example of research using simple random sampling

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Simple random sampling: definition, examples, and how to do it.

9 min read How can you pick a sample that’s truly random and representative of the participant population? Simple random sampling is the sampling method that makes this easy. Learn how it works in our ultimate guide.

Definition — what is simple random sampling?

Simple random sampling selects a smaller group (the sample) from a larger group of the total number of participants (the population). It’s one of the simplest systematic sampling methods used to gain a random sample.

The technique relies on using a selection method that provides each participant with an equal chance of being selected, giving each participant the same probability of being selected.

Since the selection process is based on probability and random selection, the end smaller sample is more likely to be representative of the total population and free from researcher bias . This method is also called a method of chances.

Simple random sampling is one of the four probability sampling techniques: Simple random sampling, systematic sampling, stratified sampling, and cluster sampling.

The process of simple random sampling

• Define the population size you’re working with. This could be based on the population of a city. For this exercise, we will assume a population size of 1000.
• Assign a random sequential number to each participant in the population, which acts as an ID number – e.g. 1, 2, 3, 4, 5, and so on to 1000.
• Decide the sample size number needed. Not sure about what the right sample size should be? Try our Sample Size Calculator . For this exercise, let’s use 100 as the sample size.
• Select your sample by running a random number generator to provide 100 randomly generated numbers from between 1 and 1000.

Why do we use simple random sampling?

Simple random sampling is normally used where there is little known about the population of participants. Researchers also need to make sure they have a method for getting in touch with each participant to enable a true population size to work from. This leads to a number of advantages and disadvantages to consider.

Advantages of simple random sampling

This sampling technique can provide some great benefits.

• Participants have an equal and fair chance of being selected. As the selection method used gives every participant a fair chance, the resulting sample is unbiased and unaffected by the research team. It is perfect for blind experiments.
• This technique also provides randomised results from a larger pool. The resulting smaller sample should be representative of the entire population of participants, meaning no further segmenting is needed to refine groups down.
• Lastly, this method is cheap, quick, and easy to carry out – great when you want to get your research project started quickly.

Disadvantages of simple random sampling

• There may be cases where the random selection does not result in a truly random sample. Sampling errors may result in similar participants being selected, where the end sample does not reflect the total population.
• This provides no control for the researcher to influence the results without adding bias. In these cases, repeating the selection process is the fairest way to resolve the issue.

What selection methods can you use?

A lottery is a good example of simple random sampling at work. You select your set of numbers, buy a ticket, and hope your numbers match the randomly selected lotto balls. The players with matching numbers are the winners, who represent a small proportion of winning participants from the total number of players.

Other selection methods used include anonymising the population – e.g. by assigning each item or person in the population a number – and then picking numbers at random.

Researchers can use a simpler version of this by placing all the participants’ names in a hat and selecting names to form the smaller sample.

Comparing simple random sampling with the three other probability sampling methods

The three other types of probability sampling techniques have some clear similarities and differences to simple random sampling:

Systematic sampling

Systematic sampling, or systematic clustering, is a sampling method based on interval sampling – selecting participants at fixed intervals.

All participants are assigned a number. A random starting point is decided to choose the first participant. A defined interval number is chosen based on the total sample size needed from the population, which is applied to every nth participant after the first participant.

For example, the researcher randomly selects the 5th person in the population. An interval number of 3 is chosen, so the sample is populated with the 8th, 11th, 14th, 17th, 20th, (and so on) participants after the first selection.

Since the starting point of the first participant is random, the selection of the rest of the sample is considered to be random.

Simple random sampling differs from systematic sampling as there is no defined starting point. This means that selections could be from anywhere across the population and possible clusters may arise.

Stratified sampling

Stratified sampling splits a population into predefined groups, or strata, based on differences between shared characteristics – e.g. race, gender, nationality. Random sampling occurs within each of these groups.

This sampling technique is often used when researchers are aware of subdivisions within a population that need to be accounted for in the research – e.g. research on gender split in wages requires a distinction between female and male participants in the samples.

Simple random sampling differs from stratified sampling as the selection occurs from the total population, regardless of shared characteristics. Where researchers apply their own reasoning for stratifying the population, leading to potential bias, there is no input from researchers in simple random sampling.

Cluster sampling

There are two forms of cluster sampling: one-stage and two-stage.

One-stage cluster sampling first creates groups, or clusters, from the population of participants that represent the total population. These groups are based on comparable groupings that exist  – e.g. zip codes, schools, or cities .

The clusters are randomly selected, and then sampling occurs within these selected clusters. There can be many clusters and these are mutually exclusive, so participants don’t overlap between the groups.

Two-stage cluster sampling first randomly selects the cluster, then the participants are randomly selected from within that cluster.

Simple random sampling differs from both cluster sampling types as the selection of the sample occurs from the total population, not the randomly selected cluster that represents the total population.

In this way, simple random sampling can provide a wider representation of the population, while cluster sampling can only provide a snapshot of the population from within a cluster.

Frequently asked questions (FAQs) about simple random sampling

What if i’m working with a large population.

Where sample sizes and the participant population are large, manual methods for selection aren’t feasible with the available time and resources.

This is where computer-aided methods are needed to help to carry out a random selection process – e.g. using a spreadsheet’s random number function, using random number tables, or a random number generator.

What is the probability formula for being selected in the sample?

Let’s take an example in practice. A company wants to sell its bread brand in a new market area. They know little about the population. The population is made up of 15,000 people and a sample size of 10% (1,500) is required. Using this example, here is how this looks as a formula:

Sample size (S) = 1,500

The total population (P) = 15,000

The probability of being included in the sample is: (S ÷ P) x 100%

E.g. = (1,500 ÷ 15,000) x 100% = 10%

What are random number tables?

One way of randomly selecting numbers is to use a random number table (visual below). This places the total population’s sequential numbers from left to right in a table of N number of rows and columns.

To randomly select numbers, researchers will select certain rows or columns for the sample group.

As sourced from Statistical Aid

How do i generate random numbers in an excel spreadsheet.

Microsoft Office’s Excel spreadsheet application has a formula that can help you generate a random number. This is:

It provides a random number between 1 and 0.

For random numbers from the total population (for example, a population of 1000 participants), the formula is updated to:

=INT( 1000 *RAND())+1

Simply copy and paste the formula into cells until you get to the desired sample size – if you need a sample size of 25, you must paste this formula into 25 cells. The returned numbers between 1 and 1000 will indicate the participant’s ID numbers that make up the sample.

Conclusion: Where to go next to learn more?

What sample size should you go for? Try our online calculator to see how many people you should be selecting: Calculate the perfect sample size

Download our eBook and learn how to manage your perfect panel

Related resources

Sampling techniques 22 min read, sampling and non-sampling errors 10 min read, determining sample size 7 min read, selection bias: how to avoid errors in research 11 min read, systematic random sampling 12 min read, convenience sampling 18 min read, non-probability sampling 17 min read, request demo.

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Simple Random Sampling Method: Definition & Example

Julia Simkus

Editor at Simply Psychology

BA (Hons) Psychology, Princeton University

Julia Simkus is a graduate of Princeton University with a Bachelor of Arts in Psychology. She is currently studying for a Master's Degree in Counseling for Mental Health and Wellness in September 2023. Julia's research has been published in peer reviewed journals.

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Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

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Simple random sampling is a technique in which each member of a population has an equal chance of being chosen through an unbiased selection method. Each subject in the sample is given a number, and then the sample is chosen randomly.

The random sampling method is one of the simplest and most common forms of collecting data, as it provides an unbiased representation of a group. The random subset of selected individuals represents an entire data set.

The goal of simple random sampling is to create a manageable, balanced subset of individuals that is representative of a larger group that would otherwise be too challenging to sample.

For example, if you wanted to conduct a survey about food preferences in a school of 1000 students, and you wanted to sample 100 students.

You could use simple random sampling by assigning each student a number from 1 to 1000, then using a random number generator to pick 100 numbers.

The students assigned those numbers would be the ones you survey.

• First, choose the target population that you wish to study and determine your desired sample size. The smaller the sample size the less likely, it can be generalized to the wider research population and is unlikely to be fully representative.
• The list of the people from which the sample is drawn is called the sampling frame. Examples of sampling frames include the electoral register, schools, drug addicts, etc.).
• Then, assign a sequential number to each subject in the sampling frame.
• Next, individuals are selected using an unbiased selection method. Some examples of simple random sampling techniques include lotteries, random computer number generators, or random draws.

Minimizes Bias

It is the least biased sampling method, as every member of the target population has an equal chance of being chosen. The purpose of simple random sampling is to give each individual an equal chance of being chosen.

This is meant to represent a group that is free from researcher bias. Like any sampling technique, there is room for error, but this method is intended to be an unbiased approach.

Representativeness

Random sampling ensures that every member of the target population has an equal chance of being selected. This helps to ensure that the sample is representative of the population, making it more likely that the findings can be generalized to the entire population.

Limitations

Expensive and time-consuming.

It is a very expensive and time-consuming method; it is difficult to get the name of every member of the target population, especially if it is a very large population, so it is rarely used.

Access to respondents

This is actually quite hard to achieve – especially if the parent population is large. Since the participants do not volunteer to participate, it can be challenging for researchers to gain access to respondents when drawing from a large population.

Sampling error

Sampling errors can occur when the sample does not accurately represent the population as a whole. If this occurs, the researcher would need to restart the sampling process.

Other techniques

There are four types of random sampling techniques (simple, stratified, cluster, and systematic random sampling.

Stratified Random Sampling

• In stratified random sampling , researchers will first divide a population into subgroups, or strata, based on shared characteristics and then randomly select among these groups.
• This method is typically used when a population has distinct differences, such as demographics, level of education, or age, and can easily be broken into subgroups.

Cluster Random Sampling

• Similar to stratified random sampling, cluster random sampling begins by dividing a population into smaller groups.
• However, in cluster sampling, researchers use naturally formed groups to divide a large population up into clusters and then select randomly among the clusters to form the sample.
• Examples of these pre-existing groups could include school districts, city blocks, or households.

Systematic Random Sampling

• Systematic random sampling involves taking random samples at regular periodic intervals.
• For example, if you were conducting a survey in a cafeteria, you could give a survey to every sixth customer that comes into the cafeteria.
• A sample is the participants you select from a target population (the group you are interested in) to make generalizations about. As an entire population tends to be too large to work with, a smaller group of participants must act as a representative sample.
• Representative means the extent to which a sample mirrors a researcher’s target population and reflects its characteristics (e.g., gender, ethnicity, socioeconomic level). In an attempt to select a representative sample and avoid sampling bias (the over-representation of one category of participant in the sample), psychologists utilize various sampling methods.
• Generalisability means the extent to which their findings can be applied to the larger population of which their sample was a part.

Hayes, A. (2021). Simple Random Sample. Investopedia. Retrieved from https://www.investopedia.com/terms/s/simple-random-sample.asp

Simple random sample: Definition and examples. Statistics How To. (n.d.). Retrieved from https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/simple-random-sample/

Simple random sampling: Definition, examples, and how to do it. Qualtrics. (2022). Retrieved from https://www.qualtrics.com/experience-management/research/simple-random-sampling/ nce-management/research/simple-random-sampling/

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Simple Random Sampling: Definition and Examples

Simple random sampling is a statistical method in which everyone in a population has an equal chance of being selected into a sample. The sample represents a smaller and more manageable portion of the people that can be studied and analyzed. It’s a fundamental technique to gather data and make inferences about a population.

Simple random sampling is considered a fair and unbiased sample selection method.  This type of sampling is the most straightforward sample selection bias method.

What is Simple Random Sampling?

Simple random sampling is a technique where every item in the population has an even chance and likelihood of being selected. Here, the selection of items entirely depends on luck or probability. Therefore, this sampling technique is also a method of chance.

Simple random sampling is a fundamental method and can easily be a component of a more complex method. The main attribute of this sampling method is that every sample has the same probability of being chosen.

The sample size in a simple random sampling method should ideally be more than a few hundred so that it can be applied appropriately. This method is theoretically simple to understand but difficult to implement practically. Working with a large sample size isn’t an easy task, and it can sometimes be challenging to find a realistic sampling bias frame.

Simple Random Sampling Methods

Researchers follow these methods to select a simple random sample:

• They prepare a list of all the population members initially, and each member is marked with a specific number ( for example, if there are nth members, then they will be numbered from 1 to N).
• Researchers from this population choose random samples using random number tables and random number generator software. Researchers prefer random number generator software, as no human interference is necessary to generate samples.

Two approaches aim to minimize any biases in the process of this method:

01. Method of lottery

Using the lottery method is one of the oldest ways and is a mechanical example of a random sample . Researchers draw numbers from the box randomly to choose samples. In this method, the researcher gives each member of the population a number.

02. Use of random numbers

Using random numbers is an alternative method that also involves numbering the population. A numbered table similar to the one below can help with this sampling technique.

Simple Random Sampling Formula

Consider that a hospital has 1000 staff members and must allocate a night shift to 100 members. All their names will be put in a bucket to be randomly selected. Since each person has an equal chance of being selected. Since we know the population size (N) and sample size (n), the calculation can be as follows:

• P = 1 – {( N – 1 ) / N } . ( N – 2) / ( N – 1) . . . (N-n) / {N – ( n – 1 )}
• Cancelling = 1 – {( N – n ) / N } = n / N = 100 / 1000 = 10%

Simple Random Sampling Steps

Simple random sampling is a crucial method in statistical analysis for drawing unbiased conclusions about a population. Below are the steps to perform simple random sampling to select a sample of 100 employees out of a total of 500 in an organization.

Step 1: Make a List

To start simple random sampling, first, make a complete list of all 500 employees in the organization. It’s important that the list includes the names of every employee to guarantee that each person is considered.

A precise and thorough list is crucial to ensure the sampling accurately reflects the entire population.

Step 2: Assign a Sequential Number

After creating the list of employees, the next thing to do is give each employee a number in order. This is your sampling frame (the list from which you draw your sample). This numbering helps organize the list, making identifying each person in the group easier.

Every employee should have their own number, starting from 1 and going up to n, which is the total number of employees in the organization.

Step 3: Choose Sample Size

Selecting the right sample size is important in simple random sampling. In this situation, we’ve chosen a sample of 100 employees from a total population of 500. It’s essential to pick a sample size that’s large enough for dependable results but still practical for analysis.

Step 4: Use a Random Number Generator

To choose a sample from the group, use a random number generator. First, find the total number of people (Step 2) and decide how many we want in our sample (Step 3).

Then, use a random number table or generator to create 100 different random numbers between 1 and 500. These numbers match the order given to each employee, which helps you pick who will be in the sample.

This method ensures that each employee has an equal opportunity for selection, maintaining fairness and impartiality in sample selection.

It is important to note that Simple Random Sampling is just one of many sampling methods available, and it may not always be the best option for your specific research needs.

Simple Random Sample vs Other Sampling Methods

When thinking about how to sample, people often look at different methods like simple random sampling, stratified sampling, systematic sampling, and cluster sampling. Each method has its pros and cons, so it’s crucial to choose the right one depending on what you’re studying and the features of the group you’re looking at.

Simple vs Stratified Random Sample

The simple random sampling techniques and stratified random sampling have different ways of choosing samples from a population.

• Involves the entire population of data.
• Every person or item is equally likely to be chosen.
• Separates the population into groups with similar characteristics.
• Samples are selected independently from each group.

Simple vs Cluster Sampling

While simple random samples treat each individual in the population as a potential sample unit, cluster sampling involves grouping individuals into clusters or natural units before selecting samples.

• No clusters or divisions within the population.
• Each individual has an equal chance of selection.
• Depends on one or more clusters.
• Groups individuals into clusters, and then samples are selected from these clusters.

Simple vs Systematic Sampling

Systematic sampling involves selecting samples at regular intervals after starting randomly.

• No starting point or predetermined pattern.
• It involves choosing samples at regular intervals after a random start.
• It can be easier to implement but may lead to biased results if patterns exist in the data.

LEARN ABOUT: Purposive Sampling

Simple Random Sampling in Research

Today’s market research projects are much larger and involve an indefinite number of items. It is practically impossible to study every member of the population’s thought process and derive interference from the study.

If, as a researcher, you want to save your time and money, simple random sampling is one of the best probability sampling methods that you can use. Getting data from a sample is more advisable and practical.

Using a census or a sample depends on several factors, such as the type of census, the degree of homogeneity/heterogeneity, costs, time, feasibility of study, the degree of accuracy needed, etc.

Advantages of Simple Random Sampling

Simple random sampling has several advantages, including:

• It is a fair sampling method, and if applied appropriately, it helps reduce any bias involved compared to any other sampling method.
• Since it involves a large sample frame, it is usually easy to pick a smaller sample size from the existing larger population.
• The person conducting the research doesn’t need to have prior knowledge of the data he/ she is collecting. One can ask a question to gather the researcher need not be a subject expert.
• This sampling method is a fundamental method of collecting the data . You don’t need any technical knowledge. You only require essential listening and recording skills.
• Since the population size is vast in this type of sampling method, there is no restriction on the sample size that the researcher needs to create. From a larger population, you can get a small sample quite quickly.
• The data collected using this sampling method is valuable. The higher the number of samples, the better the quality of the data.

Overall, this is a valuable and versatile method for gathering data and making inferences about populations.

Disadvantages of Simple Random Sampling

Simple random sampling has some drawbacks that can affect the relevance of the collected data:

• Sampling errors may happen if the sample doesn’t accurately reflect the intended population.
• Excluding specific groups could lead to skewed results because of imbalanced population demographics.
• Analyzing research results from simple random sampling can be time-consuming and expensive, especially depending on the data’s size and format.
• The sample’s random selection may cause differences in the representation of the population.
• Inaccurate results may arise due to non-response bias when certain groups choose not to participate in the research.

LEARN ABOUT: Survey Sampling

Researchers use simple random sampling in statistical analysis methods valuable for various applications. Selecting a sample of individuals from a population in a random and unbiased manner provides a representative sample and a cost-effective way of gathering data and making inferences about populations.

With QuestionPro, researchers and data analysts can easily and efficiently implement simple random sampling in their research and studies. We are here to help to ensure that the results are accurate.

If you’re a market researcher trying to learn more about your target audience or a social scientist aiming to study a population, Simple Random Sampling with QuestionPro is a dependable and efficient method to explore.

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Simple Random Sampling

Simple random sampling (also referred to as random sampling or method of chances) is the purest and the most straightforward probability sampling strategy. It is also the most popular method for choosing a sample among population for a wide range of purposes. This method is considered to be the most unbiased representation of population. Nevertheless, sampling error persists with this method, similar to other sampling methods.

In simple random sampling each member of population is equally likely to be chosen as part of the sample. It has been stated that “the logic behind simple random sampling is that it removes bias from the selection procedure and should result in representative samples” [1] .

Ideally, the sample size of more than a few hundred is required in order to be able to apply simple random method in an appropriate manner. [2] It can be argued that this method is easy to understand in theory, but difficult to perform in practice. This is because working with a large sample size is not easy and it can be a challenge to get a realistic sampling frame.

Many dissertation supervisors advice the choice of random sampling methods due to the representativeness of sample group and less room for researcher bias compared to non-random sampling techniques. However, application of these methods in practice can be quite difficult due to the need for the complete list of relevant population members and a large sample size.

Other variations of random sampling include the following:

• Stratified random sampling
• Systematic random sampling
• Multistage random sampling
• Cluster sampling

There are two popular approaches that are aimed to minimize the relevance of bias in the process of random sampling selection: method of lottery and the use of random numbers.

The method of lottery is the most primitive and mechanical example of random sampling. In this method you will have to number each member of population in a consequent manner, writing numbers in separate pieces of paper. These pieces of papers are to be folded and mixed into a box. Lastly, samples are to be taken randomly from the box by choosing folded pieces of papers in a random manner.

The use of random numbers , an alternative method also involves numbering of population members from 1 to  N.  Then, the sample size of  N  has to be determined by selecting numbers randomly. The use of random number table similar to one below can help greatly with the application of this sampling technique.

Application of Simple Random Sampling: an Example

Let’s assume that as part of your dissertation you are assessing leadership practices on work-life balance in ABC Limited that has 600 employees. You have chosen survey as primary data collection method for this research. In this scenario you can apply simple random sampling method involves the following manner:

• Prepare the list of all 600 employees working for ABC Limited
• Assign a sequential number for each employee from 1 to N (in your case from 1 to 600).
• Determine the sample size. In your case the sample size of 150 respondents might be sufficient to achieve research objectives.
• Use random number generator and generate 150 numbers from 1 to 600. You can do it using software such as Research Randomizer, Stat Trek or any other. Once random numbers are generated, in total 150 employees assigned with respective generated numbers are going to represent sample group members for your research.

Advantages of Simple Random Sampling

• If applied appropriately, simple random sampling is associated with the minimum amount of sampling bias compared to other sampling methods.
• Given the large sample frame is available, the ease of forming the sample group i.e. selecting samples is one of the main advantages of this method.
• Research findings can be generalized due to representativeness of this sampling technique and a little relevance of bias.
• It is straightforward sampling method that requires no advanced technical knowledge

Disadvantages of Simple Random Sampling

• It is important to note that application of random sampling method requires a list of all potential respondents (sampling frame) to be available beforehand and this can be costly and time-consuming for large studies.
• The necessity to have a large sample size can be a major disadvantage in practical levels.
• This sampling method is not suitable for studies that involve face-to-face interviews covering a large geographical area due to cost and time considerations.

My e-book,  The Ultimate Guide to Writing a Dissertation in Business Studies: a step by step approach contains a detailed, yet simple explanation of sampling methods. The e-book explains all stages of the research process starting from the selection of the research area to writing personal reflection. Important elements of dissertations such as research philosophy, research approach, research design, methods of data collection and data analysis are explained in this e-book in simple words.

John Dudovskiy

[1] Gravetter, F.J & Forzano, L.B. (2011) “Research Methods for the Behavioural Sciences” Cengage Learning p.146

[2] Saunders, M., Lewis, P. & Thornhill, A. (2012) “Research Methods for Business Students” 6 th  edition, Pearson Education Limited

Simple Random Sampling

Definition and Different Approaches

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Simple random sampling is the most basic and common type of  sampling method  used in quantitative social science research and in scientific research generally .  The main benefit of the simple random sample is that each member of the population has an equal chance of being chosen for the study. This means that it guarantees that the sample chosen is representative of the population and that the sample is selected in an unbiased way. In turn, the statistical conclusions drawn from the analysis of the sample will ​be valid .​

There are multiple ways of creating a simple random sample. These include the lottery method, using a random number table, using a computer, and sampling with or without replacement.

Lottery Method of Sampling

The lottery method of creating a simple random sample is exactly what it sounds like. A researcher randomly picks numbers, with each number corresponding to a subject or item, in order to create the sample. To create a sample this way, the researcher must ensure that the numbers are well mixed before selecting the sample population.

Using a Random Number Table

One of the most convenient ways of creating a simple random sample is to use a random number table . These are commonly found at the back of textbooks on the topics of statistics or research methods. Most random number tables will have as many as 10,000 random numbers. These will be composed of integers between zero and nine and arranged in groups of five. These tables are carefully created to ensure that each number is equally probable, so using it is a way to produce a random sample required for valid research outcomes.

To create a simple random sample using a random number table just follow these steps.

• Number each member of the population 1 to N.
• Determine the population size and sample size.
• Select a starting point on the random number table. (The best way to do this is to close your eyes and point randomly onto the page. Whichever number your finger is touching is the number you start with.)
• Choose a direction in which to read (up to down, left to right, or right to left).
• Select the first n numbers (however many numbers are in your sample) whose last X digits are between 0 and N. For instance, if N is a 3 digit number, then X would be 3. Put another way, if your population contained 350 people, you would use numbers from the table whose last 3 digits were between 0 and 350. If the number on the table was 23957, you would not use it because the last 3 digits (957) is greater than 350. You would skip this number and move to the next one. If the number is 84301, you would use it and you would select the person in the population who is assigned the number 301.
• Continue this way through the table until you have selected your entire sample , whatever your n is. The numbers you selected then correspond to the numbers assigned to the members of your population, and those selected become your sample.

Using a Computer

In practice, the lottery method of selecting a random sample can be quite burdensome if done by hand. Typically, the population being studied is large and choosing a random sample by hand would be very time-consuming. Instead, there are several computer programs that can assign numbers and select n random numbers quickly and easily. Many can be found online for free.

Sampling With Replacement

Sampling with replacement is a method of random sampling in which members or items of the population can be chosen more than once for inclusion in the sample. Let’s say we have 100 names each written on a piece of paper. All of those pieces of paper are put into a bowl and mixed up. The researcher picks a name from the bowl, records the information to include that person in the sample, then puts the name back in the bowl, mixes up the names, and selects another piece of paper. The person that was just sampled has the same chance of being selected again. This is known as sampling with replacement.

Sampling Without Replacement

Sampling without replacement is a method of random sampling in which members or items of the population can only be selected one time for inclusion in the sample. Using the same example above, let’s say we put the 100 pieces of paper in a bowl, mix them up, and randomly select one name to include in the sample. This time, however, we record the information to include that person in the sample and then set that piece of paper aside rather than putting it back into the bowl. Here, each element of the population can only be selected one time.

• Simple Random Samples From a Table of Random Digits
• How Systematic Sampling Works
• The Difference Between Simple and Systematic Random Sampling
• The Different Types of Sampling Designs in Sociology
• What Is a Table of Random Digits in Statistics?
• Understanding Stratified Samples and How to Make Them
• Cluster Sample in Sociology Research
• What Is Statistical Sampling?
• Types of Samples in Statistics
• Sampling With or Without Replacement
• What Is a Systematic Sample?
• What Is a Sampling Distribution
• What Is a Population in Statistics?
• How to Calculate the Margin of Error
• Sampling in Archaeology
• Calculate a Confidence Interval for a Mean When You Know Sigma

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Neag School of Education

Educational Research Basics by Del Siegle

Simple random sampling.

SIMPLE RANDOM SAMPLING – Each subject in the population has an equal chance of being selected regardless of what other subjects have or will be selected. While this is desirable, it may not be possible.

A random number table or computer program is often employed to generate a list of random numbers to use.

A simple procedure is to place the names from the population is a hat and draw out the number of names one wishes to use for a sample.

Del Siegle, Ph.D. Neag School of Education – University of Connecticut [email protected] www.delsiegle.com

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Simple Random Sampling – Definition & Examples

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In simple random sampling, each member of the target population has an equal chance of being selected, ensuring an unbiased representation. This methodology allows researchers to make generalized conclusions about the population based on the sample, bolstering the reliability and validity of the study’s findings. Moreover, the ease of understanding and implementation makes simple random sampling a popular choice among researchers across various fields.

Inhaltsverzeichnis

• 1 Simple Random Sampling – In a Nutshell
• 2 Definition: Simple random sampling
• 3 When do you use simple random sampling?
• 4 Simple random sampling: 4 Steps

Simple Random Sampling – In a Nutshell

There are several methods of simple random sampling which aim to produce the most accurate sample.

Simple random sampling has many benefits as it generally reduces bias and gives every member of the population an equal chance to participate in a study.

Definition: Simple random sampling

Simple random sampling refers to the process of randomly picking a sample from a population without any prior defined selection process.

Since the sample selection is entirely arbitrary, simple random selection is used in research as an unbiased method of studying subsets in a given population.

When do you use simple random sampling?

Depending on several factors, such as population size, it may be challenging to undertake simple random sampling. Some of the conditions for simple random sampling include:

• A comprehensive list of all the members in the target population
• A reliable method of contacting the members who have been selected for the study
• Adequate time and resources such as manpower, collection materials, and budgetary allocations.

Simple random sampling is used in research cases that involve a large population. It is the best approach in such instances since every sample is picked randomly. Thus, the resulting sample is assumed to be more inclusive of the main themes in the larger population. Additionally, simple random sampling can be used in cases where time and resources are readily available.

Researchers may use a combination of two probability sampling techniques based on the objectives of a case study . For example, simple random sampling may be used to construct the initial sample then systematic sampling may be applied to further distill the sample. The main types of probability sampling used in research include:

Simple random sampling: 4 Steps

Step 1 of simple random sampling: Define the population

• In the study of Teaching Staff in the US, the population equals all the 3.2 million teachers in different capacities within the US.

Step 2 of simple random sampling: Decide on the sample size

You can use standard deviation, confidence interval , and confidence level metrics. The most preferred confidence interval is 0.05 , while the confidence level usually is 0.95 .

If you are unsure of the standard deviation , choose a number such as 0.5 , which can accommodate a range of possibilities. A sample size calculator can then be used to estimate the sample size.

• The Harvard study on well-being and happiness has been studying the lives of 724 men over the last few decades.
• This group of men was identified at a young age from different socioeconomic backgrounds.
• While this sample is small, it accommodates a range of factors such as income, family size, and education.
• These variables are distributed among the study members, offering a detailed report.

Step 3 of simple random sampling: Randomly select your sample

• Each member is assigned a number; these numbers are drawn randomly from a pool.
• Computer software may be used to do the same task.
• The members of the population are tagged with numbers.
• Rearchers then use different number generators to generate random numbers to be used in the sample.
• Other tools used in number generation include the RAND function in Microsoft Excel.
• The World Health Organization stipulates the random sampling of patients on new drug test runs.

Step 4 of simple random sampling: Collect data from your sample

Researchers need to ensure every member selected for sampling is available and willing to participate in the study. If any members fail to co-operate or withdraw from the study, it may interfere with the accuracy of the findings.

• The American Housing Survey invites participants through their website.
• If the recipients fail to respond, a follow-up email and a physical visit may be arranged.
• This ensures that most if not all of the respondents participate in the study to inform policy development.

What are the advantages of simple random sampling?

Simple random sampling reduces the chances of errors from pre-selected members of a sample. It is also easy to carry out as the methods are relatively straightforward.

What are the downsides of simple random sampling?

Simple random sampling may not be applicable where the population is distributed across a large area.

Researchers may also face challenges accessing the sample group.

Additionally, simple random selection may be time-consuming and expensive over a period of time.

What is simple random sampling?

It is a probabilistic method of sample selection.

Members of a population are selected based on homogenous and heterogeneous characteristics.

Researchers use this type of sampling to study defined research goals in a large population.

What are the methods used in simple random sampling?

The main methods used include;

• systematic sampling
• clustered sampling
• stratified sampling

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How to collect a simple random sample

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It’s nearly impossible to get insights from your entire group of consumers, which is why random sampling is a good way to tap into those insights. Simple random samples are a subset of individuals that is representative of the whole group. Read on to find out more about simple random samples and the steps needed to collect yours.

What is a simple random sample?

A simple random sample is a type of probability sampling method used in market research and other types of studies. Simple random sampling selects a small subset from a larger group of participants. The technique provides each person from the larger population with an equal and fair chance of being selected for the smaller group. This is just one of several types of sampling for market research .

Using the simple random sampling process ensures that your small sample group will be representative of the total population—and free from researcher bias. For example, if a business owner with a large corporate office is studying the effects of employees working from home, his belief that he needs people to inhabit the space could prompt him to choose a sampling of people who are like-minded. This research bias would influence the results and skew them towards his desired outcome of having his employees in the office. Simple random samples prevent bias from influencing the results.

Want to calculate your sample size?

Check out our sample size calculator to help determine the right number of responses you need for your survey.

SurveyMonkey Audience makes simple random sampling even simpler. The tool ensures high-quality results easily, quickly, and on-demand. If you don’t have the contact details or the number of participants for the population you want to survey, give SurveyMonkey Audience a try. Once you have your sample selected and you send your survey, your data will be collected in a customizable dashboard for easy analysis and sharing.

Advantages of simple random samples

There are some definite advantages to using simple random samples:

• Your data set is unaffected by researcher bias
• All members of your larger population have an equal and fair chance of being selected
• Data represents the larger population, so no segmenting is needed to refine results
• Generalized results provide accurate information for sweeping decisions
• It’s fast and easy to complete
• No technical knowledge is required

Now that you understand what it is and its advantages, let’s talk about when you should use simple random sampling.

When to use simple random sampling

Simple random sampling is used when you need to make generalizations about a specific population without any bias. It works best if you use an online tool like SurveyMonkey for conducting simple random sampling studies, collecting data, and distributing results. You also need access to a complete list of the population you are targeting and a way to contact each person who is selected for the study. SurveyMonkey Audience is very useful in identifying and contacting individuals in your sample. 

Simple vs. stratified random sampling

Sometimes, simple random sampling isn’t the best method for finding your sample group. Simple random sampling takes its participants randomly from the total population you’ve identified. 

Stratified random sampling , another form of probability sampling, uses subdivisions in the population that need to be accounted for. Each smaller group is identified as strata and an equal number from the strata is randomly selected to ensure all groups are represented. So, if you’re studying the wage gap between gender identities, you’ll need to distinguish between male, female, and those who do not identify as either male or female participants to ensure that they are equally represented within your sample group. 

If simple random sampling is right for your research, use the following steps to collect your simple random sample.

There are four key steps in selecting a simple random sample.

Step 1: Define the population

What population do you want to research? Remember, you need to be able to contact each member of the population you choose so that you can collect data from everyone selected for the sample. This, again, is where SurveyMonkey Audience is a lifesaver.

Step 2: Determine the sample size

While a larger sample size yields more statistical certainty, it will cost more and take more time. But if your sample size is too small, your data may not be accurate. How do you know what your sample size should be? 

N = population size ᐧ e = Margin of error (percentage in decimal form) ᐧ z = z-score

Step 3: Randomly select the sample

There are two ways to select your sample randomly. Both remove bias from the selection process. Before you begin, prepare a list of the full population you are choosing from, along with their contact information. 

Lottery method

You’ve probably used the lottery method to make selections in other circumstances. You start with a list of names of the people in your full population—ensure that you have contact information for each one.

• Print out the names of the people in your population
• Cut each name out
• Put each individual piece of paper with a name on it into a bowl
• Make sure the name papers are well mixed before beginning to make selections
• Pull names out at random until you reach your selected sample size
• Create a table with the corresponding contact information for each selection for easy reference.

Use of random numbers

If you prefer, you can use a random number generator —it’s easy to create one in an Excel spreadsheet using the formula =RAND() . Follow these steps to create your simple random sample with Excel:

• Enter the names of the customers you have contact information for in the first column
• Add a new column to the right and name it Random_number
• Make a third column for the email addresses of each customer
• In the first row under the heading row, in the Random_number column, enter the formula =RAND()
• Press enter and a random number will appear in the selected cell
• Select the cell with the new random number in it
• Drag the small box at the bottom right corner of the cell and drag the box down the column to the bottom of the list—this generates a new random number for each name on your list
• Highlight all random numbers in the Random_number column
• Highlight the random numbers again and right-click on them
• Click paste special
• Click paste values
• This removes the random function from the cells
• Highlight the columns with data and numbers in them
• Click Sort and Filter
• Click Custom Sort
• Sort by the column with the random numbers
• Order smallest to largest
• Your list has now been randomly sorted, and you can select the first 10 or 200—whatever you need your sample size to be—and that’s the list of your randomized participants.

Step 4: Collect data from your sample

Once you have your random sample selected, it’s time to collect data. Do your best to ensure that every individual participates in the study, or your findings may be biased because a group is underrepresented in your sample.

Set a due date for individuals to complete your survey. If any do not respond, send an email requesting that they do so. You may need to call to speak to non-responding participants to prompt them to participate. A higher response rate equals more valid results.

Example of random sampling

Wondering how this looks in practice? Let’s look at some examples of circumstances that use simple random sampling:

• At a children’s party, teams are chosen for games by putting everyone’s name in a hat and choosing them at random
• A pharmaceutical company is ready to test the efficacy of a new drug. Volunteers are chosen at random—half receiving the medication and half receiving a placebo
• The American Community Survey (ACS) is used by the US Census Bureau to follow a random sample of US citizens for a year to draw conclusions about the entire US population

How will you use simple random sampling?

As long as you have a list of your target population and ways to reach them, you can use simple random sampling. If you don’t have a list, SurveyMonkey Audience will help you find your ideal population—customized to your needs. And if you’re not sure what sample size is right for your study, use our sample size calculator . Just plug in your total population, the margin of error, and confidence level. Good luck!

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Home » Sampling Methods – Types, Techniques and Examples

Sampling Methods – Types, Techniques and Examples

Table of Contents

Sampling refers to the process of selecting a subset of data from a larger population or dataset in order to analyze or make inferences about the whole population.

In other words, sampling involves taking a representative sample of data from a larger group or dataset in order to gain insights or draw conclusions about the entire group.

Sampling Methods

Sampling methods refer to the techniques used to select a subset of individuals or units from a larger population for the purpose of conducting statistical analysis or research.

Sampling is an essential part of the Research because it allows researchers to draw conclusions about a population without having to collect data from every member of that population, which can be time-consuming, expensive, or even impossible.

Types of Sampling Methods

Sampling can be broadly categorized into two main categories:

Probability Sampling

This type of sampling is based on the principles of random selection, and it involves selecting samples in a way that every member of the population has an equal chance of being included in the sample.. Probability sampling is commonly used in scientific research and statistical analysis, as it provides a representative sample that can be generalized to the larger population.

Type of Probability Sampling :

• Simple Random Sampling: In this method, every member of the population has an equal chance of being selected for the sample. This can be done using a random number generator or by drawing names out of a hat, for example.
• Systematic Sampling: In this method, the population is first divided into a list or sequence, and then every nth member is selected for the sample. For example, if every 10th person is selected from a list of 100 people, the sample would include 10 people.
• Stratified Sampling: In this method, the population is divided into subgroups or strata based on certain characteristics, and then a random sample is taken from each stratum. This is often used to ensure that the sample is representative of the population as a whole.
• Cluster Sampling: In this method, the population is divided into clusters or groups, and then a random sample of clusters is selected. Then, all members of the selected clusters are included in the sample.
• Multi-Stage Sampling : This method combines two or more sampling techniques. For example, a researcher may use stratified sampling to select clusters, and then use simple random sampling to select members within each cluster.

Non-probability Sampling

This type of sampling does not rely on random selection, and it involves selecting samples in a way that does not give every member of the population an equal chance of being included in the sample. Non-probability sampling is often used in qualitative research, where the aim is not to generalize findings to a larger population, but to gain an in-depth understanding of a particular phenomenon or group. Non-probability sampling methods can be quicker and more cost-effective than probability sampling methods, but they may also be subject to bias and may not be representative of the larger population.

Types of Non-probability Sampling :

• Convenience Sampling: In this method, participants are chosen based on their availability or willingness to participate. This method is easy and convenient but may not be representative of the population.
• Purposive Sampling: In this method, participants are selected based on specific criteria, such as their expertise or knowledge on a particular topic. This method is often used in qualitative research, but may not be representative of the population.
• Snowball Sampling: In this method, participants are recruited through referrals from other participants. This method is often used when the population is hard to reach, but may not be representative of the population.
• Quota Sampling: In this method, a predetermined number of participants are selected based on specific criteria, such as age or gender. This method is often used in market research, but may not be representative of the population.
• Volunteer Sampling: In this method, participants volunteer to participate in the study. This method is often used in research where participants are motivated by personal interest or altruism, but may not be representative of the population.

Applications of Sampling Methods

Applications of Sampling Methods from different fields:

• Psychology : Sampling methods are used in psychology research to study various aspects of human behavior and mental processes. For example, researchers may use stratified sampling to select a sample of participants that is representative of the population based on factors such as age, gender, and ethnicity. Random sampling may also be used to select participants for experimental studies.
• Sociology : Sampling methods are commonly used in sociological research to study social phenomena and relationships between individuals and groups. For example, researchers may use cluster sampling to select a sample of neighborhoods to study the effects of economic inequality on health outcomes. Stratified sampling may also be used to select a sample of participants that is representative of the population based on factors such as income, education, and occupation.
• Social sciences: Sampling methods are commonly used in social sciences to study human behavior and attitudes. For example, researchers may use stratified sampling to select a sample of participants that is representative of the population based on factors such as age, gender, and income.
• Marketing : Sampling methods are used in marketing research to collect data on consumer preferences, behavior, and attitudes. For example, researchers may use random sampling to select a sample of consumers to participate in a survey about a new product.
• Healthcare : Sampling methods are used in healthcare research to study the prevalence of diseases and risk factors, and to evaluate interventions. For example, researchers may use cluster sampling to select a sample of health clinics to participate in a study of the effectiveness of a new treatment.
• Environmental science: Sampling methods are used in environmental science to collect data on environmental variables such as water quality, air pollution, and soil composition. For example, researchers may use systematic sampling to collect soil samples at regular intervals across a field.
• Education : Sampling methods are used in education research to study student learning and achievement. For example, researchers may use stratified sampling to select a sample of schools that is representative of the population based on factors such as demographics and academic performance.

Examples of Sampling Methods

Probability Sampling Methods Examples:

• Simple random sampling Example : A researcher randomly selects participants from the population using a random number generator or drawing names from a hat.
• Stratified random sampling Example : A researcher divides the population into subgroups (strata) based on a characteristic of interest (e.g. age or income) and then randomly selects participants from each subgroup.
• Systematic sampling Example : A researcher selects participants at regular intervals from a list of the population.

Non-probability Sampling Methods Examples:

• Convenience sampling Example: A researcher selects participants who are conveniently available, such as students in a particular class or visitors to a shopping mall.
• Purposive sampling Example : A researcher selects participants who meet specific criteria, such as individuals who have been diagnosed with a particular medical condition.
• Snowball sampling Example : A researcher selects participants who are referred to them by other participants, such as friends or acquaintances.

How to Conduct Sampling Methods

some general steps to conduct sampling methods:

• Define the population: Identify the population of interest and clearly define its boundaries.
• Choose the sampling method: Select an appropriate sampling method based on the research question, characteristics of the population, and available resources.
• Determine the sample size: Determine the desired sample size based on statistical considerations such as margin of error, confidence level, or power analysis.
• Create a sampling frame: Develop a list of all individuals or elements in the population from which the sample will be drawn. The sampling frame should be comprehensive, accurate, and up-to-date.
• Select the sample: Use the chosen sampling method to select the sample from the sampling frame. The sample should be selected randomly, or if using a non-random method, every effort should be made to minimize bias and ensure that the sample is representative of the population.
• Collect data: Once the sample has been selected, collect data from each member of the sample using appropriate research methods (e.g., surveys, interviews, observations).
• Analyze the data: Analyze the data collected from the sample to draw conclusions about the population of interest.

When to use Sampling Methods

Sampling methods are used in research when it is not feasible or practical to study the entire population of interest. Sampling allows researchers to study a smaller group of individuals, known as a sample, and use the findings from the sample to make inferences about the larger population.

Sampling methods are particularly useful when:

• The population of interest is too large to study in its entirety.
• The cost and time required to study the entire population are prohibitive.
• The population is geographically dispersed or difficult to access.
• The research question requires specialized or hard-to-find individuals.
• The data collected is quantitative and statistical analyses are used to draw conclusions.

Purpose of Sampling Methods

The main purpose of sampling methods in research is to obtain a representative sample of individuals or elements from a larger population of interest, in order to make inferences about the population as a whole. By studying a smaller group of individuals, known as a sample, researchers can gather information about the population that would be difficult or impossible to obtain from studying the entire population.

Sampling methods allow researchers to:

• Study a smaller, more manageable group of individuals, which is typically less time-consuming and less expensive than studying the entire population.
• Reduce the potential for data collection errors and improve the accuracy of the results by minimizing sampling bias.
• Make inferences about the larger population with a certain degree of confidence, using statistical analyses of the data collected from the sample.
• Improve the generalizability and external validity of the findings by ensuring that the sample is representative of the population of interest.

Characteristics of Sampling Methods

Here are some characteristics of sampling methods:

• Randomness : Probability sampling methods are based on random selection, meaning that every member of the population has an equal chance of being selected. This helps to minimize bias and ensure that the sample is representative of the population.
• Representativeness : The goal of sampling is to obtain a sample that is representative of the larger population of interest. This means that the sample should reflect the characteristics of the population in terms of key demographic, behavioral, or other relevant variables.
• Size : The size of the sample should be large enough to provide sufficient statistical power for the research question at hand. The sample size should also be appropriate for the chosen sampling method and the level of precision desired.
• Efficiency : Sampling methods should be efficient in terms of time, cost, and resources required. The method chosen should be feasible given the available resources and time constraints.
• Bias : Sampling methods should aim to minimize bias and ensure that the sample is representative of the population of interest. Bias can be introduced through non-random selection or non-response, and can affect the validity and generalizability of the findings.
• Precision : Sampling methods should be precise in terms of providing estimates of the population parameters of interest. Precision is influenced by sample size, sampling method, and level of variability in the population.
• Validity : The validity of the sampling method is important for ensuring that the results obtained from the sample are accurate and can be generalized to the population of interest. Validity can be affected by sampling method, sample size, and the representativeness of the sample.

Advantages of Sampling Methods

Sampling methods have several advantages, including:

• Cost-Effective : Sampling methods are often much cheaper and less time-consuming than studying an entire population. By studying only a small subset of the population, researchers can gather valuable data without incurring the costs associated with studying the entire population.
• Convenience : Sampling methods are often more convenient than studying an entire population. For example, if a researcher wants to study the eating habits of people in a city, it would be very difficult and time-consuming to study every single person in the city. By using sampling methods, the researcher can obtain data from a smaller subset of people, making the study more feasible.
• Accuracy: When done correctly, sampling methods can be very accurate. By using appropriate sampling techniques, researchers can obtain a sample that is representative of the entire population. This allows them to make accurate generalizations about the population as a whole based on the data collected from the sample.
• Time-Saving: Sampling methods can save a lot of time compared to studying the entire population. By studying a smaller sample, researchers can collect data much more quickly than they could if they studied every single person in the population.
• Less Bias : Sampling methods can reduce bias in a study. If a researcher were to study the entire population, it would be very difficult to eliminate all sources of bias. However, by using appropriate sampling techniques, researchers can reduce bias and obtain a sample that is more representative of the entire population.

Limitations of Sampling Methods

• Sampling Error : Sampling error is the difference between the sample statistic and the population parameter. It is the result of selecting a sample rather than the entire population. The larger the sample, the lower the sampling error. However, no matter how large the sample size, there will always be some degree of sampling error.
• Selection Bias: Selection bias occurs when the sample is not representative of the population. This can happen if the sample is not selected randomly or if some groups are underrepresented in the sample. Selection bias can lead to inaccurate conclusions about the population.
• Non-response Bias : Non-response bias occurs when some members of the sample do not respond to the survey or study. This can result in a biased sample if the non-respondents differ from the respondents in important ways.
• Time and Cost : While sampling can be cost-effective, it can still be expensive and time-consuming to select a sample that is representative of the population. Depending on the sampling method used, it may take a long time to obtain a sample that is large enough and representative enough to be useful.
• Limited Information : Sampling can only provide information about the variables that are measured. It may not provide information about other variables that are relevant to the research question but were not measured.
• Generalization : The extent to which the findings from a sample can be generalized to the population depends on the representativeness of the sample. If the sample is not representative of the population, it may not be possible to generalize the findings to the population as a whole.

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• v.91(3); May-Jun 2016

Sampling: how to select participants in my research study? *

Jeovany martínez-mesa.

1 Faculdade Meridional (IMED) - Passo Fundo (RS), Brazil.

David Alejandro González-Chica

2 University of Adelaide - Adelaide, Australia.

Rodrigo Pereira Duquia

3 Universidade Federal de Ciências da Saúde de Porto Alegre (UFCSPA) - Porto Alegre (RS), Brazil.

Renan Rangel Bonamigo

João luiz bastos.

4 Universidade Federal de Santa Catarina (UFSC) - Florianópolis (RS), Brazil.

In this paper, the basic elements related to the selection of participants for a health research are discussed. Sample representativeness, sample frame, types of sampling, as well as the impact that non-respondents may have on results of a study are described. The whole discussion is supported by practical examples to facilitate the reader's understanding.

To introduce readers to issues related to sampling.

INTRODUCTION

The essential topics related to the selection of participants for a health research are: 1) whether to work with samples or include the whole reference population in the study (census); 2) the sample basis; 3) the sampling process and 4) the potential effects nonrespondents might have on study results. We will refer to each of these aspects with theoretical and practical examples for better understanding in the sections that follow.

TO SAMPLE OR NOT TO SAMPLE

In a previous paper, we discussed the necessary parameters on which to estimate the sample size. 1 We define sample as a finite part or subset of participants drawn from the target population. In turn, the target population corresponds to the entire set of subjects whose characteristics are of interest to the research team. Based on results obtained from a sample, researchers may draw their conclusions about the target population with a certain level of confidence, following a process called statistical inference. When the sample contains fewer individuals than the minimum necessary, but the representativeness is preserved, statistical inference may be compromised in terms of precision (prevalence studies) and/or statistical power to detect the associations of interest. 1 On the other hand, samples without representativeness may not be a reliable source to draw conclusions about the reference population (i.e., statistical inference is not deemed possible), even if the sample size reaches the required number of participants. Lack of representativeness can occur as a result of flawed selection procedures (sampling bias) or when the probability of refusal/non-participation in the study is related to the object of research (nonresponse bias). 1 , 2

Although most studies are performed using samples, whether or not they represent any target population, census-based estimates should be preferred whenever possible. 3 , 4 For instance, if all cases of melanoma are available on a national or regional database, and information on the potential risk factors are also available, it would be preferable to conduct a census instead of investigating a sample.

However, there are several theoretical and practical reasons that prevent us from carrying out census-based surveys, including:

• Ethical issues: it is unethical to include a greater number of individuals than that effectively required;
• Budgetary limitations: the high costs of a census survey often limits its use as a strategy to select participants for a study;
• Logistics: censuses often impose great challenges in terms of required staff, equipment, etc. to conduct the study;
• Time restrictions: the amount of time needed to plan and conduct a census-based survey may be excessive; and,
• Unknown target population size: if the study objective is to investigate the presence of premalignant skin lesions in illicit drugs users, lack of information on all existing users makes it impossible to conduct a census-based study.

All these reasons explain why samples are more frequently used. However, researchers must be aware that sample results can be affected by the random error (or sampling error). 3 To exemplify this concept, we will consider a research study aiming to estimate the prevalence of premalignant skin lesions (outcome) among individuals >18 years residing in a specific city (target population). The city has a total population of 4,000 adults, but the investigator decided to collect data on a representative sample of 400 participants, detecting an 8% prevalence of premalignant skin lesions. A week later, the researcher selects another sample of 400 participants from the same target population to confirm the results, but this time observes a 12% prevalence of premalignant skin lesions. Based on these findings, is it possible to assume that the prevalence of lesions increased from the first to the second week? The answer is probably not. Each time we select a new sample, it is very likely to obtain a different result. These fluctuations are attributed to the "random error." They occur because individuals composing different samples are not the same, even though they were selected from the same target population. Therefore, the parameters of interest may vary randomly from one sample to another. Despite this fluctuation, if it were possible to obtain 100 different samples of the same population, approximately 95 of them would provide prevalence estimates very close to the real estimate in the target population - the value that we would observe if we investigated all the 4,000 adults residing in the city. Thus, during the sample size estimation the investigator must specify in advance the highest or maximum acceptable random error value in the study. Most population-based studies use a random error ranging from 2 to 5 percentage points. Nevertheless, the researcher should be aware that the smaller the random error considered in the study, the larger the required sample size. 1

SAMPLE FRAME

The sample frame is the group of individuals that can be selected from the target population given the sampling process used in the study. For example, to identify cases of cutaneous melanoma the researcher may consider to utilize as sample frame the national cancer registry system or the anatomopathological records of skin biopsies. Given that the sample may represent only a portion of the target population, the researcher needs to examine carefully whether the selected sample frame fits the study objectives or hypotheses, and especially if there are strategies to overcome the sample frame limitations (see Chart 1 for examples and possible limitations).

Examples of sample frames and potential limitations as regards representativeness

Sampling can be defined as the process through which individuals or sampling units are selected from the sample frame. The sampling strategy needs to be specified in advance, given that the sampling method may affect the sample size estimation. 1 , 5 Without a rigorous sampling plan the estimates derived from the study may be biased (selection bias). 3

TYPES OF SAMPLING

In figure 1 , we depict a summary of the main sampling types. There are two major sampling types: probabilistic and nonprobabilistic.

Sampling types used in scientific studies

NONPROBABILISTIC SAMPLING

In the context of nonprobabilistic sampling, the likelihood of selecting some individuals from the target population is null. This type of sampling does not render a representative sample; therefore, the observed results are usually not generalizable to the target population. Still, unrepresentative samples may be useful for some specific research objectives, and may help answer particular research questions, as well as contribute to the generation of new hypotheses. 4 The different types of nonprobabilistic sampling are detailed below.

Convenience sampling : the participants are consecutively selected in order of apperance according to their convenient accessibility (also known as consecutive sampling). The sampling process comes to an end when the total amount of participants (sample saturation) and/or the time limit (time saturation) are reached. Randomized clinical trials are usually based on convenience sampling. After sampling, participants are usually randomly allocated to the intervention or control group (randomization). 3 Although randomization is a probabilistic process to obtain two comparable groups (treatment and control), the samples used in these studies are generally not representative of the target population.

Purposive sampling: this is used when a diverse sample is necessary or the opinion of experts in a particular field is the topic of interest. This technique was used in the study by Roubille et al, in which recommendations for the treatment of comorbidities in patients with rheumatoid arthritis, psoriasis, and psoriatic arthritis were made based on the opinion of a group of experts. 6

Quota sampling: according to this sampling technique, the population is first classified by characteristics such as gender, age, etc. Subsequently, sampling units are selected to complete each quota. For example, in the study by Larkin et al., the combination of vemurafenib and cobimetinib versus placebo was tested in patients with locally-advanced melanoma, stage IIIC or IV, with BRAF mutation. 7 The study recruited 495 patients from 135 health centers located in several countries. In this type of study, each center has a "quota" of patients.

"Snowball" sampling : in this case, the researcher selects an initial group of individuals. Then, these participants indicate other potential members with similar characteristics to take part in the study. This is frequently used in studies investigating special populations, for example, those including illicit drugs users, as was the case of the study by Gonçalves et al, which assessed 27 users of cocaine and crack in combination with marijuana. 8

PROBABILISTIC SAMPLING

In the context of probabilistic sampling, all units of the target population have a nonzero probability to take part in the study. If all participants are equally likely to be selected in the study, equiprobabilistic sampling is being used, and the odds of being selected by the research team may be expressed by the formula: P=1/N, where P equals the probability of taking part in the study and N corresponds to the size of the target population. The main types of probabilistic sampling are described below.

Simple random sampling: in this case, we have a full list of sample units or participants (sample basis), and we randomly select individuals using a table of random numbers. An example is the study by Pimenta et al, in which the authors obtained a listing from the Health Department of all elderly enrolled in the Family Health Strategy and, by simple random sampling, selected a sample of 449 participants. 9

Systematic random sampling: in this case, participants are selected from fixed intervals previously defined from a ranked list of participants. For example, in the study of Kelbore et al, children who were assisted at the Pediatric Dermatology Service were selected to evaluate factors associated with atopic dermatitis, selecting always the second child by consulting order. 10

Stratified sampling: in this type of sampling, the target population is first divided into separate strata. Then, samples are selected within each stratum, either through simple or systematic sampling. The total number of individuals to be selected in each stratum can be fixed or proportional to the size of each stratum. Each individual may be equally likely to be selected to participate in the study. However, the fixed method usually involves the use of sampling weights in the statistical analysis (inverse of the probability of selection or 1/P). An example is the study conducted in South Australia to investigate factors associated with vitamin D deficiency in preschool children. Using the national census as the sample frame, households were randomly selected in each stratum and all children in the age group of interest identified in the selected houses were investigated. 11

Cluster sampling: in this type of probabilistic sampling, groups such as health facilities, schools, etc., are sampled. In the above-mentioned study, the selection of households is an example of cluster sampling. 11

Complex or multi-stage sampling: This probabilistic sampling method combines different strategies in the selection of the sample units. An example is the study of Duquia et al. to assess the prevalence and factors associated with the use of sunscreen in adults. The sampling process included two stages. 12 Using the 2000 Brazilian demographic census as sampling frame, all 404 census tracts from Pelotas (Southern Brazil) were listed in ascending order of family income. A sample of 120 tracts were systematically selected (first sampling stage units). In the second stage, 12 households in each of these census tract (second sampling stage units) were systematically drawn. All adult residents in these households were included in the study (third sampling stage units). All these stages have to be considered in the statistical analysis to provide correct estimates.

NONRESPONDENTS

Frequently, sample sizes are increased by 10% to compensate for potential nonresponses (refusals/losses). 1 Let us imagine that in a study to assess the prevalence of premalignant skin lesions there is a higher percentage of nonrespondents among men (10%) than among women (1%). If the highest percentage of nonresponse occurs because these men are not at home during the scheduled visits, and these participants are more likely to be exposed to the sun, the number of skin lesions will be underestimated. For this reason, it is strongly recommended to collect and describe some basic characteristics of nonrespondents (sex, age, etc.) so they can be compared to the respondents to evaluate whether the results may have been affected by this systematic error.

Often, in study protocols, refusal to participate or sign the informed consent is considered an "exclusion criteria". However, this is not correct, as these individuals are eligible for the study and need to be reported as "nonrespondents".

SAMPLING METHOD ACCORDING TO THE TYPE OF STUDY

In general, clinical trials aim to obtain a homogeneous sample which is not necessarily representative of any target population. Clinical trials often recruit those participants who are most likely to benefit from the intervention. 3 Thus, the more strict criteria for inclusion and exclusion of subjects in clinical trials often make it difficult to locate participants: after verification of the eligibility criteria, just one out of ten possible candidates will enter the study. Therefore, clinical trials usually show limitations to generalize the results to the entire population of patients with the disease, but only to those with similar characteristics to the sample included in the study. These peculiarities in clinical trials justify the necessity of conducting a multicenter and/or global studiesto accelerate the recruitment rate and to reach, in a shorter time, the number of patients required for the study. 13

In turn, in observational studies to build a solid sampling plan is important because of the great heterogeneity usually observed in the target population. Therefore, this heterogeneity has to be also reflected in the sample. A cross-sectional population-based study aiming to assess disease estimates or identify risk factors often uses complex probabilistic sampling, because the sample representativeness is crucial. However, in a case-control study, we face the challenge of selecting two different samples for the same study. One sample is formed by the cases, which are identified based on the diagnosis of the disease of interest. The other consists of controls, which need to be representative of the population that originated the cases. Improper selection of control individuals may introduce selection bias in the results. Thus, the concern with representativeness in this type of study is established based on the relationship between cases and controls (comparability).

In cohort studies, individuals are recruited based on the exposure (exposed and unexposed subjects), and they are followed over time to evaluate the occurrence of the outcome of interest. At baseline, the sample can be selected from a representative sample (population-based cohort studies) or a non-representative sample. However, in the successive follow-ups of the cohort member, study participants must be a representative sample of those included in the baseline. 14 , 15 In this type of study, losses over time may cause follow-up bias.

Researchers need to decide during the planning stage of the study if they will work with the entire target population or a sample. Working with a sample involves different steps, including sample size estimation, identification of the sample frame, and selection of the sampling method to be adopted.

Financial Support: None.

* Study performed at Faculdade Meridional - Escola de Medicina (IMED) - Passo Fundo (RS), Brazil.

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What Is Simple Random Sampling?

• Simple Random Sample
• Disadvantages
• Random Sampling FAQs

The Bottom Line

Simple random sampling definition, advantages and disadvantage.

Simple random sampling is a technique in which a researcher selects a random subset of people from a larger group or population. In simple random sampling, each member of the group has an equal chance of getting selected. The method is commonly used in statistics to obtain a sample that is representative of the larger population.

Statistics is a branch of applied mathematics that helps us learn about large datasets by studying smaller events or objects. Put simply, you can make inferences about a large population by examining a smaller sample. Statistical analysis is commonly used to identify trends in many different areas, including business and finance. Individuals can use findings from statistical research to make better decisions about their money, businesses, and investments.

The simple random sampling method allows researchers to statistically measure a subset of individuals selected from a larger group or population to approximate a response from the entire group. This research method has both benefits and drawbacks. We highlight these pros and cons in this article, along with an overview of simple random sampling.

Key Takeaways

• A simple random sample is one of the methods researchers use to choose a sample from a larger population.
• This method works if there is an equal chance that any of the subjects in a population will be chosen.
• Researchers choose simple random sampling to make generalizations about a population.
• Major advantages include its simplicity and lack of bias.
• Among the disadvantages are difficulty gaining access to a list of a larger population, time, costs, and that bias can still occur under certain circumstances.

Simple Random Sample: An Overview

As noted above, simple random sampling involves choosing a smaller subset of a larger population. This is done randomly. But the catch here is that there is an equal chance that any of the samples in the subset will be chosen. Researchers tend to choose this method of sampling when they want to make generalizations about the larger population.

Simple random sampling can be conducted by using:

• The lottery method. This method involves assigning a number to each member of the dataset then choosing a prescribed set of numbers from those members at random.
• Technology. Using software programs like Excel makes it easier to conduct random sampling. Researchers just have to make sure that all the formulas and inputs are correctly laid out.

For simple random sampling to work, researchers must know the total population size. They must also be able to remove all hints of bias as simple random sampling is meant to be a completely unbiased approach to garner responses from a large group.

Keep in mind that there is room for error with random sampling. This is noted by adding a plus or minus variance to the results. In order to avoid any errors, researchers must study the entire population, which for all intents and purposes, isn't always possible.

To ensure bias does not occur, researchers must acquire responses from an adequate number of respondents, which may not be possible due to time or budget constraints.

Advantages of a Simple Random Sample

Simple random sampling may be simple to perform (as the name suggests) but it isn't used that often. But that doesn't mean it shouldn't be used. As long as it is done properly, there are certain distinct advantages to this sampling method.

Lack of Bias

The use of simple random sampling removes all hints of bias —or at least it should. Because individuals who make up the subset of the larger group are chosen at random, each individual in the large population set has the same probability of being selected. In most cases, this creates a balanced subset that carries the greatest potential for representing the larger group as a whole.

Here's a simple way to show how a researcher can remove bias when conducting simple random sampling. Let's say there are 100 bingo balls in a bowl, from which the researcher must choose 10. In order to remove any bias, the individual must close their eyes or look away when choosing the balls.

As its name implies, producing a simple random sample is much less complicated than other methods . There are no special skills involved in using this method, which can result in a fairly reliable outcome. This is in contrast to other sampling methods like stratified random sampling . This method involves dividing larger groups into smaller subgroups that are called strata. Members are divided up into these groups based on any attributes they share. As mentioned, individuals in the subset are selected randomly and there are no additional steps.

Less Knowledge Required

We've already established that simple random sampling is a very simple sampling method to execute. But there's also another, similar benefit: It requires little to no special knowledge. This means that the individual conducting the research doesn't need to have any information or knowledge about the larger population in order to effectively do their job.

Be sure that the sample subset from the larger group is inclusive enough. A sample that doesn't adequately reflect the population as a whole will result in a skewed result.

Disadvantages of a Simple Random Sample

Although there are distinct advantages to using a simple random sample, it does come with inherent drawbacks. These disadvantages include the time needed to gather the full list of a specific population, the capital necessary to retrieve and contact that list, and the bias that could occur when the sample set is not large enough to adequately represent the full population. We go into more detail below.

Difficulty Accessing Lists of the Full Population

An accurate statistical measure of a large population can only be obtained in simple random sampling when a full list of the entire population to be studied is available. Think of a list of students at a university or a group of employees at a specific company.

The problem lies in the accessibility of these lists. As such, getting access to the whole list can present challenges. Some universities or colleges may not want to provide a complete list of students or faculty for research. Similarly, specific companies may not be willing or able to hand over information about employee groups due to privacy policies.

Time Consuming

When a full list of a larger population is not available, individuals attempting to conduct simple random sampling must gather information from other sources. If publicly available, smaller subset lists can be used to recreate a full list of a larger population, but this strategy takes time to complete.

Organizations that keep data on students, employees, and individual consumers often impose lengthy retrieval processes that can stall a researcher's ability to obtain the most accurate information on the entire population set.

In addition to the time it takes to gather information from various sources, the process may cost a company or individual a substantial amount of capital. Retrieving a full list of a population or smaller subset lists from a third-party data provider may require payment each time data is provided.

If the sample is not large enough to represent the views of the entire population during the first round of simple random sampling, purchasing additional lists or databases to avoid a sampling error can be prohibitive.

Sample Selection Bias

Although simple random sampling is intended to be an unbiased approach to surveying, sample selection bias can occur. When a sample set of the larger population is not inclusive enough, representation of the full population is skewed and requires additional sampling techniques.

Data Quality Is Reliant on Researcher Qualify

The success of any sampling method relies on the researcher's willingness to thoroughly do their job. Someone who isn't willing to follow the rules or deviates from the task at hand won't help get a reliable result. For instance, there may be issues if a researcher doesn't ask the appropriate questions or asks the wrong ones. This could create implicit bias, ending up in a skewed study.

The term simple random sampling refers to a smaller section of a larger population. There is an equal chance that each member of this section will be chosen. For this reason, a simple random sampling is meant to be unbiased in its representation of the larger group. There is normally room for error with this method, which is indicated by a plus or minus variant. This is known as a sampling error.

How Is Simple Random Sampling Conducted?

Simple random sampling involves the study of a larger population by taking a smaller subset. This subgroup is chosen at random and studied to get the desired result. In order for this sampling method to work, the researcher must know the size of the larger population. The selection of the subset must be unbiased.

What Are the 4 Types of Random Sampling?

There are four types of random sampling. Simple random sampling involves an unbiased study of a smaller subset of a larger population. Stratified random sampling uses smaller groups derived from a larger population that is based on shared characteristics and attributes. Systematic sampling is a method that involves specific members of a larger dataset. These samples are selected based on a random starting point using a fixed, periodic interval. The final type of random sampling is cluster sampling, which takes members of a dataset and places them into clusters based on shared characteristics. Researchers then randomly select clusters to study.

When Is It Best to Use Simple Random Sampling?

It's always a good idea to use simple random sampling when you have smaller data sets to study. This allows you to produce better results that are more representative of the overall population. Keep in mind that this method requires each member of the larger population is identified and selected individually, which can often be challenging and time consuming.

Studying large populations can be very difficult. Getting information from each individual member can be costly and time-consuming. That's why researchers turn to random sampling to help reach the conclusions they need to make key decisions, whether that means helping provide the services that residents need, making better business decisions, or executing changes in an investor's portfolio.

Simple random sampling is relatively easy to conduct as long as you remove any and all hints of bias. Doing so means you must have information about each member of the larger population at your disposal before you conduct your research. This can be relatively simple and require very little knowledge. But keep in mind that the process can be costly and it may be hard trying to get access to information about all of the members of the population.

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• Simple Random Sampling | Definition, Steps & Examples

Simple Random Sampling | Definition, Steps & Examples

Published on 3 May 2022 by Lauren Thomas . Revised on 18 December 2023.

A simple random sample is a randomly selected subset of a population . In this sampling method, each member of the population has an exactly equal chance of being selected, minimising the risk of selection bias .

This method is the most straightforward of all the probability sampling methods , since it only involves a single random selection and requires little advance knowledge about the population. Because it uses randomisation, any research performed on this sample should have high internal and external validity.

Table of contents

When to use simple random sampling, how to perform simple random sampling, frequently asked questions about simple random sampling.

Simple random sampling is used to make statistical inferences about a population. It helps ensure high internal validity : randomisation is the best method to reduce the impact of potential confounding variables .

In addition, with a large enough sample size, a simple random sample has high external validity : it represents the characteristics of the larger population.

However, simple random sampling can be challenging to implement in practice. To use this method, there are some prerequisites:

• You have a complete list of every member of the population.
• You can contact or access each member of the population if they are selected.
• You have the time and resources to collect data from the necessary sample size.

Simple random sampling works best if you have a lot of time and resources to conduct your study, or if you are studying a limited population that can easily be sampled.

In some cases, it might be more appropriate to use a different type of probability sampling:

• Systematic sampling involves choosing your sample based on a regular interval, rather than a fully random selection. It can also be used when you don’t have a complete list of the population.
• Stratified sampling is appropriate when you want to ensure that specific characteristics are proportionally represented in the sample. You split your population into strata (for example, divided by gender or race), and then randomly select from each of these subgroups.
• Cluster sampling is appropriate when you are unable to sample from the entire population. You divide the sample into clusters that approximately reflect the whole population, and then choose your sample from a random selection of these clusters.

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There are four key steps to select a simple random sample.

Step 1: Define the population

Start by deciding on the population that you want to study.

It’s important to ensure that you have access to every individual member of the population, so that you can collect data from all those who are selected for the sample.

Step 2: Decide on the sample size

Next, you need to decide how large your sample size will be. Although larger samples provide more statistical certainty, they also cost more and require far more work.

There are several potential ways to decide upon the size of your sample, but one of the simplest involves using a formula with your desired confidence interval and confidence level , estimated size of the population you are working with, and the standard deviation of whatever you want to measure in your population.

The most common confidence interval and levels used are 0.05 and 0.95, respectively. Since you may not know the standard deviation of the population you are studying, you should choose a number high enough to account for a variety of possibilities (such as 0.5).

You can then use a sample size calculator to estimate the necessary sample size.

Step 3: Randomly select your sample

This can be done in one of two ways: the lottery or random number method.

In the lottery method , you choose the sample at random by ‘drawing from a hat’ or by using a computer program that will simulate the same action.

In the random number method , you assign every individual a number. By using a random number generator or random number tables, you then randomly pick a subset of the population. You can also use the random number function (RAND) in Microsoft Excel to generate random numbers.

Step 4: Collect data from your sample

Finally, you should collect data from your sample.

To ensure the validity of your findings, you need to make sure every individual selected actually participates in your study. If some drop out or do not participate for reasons associated with the question that you’re studying, this could bias your findings.

For example, if young participants are systematically less likely to participate in your study, your findings might not be valid due to the underrepresentation of this group.

Probability sampling means that every member of the target population has a known chance of being included in the sample.

Probability sampling methods include simple random sampling , systematic sampling , stratified sampling , and cluster sampling .

Simple random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population . Each member of the population has an equal chance of being selected. Data are then collected from as large a percentage as possible of this random subset.

The American Community Survey  is an example of simple random sampling . In order to collect detailed data on the population of the US, the Census Bureau officials randomly select 3.5 million households per year and use a variety of methods to convince them to fill out the survey.

If properly implemented, simple random sampling is usually the best sampling method for ensuring both internal and external validity . However, it can sometimes be impractical and expensive to implement, depending on the size of the population to be studied,

If you have a list of every member of the population and the ability to reach whichever members are selected, you can use simple random sampling.

Samples are used to make inferences about populations . Samples are easier to collect data from because they are practical, cost-effective, convenient, and manageable.

Sampling bias occurs when some members of a population are systematically more likely to be selected in a sample than others.

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Systematic Random Sampling

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Random Sampling Method

Random Sampling is a method of probability sampling where a researcher randomly chooses a subset of individuals from a larger population. In this method, every individual has the same probability of being selected. The researcher aims to collect data from as large a portion as possible of this randomly chosen subset.

In the field of statistics, sampling serves as the technique for selecting a portion of the population to draw statistical inferences. This subset’s characteristics allow us to estimate the attributes of the entire population. In the realm of market research, sampling methods fall into two primary categories: Random or probability sampling and non-probability sampling.

This article discusses the specific category of probability sampling known as random sampling and its types, formulas, advantages, examples, etc.

Table of Content

What is Random Sampling?

Types of random sampling, when to use random sampling, random sampling formula, advantages of simple random sampling, random sampling vs non-probability sampling, random sampling examples, practice questions on random sampling.

Random sampling is a method used in statistics to select a subset of individuals or items from a larger population in such a way that each member of the population has an equal and independent chance of being included in the sample. It is a fundamental technique for conducting surveys and experiments.

Random Sampling Definition

Random sampling is a method employed for selecting observations from a population, facilitating generalization about the entire population.

Random Sampling is sometimes referred to as probability sampling, distinguishing it from non-probability sampling. This method encompasses various techniques, including simple random sampling, stratified sampling, cluster sampling, and multistage sampling. However, it should be noted that convenience samples, which are non-arbitrary, fall outside the realm of probability sampling.

Random sampling relies on a method that involves a degree of random selection. It allows all eligible individuals an equal opportunity to be part of the sample drawn from the entire sample space. While it can be laborious and costly, probability sampling is a powerful tool for creating a representative sample of the population. There are four main categories of this sampling technique, which include:

• Simple Sampling
• Systematic Sampling
• Stratified Sampling
• Cluster Sampling

Let’s discuss the these types in detail.

Simple Random Sampling

Simple random sampling involves randomly selecting items without any specific pattern or criteria. For example simple random sampling involves the unbiased, purely random selection of individuals from the population, where each member has an equal chance of being included. Each member of the population has an equal chance of being chosen, like drawing names from a hat.

Selects individuals at regular intervals, offering an organised yet random way to choose a sample. For example in systematic random sampling, you select a starting point at random and then choose every ‘k’-th element from the population. It’s like selecting every n person from a list.

Stratified Random Sampling

Divides the population into distinct strata or subgroups and then randomly samples from each stratum, enhancing representation. For example stratified random sampling involves dividing the population into subgroups or strata based on certain characteristics. Samples are then randomly chosen from each stratum in proportion to their size.

Cluster Random Sampling

Organises the population into clusters, randomly selects some of these clusters, and samples all individuals within the chosen clusters. For example clustered sampling divides the population into clusters or groups, and then a random sample of clusters is chosen. All individuals within the selected clusters are included in the sample.

By utilising these techniques, probability sampling aims to provide reliable insights into the broader population while maintaining the essence of randomness.

• When the population is relatively homogenous: Simple random sampling works well when the population shares similar characteristics, as each individual has an equal chance of being selected.
• When the population size is known: If the total population size is known, simple random sampling ensures that every individual has a known and non-zero chance of being included in the sample.
• When there is no need for specialized knowledge: Simple random sampling is straightforward to implement and does not require extensive prior information about the population.
• When statistical inference is the primary goal: Simple random sampling is often used when researchers need to make generalizations about the population based on the sample data, as it provides an unbiased estimate of population parameters.
• When resources are limited: Simple random sampling can be more cost-effective and less time-consuming compared to other sampling methods, making it suitable when resources are limited.

Formula of random sampling is mentioned as below:

P = 1 –[(N-1)/N] × [(N-2)/(N-1)] × . . . × [(N-n)/(N-(n-1))] Where, P represents probability, n represents sample size, and N represents population.

In above formula cancelling 1-(N-n/n), it will yield a value of P = n/N .

So, sample getting selected for a chance of more than once

P = 1 – (1 – (1/N)) n Where, P represents probability, n represents sample size, and N represents population.

Below are the advantages of Simple Random Sampling :

• Simple random sampling is unbiased form of sample classification.
• Simple random sampling is easy to implement and cost-effective.
• Simple random sampling ensures that each element in the population has an equal probability of being included in the sample.
• Simple random sampling is a reliable way to estimate population characteristics.

Below are the differences between Probability Sampling vs Non-Probability Sampling:

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Example 1: A company has 500 products, and they want to randomly select 20 of them for quality testing. What is the probability of any single product getting selected?

The chance of one-time selection is: P = n/N ⇒ P = 20/500 ⇒ P = 4%

Example 2: In a conference with 200 attendees, 50 will be randomly chosen for a survey. What is the probability that one attendee gets selected more than once?

The probability of getting selected more than once is: P = 1 – (1 – (1/N)) n ⇒ P = 1 – (1 – (1/200)) 50 ⇒ P ≈ 9.56%

Example 3: A university has 1,200 students, and they want to select 100 students for a survey using simple random sampling. What is the probability of any single student being chosen?

The chance of one-time selection is: P = n/N ⇒ P = 100/1200 ⇒ P = 8.33%.

Example 4: In a raffle, 50 tickets are drawn from a pool of 1,000 tickets. What is the probability that a specific ticket does not get selected?

The chance of a specific ticket not being selected is: P = 1 – (n/N) ⇒ P = 1 – (50/1000) ⇒ P = 95%.

Example 5: A deck of 52 playing cards is shuffled, and 5 cards are drawn with replacement. What is the probability of drawing a specific card (e.g., the Ace of Spades) at least once?

The probability of drawing a specific card at least once when drawing 5 cards with replacement is: P = 1 – (1 – (1/N)) n ⇒ P = 1 – (1 – (1/52)) 5 ⇒ P ≈ 9.36%.

Question 1: You’re conducting a survey about favourite ice cream flavours in a town with 5,000 residents. How can you perform simple random sampling for your study?

Question 2: What is the key distinction between stratified and cluster sampling methods, and in what situations would each be more suitable?

Question 3: A company needs to test a random sample of 50 smartphones from a production batch of 2,000. Explain the steps they should take for a systematic sampling procedure.

Question 4: In a school of 500 students, you want to ensure your random sample includes both juniors and seniors. How can you use stratified sampling to accomplish this?

Question 5: Discuss the importance of non-response and how it can impact the validity of research using random sampling techniques.

FAQs on Random Sampling

What is random sampling method.

Random sampling is a method used in research to select a sample from a larger population in an unbiased way.

What is Simple Random Sampling?

Simple random sampling is a statistical method used to select a sample from a larger population in such a way that every possible subset of the population has an equal chance of being selected.

Why Random Sampling is Important?

Random Sampling is vital because it helps ensure the sample represents the population, making the research findings more reliable and generalisable.

What Are Some Common Methods for Random Sampling?

Common random sampling methods include: Simple Random Sampling Stratified Random Sampling Systematic Sampling Cluster Sampling

How Does Simple Random Sampling Work?

Simple Random Sampling works by randomly selecting individuals or items from a population so that each has an equal chance of being chosen, ensuring a representative sample.

What Is Stratified Random Sampling?

Stratified Random Sampling divides the population into distinct subgroups (strata) based on certain characteristics, then randomly samples from each stratum to ensure representation of various groups within the population.

When Is Systematic Sampling Used?

Systematic Sampling is used when there’s a need for simplicity and efficiency. It involves selecting every kth item from a list, starting with a random item. It’s useful for large populations and can provide a representative sample.

What Is Cluster Sampling?

Cluster Sampling involves dividing the population into clusters, randomly selecting some clusters, and then sampling all individuals within the chosen clusters. It’s useful for geographically dispersed or large populations.

Are There Any Drawbacks to Random Sampling?

Yes, there are drawbacks to random sampling, including the potential for bias due to chance, non-response, and under representation of certain groups. Large populations can be costly and time-consuming to sample completely.

How Do You Calculate Sample Size for Random Sampling?

To calculate the sample size for random sampling, consider factors like population size, desired confidence level, margin of error, and population variability. Formulas such as the one for simple random sampling help determine the required sample size.

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Performance of randomized estimators of the Hafnian of a non-negative matrix

Alexey uvarov and dmitry vinichenko, phys. rev. a 109 , 042415 – published 17 april 2024.

• No Citing Articles
• INTRODUCTION
• RANDOMIZED ESTIMATORS OF THE HAFNIAN
• RELATIVE ERROR FOR RANDOM GRAPHS
• CLASSICAL SIMULATION OF NON-NEGATIVE GBS
• ACKNOWLEDGMENTS

Gaussian boson samplers aim to demonstrate quantum advantage by performing a sampling task believed to be classically hard. The probabilities of individual outcomes in the sampling experiment are determined by the Hafnian of an appropriately constructed symmetric matrix. For non-negative matrices, there is a family of randomized estimators of the Hafnian based on generating a particular random matrix and calculating its determinant. While these estimators are unbiased (the mean of the determinant is equal to the Hafnian of interest), their variance may be so high as to prevent an efficient estimation. Here we investigate the performance of two such estimators, which we call the Barvinok and Godsil-Gutman estimators. We find that, in general, both estimators perform well for adjacency matrices of random graphs, demonstrating a slow growth of variance with the size of the problem. Nonetheless, there are simple examples where both estimators show high variance, requiring an exponential number of samples. In addition, we calculate the asymptotic behavior of the variance for the complete graph. Finally, we simulate the Gaussian boson sampling using the Godsil-Gutman estimator and show that this technique can successfully reproduce low-order correlation functions.

• Received 15 December 2023
• Accepted 27 March 2024

DOI: https://doi.org/10.1103/PhysRevA.109.042415

©2024 American Physical Society

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• Skolkovo Institute of Science and Technology, Bolshoy Boulevard, 30, p.1, Moscow 121205, Russia
• * [email protected]

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Perfect matchings counted by the Hafnian function.

Examples of perfect 2-matchings. The one on the bottom right contains cycles of odd length; such 2-matchings do not contribute to the sum ( 3 ).

Examples of perfect 2-matchings formed by two permutations (orange arrows and black arrows). Note that if both permutations map two vertices to each other, they become connected by four arrows, meaning that the corresponding term in ( 4 ) has a fourth power in g i j .

Average relative standard deviation σ / μ of (a) Godsil-Gutman and (b) Barvinok estimators for random graphs. Error bars denote confidence interval of one sigma, evaluated by bootstrap resampling and averaged over the sampled graphs.

Share of graph instances with Hafnian calculated up to relative error 0.05 using (a) Godsil-Gutman and (b) Barvinok estimators.

Relative standard deviation σ / μ of (a) Godsil-Gutman and (b) Barvinok estimators for the complete graphs of different sizes. The dashed line shows the exact values computed using the Taylor expansion of ( B6 ), the dash-dotted line shows the asymptote as per Theorem t3 .

Correlation functions for the GBS experiment obtained with Godsil-Gutman sampling versus those obtained with exact sampling. Top row: N = 10 ; bottom row: N = 1000 .

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A behind-the-scenes blog about research methods at Pew Research Center

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Can machines compete with humans in transcribing audio? A case study using sermons from U.S. religious services

A 2019 Pew Research Center study and follow-up study in 2020 involved the complicated task of transcribing more than 60,000 audio and video files of sermons delivered during religious services at churches around the United States. The primary goal of this research was to evaluate relatively broad topics discussed in the sermons to determine if there were any notable patterns or denominational differences in their length and subject matter.

The huge number of audio and video files meant that it would have been too time-consuming and expensive to ask humans to transcribe all the sermons. Instead, we used Amazon Transcribe , a speech recognition service offered by Amazon Web Services (AWS). We hoped to identify the key themes in the sermons we collected, even if the machine transcriptions were not perfect or at times lacked elements like punctuation that would often come with a traditional human transcription service.

Overall, the machine transcriptions were legible. But we did run into a few challenges. The Amazon service did not always get specific religious terminology or names right. (A few examples included “punches pilot” instead of “Pontius Pilate” and “do Toronto me” in lieu of “Deuteronomy.”) There were also some recordings for which the machine transcription was simply of low quality across the board.

A notable body of research has found that machine transcription sometimes struggles with certain accents or dialects , like regional Southern accents and African American English (AAE). This led us to wonder if the errors we were seeing in the machine transcripts of sermons was coincidental, or if we were encountering performance biases that could be making some transcriptions more reliable than others in a way that might affect the conclusions of our research.

Since we downloaded our sermon files directly as audio or audio/video, we lacked an original written transcript to compare against the machine-transcribed text. Instead, as a test, we asked a third-party human transcription service to tackle portions of some of the sermons that Amazon Transcribe had already transcribed and then compared the results between the two.

What we did

For this experiment, we were interested in using sermons that included a variety of regional accents and dialects among the speakers. One obvious challenge, however, was that we didn’t know much about the speakers themselves. We knew the location of the church where the sermon was delivered, as well as its religious tradition, but these were not necessarily sufficient to assign an accent or a dialect to the person speaking in a recording. We could only use these features as approximations.

With that caveat in mind, we focused the analysis on audio files from the four main religious traditions for which we had a reportable sample size: mainline Protestant, evangelical Protestant, historically Black Protestant and Catholic. We also examined three large geographic regions: the Midwest, the South and a combined region that merges the Northeast and the West (again to account small sample sizes in those two regions).

We took a stratified random sample of 200 sermons from churches for each combination of religious tradition and region, proportional to the number of sermons each church had in the dataset. From this sample of full audio files, we took one random snippet of audio with a duration of 30 to 210 seconds from each file and sent those audio snippets to our external human transcription service. This service was a standard online provider that claimed to have native language speakers, a multistep quality check process and experience transcribing religious content, including sermons specifically. At the end of this process, we had a total sample size of 2,387 texts with both machine and human transcriptions.

How we compared transcriptions

There are a variety of computational methods to measure the similarity or difference between two sets of text. In this analysis, we used a metric known as Levenshtein distance to compare our machine and human transcriptions.

Levenshtein distance counts the number of discrete edits – insertions, deletions and substitutions – at the character level necessary to transform one text string into another. For example, if the word “COVID” is transcribed as “cove in,” there is a Levenshtein distance of three, as the transformation requires three edits: one edit to add a space between the “v” and the “i,” one edit to add an “e” after the “v,” and one edit to substitute the “d” for an “n.”

Levenshtein distance is useful as a comparison metric because it can be normalized and used to compare texts of different lengths. It also allows for nuance by focusing on character-level edits rather than entire words, providing more granularity than something like simple word error rate by scoring how incorrect a mistranscription is.

As a final bit of housekeeping, we standardized both our machine and human transcriptions to make sure that they matched one another stylistically. We transformed all the text into lower case, spelled out numbers and symbols when appropriate, and removed punctuation, filler words and words associated with vocalizations (such as “uh” or “ooh”). We also removed the “[UNINTELLIGIBLE]” annotations that the human transcription service included at our request to flag cases in which someone was speaking but their words couldn’t be clearly understood.

Across all the audio files we evaluated, the average difference between machine transcriptions and human transcriptions was around 11 characters per 100. That is, for every 100 characters in a transcription text, approximately 11 differed from one transcription method to the other.

We were also interested in looking at the difference across religious traditions and geographical regions. To do so, we used pairwise t-tests to test for differences in means across all religious traditions and all regions. (We did not calculate comparisons between each religious tradition and region combination after determining the interaction of the two variables was not statistically significant.)

The analysis found a small but statistically significant difference in Levenshtein distances between machine and human transcriptions for several religious traditions. Text taken from Catholic sermons, for example, had more inconsistency between transcripts than was true of those taken from evangelical Protestant sermons. And sermons from historically Black Protestant churches had significantly more inconsistency in transcriptions when compared with the other religious traditions.

While these differences were statistically significant, their magnitude was relatively small. Even for historically Black Protestant sermons – the tradition with the largest mismatch between machines and humans – the differences worked out to around just 15 characters per 100, or four more than the overall average. It’s also important to remember that we cannot assume the speaker is speaking AAE simply because the sermon was given in a historically Black Protestant church.

One expectation we had going into this experiment is that machine transcription would perform worst with Southern accents. However, we found that transcriptions of sermons from churches in the Midwest had significantly more inconsistency between machine and human transcriptions than those in other regions. Anecdotally, it appears this discrepancy may be because human transcribers had more difficulty than machines in understanding speakers in the Midwest: Sermon texts from the Midwest that were transcribed by humans included a greater number of “[UNINTELLIGIBLE]” annotations than those from other regions. There may also be other factors affecting transcription quality that we cannot account for, such as the possibility that sermons from the Midwest had systematically worse audio quality than those from other regions.

Again, although these differences were statistically significant, their magnitude was relatively small. Midwestern sermons, despite having the greatest inconsistency across regions, had only two more character differences per 100 characters than the overall average.

Conclusions and suggestions

In social science research, automated transcription services have become a popular alternative to human transcription because of the costs and labor involved in the latter. All in all, we found that the machine transcriptions and the human transcriptions used in this experiment were comparable enough to justify our decision to use an automated service in our research on U.S. sermons.

However, our experience does suggest a few ideas that researchers should keep in mind should they find themselves in a similar situation.

First, issues with transcription quality can be tied to the quality of the audio being transcribed – which presents challenges for humans and computers alike. By the same token, machine transcription may perform worse or better on certain accents or dialects – but that’s also true for human transcribers.  When working with audio that has specialized vocabulary (in our case, religious terms), human transcribers sometimes made errors where machines did not. This is likely because a robust machine transcription service will have a larger dictionary of familiar terms than the average person. Similarly, we found that humans are more likely to make typos, something one will not run into with machine transcription.

More generally, reliability is usually an advantage of machine transcription. Human transcription can vary in quality based on the service used, and possibly from one transcript to another if there are multiple human transcribers. But the reliability of machine transcription can sometimes backfire. When presented with a segment of tricky audio, for example, humans can determine that the text is “unintelligible.” A machine, on the other hand, will try to match the sounds it hears as closely as possible to a word it knows with little to no regard for grammar or intelligibility. While this might produce a phonetically similar transcription, it may deviate far from what the speaker truly said.

Ultimately, both machine and human transcription services can be viable options. Beyond the obvious questions of budget and timeline that are often primary considerations, we would suggest evaluating the nature of the audio files that are being analyzed before transcription begins. Audio of mixed quality, or which features competing sound from an audience, can be tricky for humans and machines alike.

Researchers should also determine how important it is to have formatting and punctuation in the text they hope to analyze. Our researchers found that the lack of these elements can be a key barrier to understanding the meaning of a particular piece of text quickly. In our case, it wasn’t an insurmountable barrier, but it certainly added a significant cognitive burden to tasks like labeling training data. And it might have posed an even bigger problem had our analysis relied more heavily on unguided methods for identifying our topics of interest.

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