it will help you decide if this is the right sampling method for your research design.

  • Advantages of probability sampling

There are two main advantages to probability sampling.

  • Samples selected with this method are representative of the population at large. Due to this, inferences drawn from such samples can be generalised to the total population you are studying.
  • As some statistical tests, such as multiple linear regression, t test, or ANOVA, can only be applied to a sample size large enough to approximate the true distribution of the population, using probability sampling allows you to establish correlation or cause-and-effect relationship between your variables.
  • Disadvantages of probability sampling

Choosing probability sampling as your sampling method comes with some challenges, too. These include the following:

  • It may be difficult to access a list of the entire population, due to privacy concerns, or a full list may not exist. It can be expensive and time-consuming to compile this yourself.
  • Although probability sampling reduces the risk of sampling bias, it can still occur. When your selected sample is not inclusive enough, representation of the full population is skewed.

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Frequently asked questions about probability sampling

What is a sampling method?

When your population is large in size, geographically dispersed, or difficult to contact, it’s necessary to use a sampling method.

This allows you to gather information from a smaller part of the population, i.e. the sample, and make accurate statements by using statistical analysis. A few sampling methods include simple random sampling, convenience sampling, and snowball sampling.

What is the difference between stratified and cluster sampling?

Stratified and cluster sampling may look similar, but bear in mind that groups created in cluster sampling are heterogeneous, so the individual characteristics in the cluster vary. In contrast, groups created in stratified sampling are homogeneous, as units share characteristics.

Relatedly, in cluster sampling you randomly select entire groups and include all units of each group in your sample. However, in stratified sampling, you select some units of all groups and include them in your sample. In this way, both methods can ensure that your sample is representative of the target population.

What is a sampling frame?

A sampling frame is a list of every member in the entire population. It is important that the sampling frame is as complete as possible, so that your sample accurately reflects your population.

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Kassiani Nikolopoulou

Kassiani has an academic background in Communication, Bioeconomy and Circular Economy. As a former journalist she enjoys turning complex scientific information into easily accessible articles to help students. She specialises in writing about research methods and research bias.