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Simple Random Sampling – Types, Method and Examples

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Simple Random Sampling

Definition:

Simple Random Sampling is a type of probability sampling for selecting a random sample from a population, in which each member of the population has an equal chance of being selected. This means that every member of the population has the same probability of being chosen as any other member, and each possible sample of a given size has an equal probability of being selected.

Types of Simple Random Sampling

Types of Simple Random Sampling are as follows:

• Simple random sampling with replacement : In this method, each member of the population has an equal chance of being selected for the sample, and once a member is selected, they are not removed from the population. This means that the same member can be selected more than once.
• Simple random sampling without replacement : In this method, each member of the population also has an equal chance of being selected for the sample, but once a member is selected, they are removed from the population. This means that each member can only be selected once.
• Stratified random sampling: This method involves dividing the population into subgroups or strata based on certain characteristics, such as age or gender, and then selecting a simple random sample from each stratum. This ensures that the sample represents the diversity of the population.

Simple Random Sampling Formula

The formula for simple random sampling is as follows:

• n is the sample size
• N is the population size
• k is the sampling fraction, which is the ratio of the sample size to the population size

To calculate the sample size, you can rearrange the formula as follows:

For example, if you have a population of 1000 and you want to take a simple random sample with a sampling fraction of 0.10, the formula would be:

n = 1000 x 0.10 = 100

Therefore, you would need to randomly select 100 individuals from the population to create your sample.

Simple Random Sampling Method

Here are the steps to perform Simple Random Sampling Method:

• Define the population: The first step is to clearly define the population that you want to study. This population should be well-defined and include all individuals that you are interested in studying.
• Determine the sample size: Next, you need to determine the sample size that you want to use for your study. The sample size should be large enough to provide accurate results, but small enough to be manageable.
• Assign a number to each member of the population : Once you have determined the sample size, you need to assign a number to each member of the population. This can be done using a random number generator or by manually assigning numbers.
• Generate random numbers: If you are using a random number generator, you need to generate a set of random numbers that corresponds to the sample size. These random numbers will be used to select the individuals for your sample.
• Select the sample : Using the random numbers, select the individuals from the population that correspond to the random numbers generated. For example, if the first three random numbers generated were 15, 77, and 94, you would select the 15th, 77th, and 94th individuals from the population.
• Analyze the sample: Once you have selected your sample, you can analyze the data that you collect to draw conclusions about the population as a whole.

Examples of Simple Random Sampling

Here are some examples of simple random sampling:

• Polling : Suppose a research organization wants to conduct a poll to determine the approval rating of a political candidate. They can randomly select a sample of registered voters from the population and ask them about their opinion of the candidate. By ensuring that each registered voter has an equal chance of being selected, the researchers can obtain an unbiased estimate of the candidate’s approval rating.
• Quality control: A company may want to test the quality of their products by selecting a random sample from the production line. By randomly selecting items for testing, they can ensure that the sample is representative of the entire production process and obtain accurate information about the quality of their products.
• Medical research : A medical researcher may want to study the prevalence of a particular disease in a population. They can randomly select a sample of individuals from the population and perform medical tests to determine the incidence of the disease. By ensuring that each individual has an equal chance of being selected, the researcher can obtain an unbiased estimate of the prevalence of the disease.
• Education research: A researcher may want to study the effectiveness of a new teaching method on student performance. They can randomly select a sample of students from a school and assign them to either the new teaching method or the traditional teaching method. By randomly selecting students for the study, the researcher can ensure that the sample is representative of the entire student population and obtain accurate information about the effectiveness of the new teaching method.
• Social Science Research: A social science researcher wants to study the attitudes and opinions of the general population towards a particular social issue. They can use simple random sampling to select a representative sample of individuals from the population, and then survey them to collect data on their attitudes and opinions.

Simple Random Sampling Example Situation

Simple Random Sampling Example Situation is as follows:

A company wants to conduct a survey to understand the job satisfaction of its employees. The company has a total of 500 employees, and they want to select a sample of 50 employees using simple random sampling.

Formula: The formula for simple random sampling is:

n/N * (N-n)/(N-1)

• n: the sample size
• N: the population size

In this case, n = 50 and N = 500.

So, the formula for calculating the probability of selecting a simple random sample of 50 employees from a population of 500 is:

50/500 * (500-50)/(500-1) = 0.1 * 0.902 = 0.0902, or 9.02%.

Therefore, the probability of selecting a sample of 50 employees using simple random sampling is 9.02%. This means that any set of 50 employees has an equal chance of being selected, and the sample is representative of the population.

When to Use Simple Random Sampling

Here are some situations where simple random sampling may be appropriate:

• When the population is relatively small: Simple random sampling is an ideal method to use when the population size is small because it is easy to implement and doesn’t require a lot of resources.
• When the population is homogenous: Simple random sampling is suitable when the population is relatively homogenous, meaning that the characteristics of the individuals or elements are relatively similar.
• When the researcher wants to avoid potential bias: Simple random sampling is an excellent method to use when the researcher wants to avoid any potential bias in the sample selection process.
• When the data is not strongly correlated : Simple random sampling is appropriate when the data is not strongly correlated. Strong correlation between variables can result in an unrepresentative sample.

Applications of Simple Random Sampling

Simple random sampling has numerous applications in various fields, including:

• Public opinion polls : Simple random sampling is widely used in public opinion polls to collect data from a representative sample of the population.
• Medical research : In medical research, simple random sampling is used to select participants for clinical trials or to conduct surveys to collect data on health-related issues.
• Quality control: Simple random sampling is used in quality control to select products or items from a production line for inspection to ensure that they meet certain quality standards.
• Education research : Simple random sampling is used in educational research to select students or schools to participate in studies.
• Market research: Simple random sampling is used in market research to collect data on consumer behavior and preferences.
• Environmental studies: Simple random sampling is used in environmental studies to collect data on various environmental factors.
• Social science research : Simple random sampling is widely used in social science research to study various social phenomena.

Purpose of Simple Random Sampling

The main purpose of simple random sampling is to obtain a representative sample of a population. A representative sample is one that accurately reflects the characteristics of the entire population, such as its demographics, behaviors, opinions, or attitudes.

Simple random sampling ensures that every individual or element in the population has an equal chance of being selected for the sample. By doing so, it eliminates potential biases that could arise from non-random sampling methods, such as convenience sampling or purposive sampling.

A representative sample obtained through simple random sampling can help researchers make generalizations about the population with a high degree of confidence. The results of statistical analyses conducted on the sample can be used to make inferences about the larger population, with a margin of error that can be quantified using probability theory.

Characteristics of Simple Random Sampling

Characteristics of Simple Random Sampling are as follows:

• Randomness : Every element or individual in the population has an equal chance of being selected for the sample. This ensures that the sample is representative of the population and reduces the potential for bias.
• Independence : Each element or individual in the population is selected independently of the others. The selection of one element does not influence the selection of another element.
• Objectivity : The selection of elements for the sample is based solely on chance, and there is no subjective judgment or influence involved in the selection process.
• Equal probability: Each element in the population has the same probability of being selected for the sample. This means that every possible sample of a given size has an equal chance of being selected.
• Simple to use: Simple random sampling is easy to understand, implement, and analyze, making it one of the most commonly used sampling methods in statistical research.
• Appropriate for any population : Simple random sampling can be applied to any population, regardless of size or characteristics, as long as a complete list of all elements or individuals in the population is available.

Advantages of Simple Random Sampling

Simple random sampling has several advantages over other sampling methods, including:

• Representativeness : Simple random sampling ensures that every individual or element in the population has an equal chance of being selected for the sample, which makes it a highly representative sample of the population.
• Unbiased : Simple random sampling eliminates potential biases that can arise from non-random sampling methods, such as convenience sampling or purposive sampling.
• Easy to use : Simple random sampling is easy to understand, implement, and analyze, making it a popular choice for researchers with limited resources or time.
• Probability theory : Simple random sampling allows for the application of probability theory to estimate the margin of error and the confidence interval of the sample, which provides a measure of the accuracy of the results.
• Flexibility : Simple random sampling can be used in a wide range of research applications and is suitable for any population, as long as a complete list of all elements or individuals in the population is available.

Disadvantages of Simple Random Sampling

While simple random sampling has several advantages, it also has some disadvantages, including:

• Large sample size : Simple random sampling requires a large sample size to be representative of the population. A larger sample size can increase the cost and time required to conduct the research.
• Inefficiency: Simple random sampling can be inefficient when the population is large and geographically dispersed, as it requires a complete list of all elements or individuals in the population.
• Under-representation: Simple random sampling can result in under-representation of certain subgroups within the population if they are not properly identified in the sampling process.
• Selection bias: While simple random sampling eliminates selection bias, it does not eliminate other forms of bias, such as measurement bias or response bias.
• Not suitable for small populations : Simple random sampling is not suitable for small populations as it can result in a very small sample size that may not be representative of the population.

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Simple Random Sampling: Definition, Methods, and Examples

Researchers often rely on samples to draw conclusions about a larger population. Allowing researchers to study a subset of the population makes the research process more manageable and cost-effective. Here, we discuss Simple Random Sampling , considered one of the most straightforward and unbiased sampling methods.   

Table of Contents

Simple random sampling is employed when the researcher believes that each member of the population has an equal chance of being selected, ensuring the sample’s representativeness. This method is particularly suitable for relatively homogeneous populations and minimizes bias, facilitating the generalization of research findings to the larger population. Simple random sampling can be used in various scenarios across different fields. Here are a few examples of cases where simple random sampling can be applied .  

• Medical Research : A hospital wants to study the average recovery time of patients who have undergone a specific surgery. To ensure the study is unbiased, researchers use simple random sampling to select 100 patients from the hospital’s database of all patients who had this surgery in the past year. This way, every patient has an equal chance of being included in the study.  
• Market Research : A company wants to understand customer satisfaction with its new product. The marketing team uses simple random sampling to select 200 customers from a list of all customers who purchased the product. This ensures that the sample represents the entire customer base, avoiding any biases that might come from targeting a specific group.  
• Education Studies : A school district is interested in evaluating the effectiveness of a new teaching method. Researchers randomly select 10 schools from the district’s total of 50 schools. Then, within each selected school, they randomly choose 50 students to participate in the study. This two-stage simple random sampling helps ensure that the sample is representative of the entire district.  
• Public Health Surveys : A city health department wants to estimate smoking prevalence among adults in the city. They use simple random sampling to select 1,000 residents from the city’s census data. By doing so, they can obtain a representative sample that accurately reflects the smoking habits of the city’s population.  
• Environmental Studies : Scientists studying the biodiversity of a forest may use simple random sampling to select 100 plots of land from a larger forest area. By analyzing the selected plots, they can make inferences about the entire forest’s biodiversity without studying every plot.  

This article will provide a clear understanding of the importance and practicality of simple random sampling in research. We explore what simple random sampling entails, including its definition and how it is conducted . We will also explore when to use simple random sampling in research and highlight the advantages and disadvantages .   

What is Simple Random Sampling? 

Simple random sampling is defined as “ a sampling technique where each member of the population has an equal and independent chance of being selected “. 1  

In simple random sampling , the selection of each unit is entirely independent of the selection of any other unit. This allows a fair sample selection mechanism, making simple random sampling suitable for many types of quantitative research. The key features of simple random sampling are as follows:  

• Equal Probability: Each member of the population has an equal chance of being selected.  
• Independence: The selection of one member does not influence the selection of another.  
• Unbiased: This method minimizes the risk of bias, making the sample representative of the population.  
• Simplicity: The process is straightforward to understand and implement.  

When to Use Simple Random Sampling in Research ?  

Simple random sampling is most appropriate when the following conditions are met: 2  

• Availability of the Complete Population List : A comprehensive and accessible list of the entire population is available, allowing every member an equal chance of being selected.  
• Homogeneous Population : The population is relatively uniform in characteristics relevant to the study, reducing the risk of bias and ensuring that the sample accurately represents the whole.  
• Smaller or Manageable Population Size : The population size is sufficiently small to allow for the practical implementation of the sampling process without excessive time and resource demands.  
• Need for Unbiased Results : The research aims to produce unbiased results, making it crucial to avoid systematic errors in sample selection.  
• Knowledge of Statistical Analysis : The study requires precise statistical analysis, and the researcher needs to apply techniques that assume random sampling, such as certain inferential statistics.  

How to Do Simple Random Sampling (Step by Step) 

The steps involved in simple random sampling are as follows:  

1. Define the Population:  

• Identify the population from which you want to sample. This includes determining the total number of units (people, items, etc.) in the population.  
• Example: If you’re studying the sleep patterns of students in a university, your population might be all students enrolled in that university.  

2. Determine the Sample Size:  

• Decide how many units you need to include in your sample. This depends on factors like the research objective, population size, and desired level of accuracy.  
• Example: If the university has 10,000 students and you decide to sample 500 students, 500 is your sample size.  

3. Assign Numbers to Each Member:  

• Give each member of the population a unique identifier (usually a number). This is essential for random selection.  
• Example: Assign numbers 1 to 10,000 to the students.  

4. Randomly Select the Sample:  

• Use a random method to select the desired number of units. This can be done using random number generators, drawing lots (lottery method), or software designed for random sampling. The students corresponding to these numbers form your sample.  
• Example: Use a random number generator to pick 500 numbers between 1 and 10,000. The students assigned these numbers are then surveyed about their sleeping habits.   

In the given example, simple random sampling ensures that every student in the university has an equal chance of being selected for the study. This helps to ensure that the sample is representative of the entire student population, allowing for accurate conclusions about students’ sleeping patterns.   

What are the Advantages of Simple Random Sampling? 

Simple random sampling is widely used in research and statistics due to its various advantages .  

1. Unbiased Representation :  

• Each individual in the population has an equal probability of being chosen, which minimizes selection bias and promotes fairness and equality.  
• It ensures that the sample represents the population accurately.  
• Reduces the likelihood of favoritism or systematic exclusion.  

2. Ease of Use :  

• Simple to understand and implement.  
• Requires minimal technical knowledge and statistical tools.  

3. High Level of Validity :  

• Results are highly reliable and valid for making inferences about the population.  
• It helps in achieving the generalizability of the findings.  

4. Data Analysis :  

• Simplifies the process of data analysis as the statistical formulas are straightforward.  
• Facilitates the use of various statistical techniques to analyze the data.  

5. Flexibility :  

• Can be applied to any known population size, regardless of nature.  
• Suitable for small and large populations.  

6. Foundation for Advanced Techniques :  

• Serves as a basis for more complex sampling methods.  
• Provides a solid foundation for stratified, cluster, and systematic sampling.  

7. Reduced Sampling Error :  

• Random selection helps reduce sampling errors.  
• Enhances the accuracy and reliability of the results.  

These advantages make simple random sampling a preferred choice in many research and statistical applications.  

What Are the Limitations of Simple Random Sampling? 

Despite its many advantages , simple random sampling has some limitations that researchers need to consider.  

1. Complexity in Large Populations :  

• Identifying and listing every member of a large population can be difficult and time-consuming.  
• It may require considerable resources to manage large datasets.  

2. Not Always Practical :  

• In some cases, a complete list of the population is not available or up-to-date, making it impossible to implement simple random sampling .  
• Can be impractical for populations that are geographically dispersed.  

3. Homogeneity Issues :  

• If the population is very homogeneous, simple random sampling may not capture the diversity within the population.  
• May result in samples that do not adequately reflect subgroups within the population.  

4. Sample Size Concerns :  

• Requires a sufficiently large sample size for large populations to ensure accurate representation and reliability of results.  
• Small sample sizes can lead to high sampling errors and unreliable results.  

5. Implementation Costs :  

• Can be costly and resource-intensive, especially for large-scale studies.  
• Requires significant effort in terms of time, money, and human resources to implement properly.  

6. Data Collection Challenges :  

• Gathering data from randomly selected individuals may be difficult if they are unwilling or unable to participate.  
• Non-response or low response rates can affect the validity of the sample.  

7. Risk of Sampling Error :  

• Random selection does not guarantee that the sample will perfectly represent the population.  
• Although reduced, there is still a possibility of sampling error.  

8. Need for Statistical Knowledge :  

• Proper implementation and analysis require a good understanding of statistical principles.  
• Errors in design or execution can compromise the validity of the results.  

While simple random sampling is a fundamental and widely used method in research, its limitations must be carefully considered before selection. Researchers need to weigh the practicality, cost, and potential implementation challenges against the need for unbiased, representative samples. In some cases, alternative sampling methods may be more suitable to address specific research needs and constraints.  

Key Takeaways  

• Simple random sampling is a powerful technique used to ensure that every member of a population has an equal chance of being included in the sample.   
• Simple random sampling is ideal for studies where the population is equally accessible, and no sub-groups need specific representation.  
• Simple random sampling helps to eliminate bias and provides a representative sample, which is crucial for the validity of research findings.   
• While it is easy to implement, s imple random sampling requires a complete and accurate list of the population and can be time-consuming for large populations.   
• Despite these limitations , simple random sampling remains a powerful tool for obtaining reliable and valid research data when executed correctly.   

References  

• Levy, P. S., & Lemeshow, S. (2013). Sampling of Populations: Methods and Applications. Wiley.  
• Pandey, P., & Pandey, M. M. (2021).  Research methodology tools and techniques . Bridge Center.  

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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

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• GETTING STARTED
• Introduction
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• Data Analysis

Simple random sampling

Simple random sampling is a type of probability sampling technique [see our article, Probability sampling , if you do not know what probability sampling is]. With the simple random sample, there is an equal chance ( probability ) of selecting each unit from the population being studied when creating your sample [see our article, Sampling: The basics , if you are unsure about the terms unit , sample and population ]. This article (a) explains what simple random sampling is, (b) how to create a simple random sample, and (c) the advantages and disadvantages of simple random sampling.

Simple random sampling explained

Creating a simple random sample, advantages and disadvantages of simple random sampling.

Imagine that a researcher wants to understand more about the career goals of students at a single university. Let's say that the university has roughly 10,000 students. These 10,000 students are our population ( N ). Each of the 10,000 students is known as a unit (although sometimes other terms are used to describe a unit; see Sampling: The basics ). In order to select a sample ( n ) of students from this population of 10,000 students, we could choose to use a simple random sample.

With simple random sampling, there would an equal chance ( probability ) that each of the 10,000 students could be selected for inclusion in our sample. If our desired sample size was around 200 students, each of these students would subsequently be sent a questionnaire to complete (imagining we choose to collect our data using a questionnaire).

To create a simple random sample, there are six steps : (a) defining the population; (b) choosing your sample size; (c) listing the population; (d) assigning numbers to the units; (e) finding random numbers; and (f) selecting your sample.

• STEP ONE: Define the population
• STEP TWO: Choose your sample size
• STEP THREE: List the population
• STEP FOUR: Assign numbers to the units
• STEP FIVE: Find random numbers
• STEP SIX: Select your sample

STEP ONE Define the population

In our example, the population is the 10,000 students at the single university. The population is expressed as N. Since we are interested in all of these university students, we can say that our sampling frame is all 10,000 students. If we were only interested in female university students, for example, we would exclude all males in creating our sampling frame, which would be much less than 10,000 students.

STEP TWO Choose your sample size

Let's imagine that we choose a sample size of 200 students. The sample is expressed as n . This number was chosen because it reflects the limit of our budget and the time we have to distribute our questionnaire to students. However, we could have also determined the sample size we needed using a sample size calculation , which is a particularly useful statistical tool. This may have suggested that we needed a larger sample size; perhaps as many as 400 students.

STEP THREE List the population

To select a sample of 200 students, we need to identify all 10,000 students at the university. If you were actually carrying out this research, you would most likely have had to receive permission from Student Records (or another department in the university) to view a list of all students studying at the university. You can read about this later in the article under Disadvantages of simple random sampling .

STEP FOUR Assign numbers to the units

We now need to assign a consecutive number from 1 to N , next to each of the students. In our case, this would mean assigning a consecutive number from 1 to 10,000 (i.e., N = 10,000; the population of students at the university).

STEP FIVE Find random numbers

Next, we need a list of random numbers before we can select the sample of 200 students from the total list of 10,000 students. These random numbers can either be found using random number tables or a computer program that generates these numbers for you.

STEP SIX Select your sample

Finally, we select which of the 10,000 students will be invited to take part in the research. In this case, this would mean selecting 200 random numbers from the random number table . Imagine the first three numbers from the random number table were:

We would select the 11 th , 9,292 nd and 2,001 st students from our list to be part of the sample. We keep doing this until we have all 200 students that we want in our sample.

The advantages and disadvantages of simple random sampling are explained below. Many of these are similar to other types of probability sampling technique, but with some exceptions. Whilst simple random sampling is one of the 'gold standards' of sampling techniques, it presents many challenges for students conducting dissertation research at the undergraduate and master's level.

Advantages of simple random sampling

The aim of the simple random sample is to reduce the potential for human bias in the selection of cases to be included in the sample. As a result, the simple random sample provides us with a sample that is highly representative of the population being studied, assuming that there is limited missing data.

Since the units selected for inclusion in the sample are chosen using probabilistic methods , simple random sampling allows us to make generalisations (i.e., statistical inferences ) from the sample to the population . This is a major advantage because such generalisations are more likely to be considered to have external validity .

Disadvantages of simple random sampling

A simple random sample can only be carried out if the list of the population is available and complete .

Attaining a complete list of the population can be difficult for a number of reasons:

Even if a list is readily available, it may be challenging to gain access to that list. The list may be protected by privacy policies or require a lengthy process to attain permissions.

There may be no single list detailing the population you are interested in. As a result, it may be difficult and time consuming to bring together numerous sub-lists to create a final list from which you want to select your sample. As an undergraduate and master?s level dissertation student, you may simply not have sufficient time to do this.

Many lists will not be in the public domain and their purchase may be expensive; at least in terms of the research funds of a typical undergraduate or master's level dissertation student.

In terms of human populations (as opposed to other types of populations; see the article: Sampling: The basics ), some of these populations will be expensive and time consuming to contact, even where a list is available. Assuming that your list has all the contact details of potential participants in the first instance, managing the different ways (e.g., postal, telephone, email) that may be required to contact your sample may be challenging, not forgetting the fact that your sample may also be geographical scattered.

In the case of human populations, to avoid potential bias in your sample, you will also need to try and ensure that an adequate proportion of your sample takes part in the research. This may require re-contacting non-respondents, can be very time consuming, or reaching out to new respondents.

If you are an undergraduate or master's level dissertation student considering using simple random sampling , you may also want to read more about how to put together your sampling strategy [see the section: Sampling Strategy ].

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Simple Random Sampling: Definition & Examples

By Jim Frost Leave a Comment

What is Simple Random Sampling?

Simple random sampling (SRS) is a probability sampling method where researchers randomly choose participants from a population . All population members have an equal probability of being selected. This method tends to produce representative, unbiased samples.

For example, if you randomly select 1000 people from a town with a population of 100,000 residents, each person has a 1000/100000 = 0.01 probability. That’s a simple calculation requiring no additional knowledge about the population’s composition. Hence, simple random sampling.

Simple random sampling is a probability sampling method that helps ensure the sample mirrors the population. The process proportionately samples from larger subpopulations more frequently than smaller subpopulations.

Suppose the town contains subpopulation A with 40,000 people and subpopulation B with 10,000. Using SRS with a probability of 0.01, the process will tend to enlist 400 from subpopulation A and 100 from B. Hence, the process tends to produce a proportionate representation in the sample that reflects the entire population. You don’t need to know the details about the subpopulations for this process to work!

Learn more about Types of Sampling Methods in Research .

How to Use Simple Random Sampling

Performing simple random sampling requires that you have a sampling frame that contains a complete list of all population members and the ability to contact and involve them in your study. Learn more about Sampling Frames: Definition, Examples & Uses .

• Define the population.
• Create a list of all population members.
• Assign random numbers to each member.
• Use a random number generator to select participants until you reach your target sample size.

Alternatively, if the population is not too large, you can use a lottery system for drawing the sample. Place all the names in a hat and randomly draw your sample. For large populations, researchers typically use computers to select participants randomly from a database.

Example of Simple Random Sampling

Imagine we are studying the town with 100,000 residents. We want to perform simple random sampling to obtain a sample size of 1000. We first need to define the population. We’ll define it as residents of the town who pay township taxes and are at least 18 years old.

Next, we need to create a complete list of residents who meet those criteria. Perhaps we’ll work with the township tax office to make the list. We’ll add all eligible residents to our list.

Finally, we need to select participants randomly from the list. We can use a computer program to do that. Alternatively, we can print out names on slips of paper and draw them from a basket. We keep drawing from the list until we have 1000 names.

Benefits of Simple Random Sampling

Many statisticians consider simple random sampling to be the gold standard for producing representative samples. Because it is entirely random, it minimizes the potential for researchers biasing the results, even if unintentionally. As you’ll read, there are alternative sampling methods that provide concessions to real-world sampling difficulties. Unfortunately, the alternatives can unwittingly produce a biased sample. Learn more about representative samples .

Procedurally, SRS is the simplest method for obtaining an unbiased sample. While the researchers need a list of the entire population, they don’t need other information about that population, its subpopulations, and its features.

Conversely, other more complex forms of sampling require researchers to understand the population’s characteristics. Then, using that knowledge and a lot of preplanning, they divide the population into strata or clusters and perform other procedures before sampling. With SRS, you just randomly draw from the list until you have enough subjects.

Because simple random sampling tends to produce unbiased samples that mirror the population, it’s excellent for analysts who need to use a sample to infer the properties of a population (i.e., inferential statistics ). In a study, having a representative sample improves both its internal and external validity . After simple random sampling, you can use statistical hypothesis tests to use the sample to draw conclusions about the population.

For more information about inferential statistics, read my articles about Populations, Parameters, and Samples in Inferential Statistics  and Descriptive versus Inferential Statistics .

Drawbacks of Simple Random Sampling

Even though there are great benefits to using this method, simple random sampling has some significant drawbacks.

Population List

First and foremost, this method can be quite cumbersome and require ample resources for large populations. You’ll need a list of all population members, which can be a tremendous hurdle by itself. If that list doesn’t exist, you might need to expend considerable resources to create it. An incomplete list can bias your results. Only a complete list allows the researchers to have an equal probability of selecting all population members.

Attempting to perform SRS with an incomplete population list causes undercoverage bias and a nonrepresentative sample.

Learn more about Undercoverage Bias: Definition & Examples .

Then you’ll need to contact and interact with everyone you randomly select. Depending on the nature of your study, that process can be pretty expensive and time-consuming if your participants span a wide geographic range, particularly when you need a large sample size.

Insufficient Representation of Subpopulations

Despite being entirely random, simple random sampling can miss important subpopulations and features in the population. For example, in our town with 100,000 residents, imagine that we’re particularly interested in surveying those who are at least 90 years old. You plan to obtain a sample size of 1000, which is 1 out of 100 residents. However, there are only 50 people in town who are older than 90. Your sample might not include anyone in this vital group! If it does, it’ll be a tiny number that doesn’t provide a clear picture of this subgroup.

Simple random sampling can fail to provide precise data about particular subgroups and differences between subgroups. Other sampling methods can ensure sufficient numbers from small subgroups that produce a clear picture and increase the ability to compare subgroups.

Simple Random Sampling vs. Other Methods

Because you need a list of the entire population, simple random sampling is most feasible when working with a relatively small population that is already defined. For example, if you’re surveying a company and can easily obtain a list of employees from Human Resources, SRS isn’t too difficult. Large populations can require extensive amounts of time and resources just to create the complete list. Simple random sampling is a great option when you don’t know much about your population other than its membership.

However, other sampling methods can be more efficient when creating the population list is difficult, your population is large and dispersed, or you need to guarantee sufficient data for specific subpopulations. Alternative methods can reduce the need for a complete list and reduce the logistical headaches of a geographically extensive study.

For example, a national opinion poll company might consider an alternative method to assess differences between subpopulations, such as gender, race, and age.

These other methods frequently require you to have a greater understanding of your population than SRS requires. Consider the following alternatives to simple random sampling that can also obtain representative samples:

• Systematic sampling : Uses a random starting point but then samples at a fixed interval. Does not require a complete population list.
• Stratified sampling: Divides the population into dissimilar strata. Ensures that the sample includes specific subpopulations and facilitates comparisons between them.
• Cluster sampling : Divides the population into clusters that mirror the entire population. Then you randomly select from a subset of clusters. Reduces the need for a complete list of the population and eases logistics issues.

For a contrast to representative sampling methods, learn about convenience sampling , which tends to produce biased samples.

Learn about the specialized random sampling process that Political Polls use, allowing a relatively small sample to predict an election.

Sampling in Developmental Science: Situations, Shortcomings, Solutions, and Standards (nih.gov)

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Sampling Methods & Strategies 101

Everything you need to know (including examples)

By: Derek Jansen (MBA) | Expert Reviewed By: Kerryn Warren (PhD) | January 2023

If you’re new to research, sooner or later you’re bound to wander into the intimidating world of sampling methods and strategies. If you find yourself on this page, chances are you’re feeling a little overwhelmed or confused. Fear not – in this post we’ll unpack sampling in straightforward language , along with loads of examples .

Overview: Sampling Methods & Strategies

• What is sampling in a research context?
• The two overarching approaches

Simple random sampling

Stratified random sampling, cluster sampling, systematic sampling, purposive sampling, convenience sampling, snowball sampling.

• How to choose the right sampling method

What (exactly) is sampling?

At the simplest level, sampling (within a research context) is the process of selecting a subset of participants from a larger group . For example, if your research involved assessing US consumers’ perceptions about a particular brand of laundry detergent, you wouldn’t be able to collect data from every single person that uses laundry detergent (good luck with that!) – but you could potentially collect data from a smaller subset of this group.

In technical terms, the larger group is referred to as the population , and the subset (the group you’ll actually engage with in your research) is called the sample . Put another way, you can look at the population as a full cake and the sample as a single slice of that cake. In an ideal world, you’d want your sample to be perfectly representative of the population, as that would allow you to generalise your findings to the entire population. In other words, you’d want to cut a perfect cross-sectional slice of cake, such that the slice reflects every layer of the cake in perfect proportion.

Achieving a truly representative sample is, unfortunately, a little trickier than slicing a cake, as there are many practical challenges and obstacles to achieving this in a real-world setting. Thankfully though, you don’t always need to have a perfectly representative sample – it all depends on the specific research aims of each study – so don’t stress yourself out about that just yet!

With the concept of sampling broadly defined, let’s look at the different approaches to sampling to get a better understanding of what it all looks like in practice.

The two overarching sampling approaches

At the highest level, there are two approaches to sampling: probability sampling and non-probability sampling . Within each of these, there are a variety of sampling methods , which we’ll explore a little later.

Probability sampling involves selecting participants (or any unit of interest) on a statistically random basis , which is why it’s also called “random sampling”. In other words, the selection of each individual participant is based on a pre-determined process (not the discretion of the researcher). As a result, this approach achieves a random sample.

Probability-based sampling methods are most commonly used in quantitative research , especially when it’s important to achieve a representative sample that allows the researcher to generalise their findings.

Non-probability sampling , on the other hand, refers to sampling methods in which the selection of participants is not statistically random . In other words, the selection of individual participants is based on the discretion and judgment of the researcher, rather than on a pre-determined process.

Non-probability sampling methods are commonly used in qualitative research , where the richness and depth of the data are more important than the generalisability of the findings.

If that all sounds a little too conceptual and fluffy, don’t worry. Let’s take a look at some actual sampling methods to make it more tangible.

Need a helping hand?

Probability-based sampling methods

First, we’ll look at four common probability-based (random) sampling methods:

Importantly, this is not a comprehensive list of all the probability sampling methods – these are just four of the most common ones. So, if you’re interested in adopting a probability-based sampling approach, be sure to explore all the options.

Simple random sampling involves selecting participants in a completely random fashion , where each participant has an equal chance of being selected. Basically, this sampling method is the equivalent of pulling names out of a hat , except that you can do it digitally. For example, if you had a list of 500 people, you could use a random number generator to draw a list of 50 numbers (each number, reflecting a participant) and then use that dataset as your sample.

Thanks to its simplicity, simple random sampling is easy to implement , and as a consequence, is typically quite cheap and efficient . Given that the selection process is completely random, the results can be generalised fairly reliably. However, this also means it can hide the impact of large subgroups within the data, which can result in minority subgroups having little representation in the results – if any at all. To address this, one needs to take a slightly different approach, which we’ll look at next.

Stratified random sampling is similar to simple random sampling, but it kicks things up a notch. As the name suggests, stratified sampling involves selecting participants randomly , but from within certain pre-defined subgroups (i.e., strata) that share a common trait . For example, you might divide the population into strata based on gender, ethnicity, age range or level of education, and then select randomly from each group.

The benefit of this sampling method is that it gives you more control over the impact of large subgroups (strata) within the population. For example, if a population comprises 80% males and 20% females, you may want to “balance” this skew out by selecting a random sample from an equal number of males and females. This would, of course, reduce the representativeness of the sample, but it would allow you to identify differences between subgroups. So, depending on your research aims, the stratified approach could work well.

Next on the list is cluster sampling. As the name suggests, this sampling method involves sampling from naturally occurring, mutually exclusive clusters within a population – for example, area codes within a city or cities within a country. Once the clusters are defined, a set of clusters are randomly selected and then a set of participants are randomly selected from each cluster.

Now, you’re probably wondering, “how is cluster sampling different from stratified random sampling?”. Well, let’s look at the previous example where each cluster reflects an area code in a given city.

With cluster sampling, you would collect data from clusters of participants in a handful of area codes (let’s say 5 neighbourhoods). Conversely, with stratified random sampling, you would need to collect data from all over the city (i.e., many more neighbourhoods). You’d still achieve the same sample size either way (let’s say 200 people, for example), but with stratified sampling, you’d need to do a lot more running around, as participants would be scattered across a vast geographic area. As a result, cluster sampling is often the more practical and economical option.

If that all sounds a little mind-bending, you can use the following general rule of thumb. If a population is relatively homogeneous , cluster sampling will often be adequate. Conversely, if a population is quite heterogeneous (i.e., diverse), stratified sampling will generally be more appropriate.

The last probability sampling method we’ll look at is systematic sampling. This method simply involves selecting participants at a set interval , starting from a random point .

For example, if you have a list of students that reflects the population of a university, you could systematically sample that population by selecting participants at an interval of 8 . In other words, you would randomly select a starting point – let’s say student number 40 – followed by student 48, 56, 64, etc.

What’s important with systematic sampling is that the population list you select from needs to be randomly ordered . If there are underlying patterns in the list (for example, if the list is ordered by gender, IQ, age, etc.), this will result in a non-random sample, which would defeat the purpose of adopting this sampling method. Of course, you could safeguard against this by “shuffling” your population list using a random number generator or similar tool.

Non-probability-based sampling methods

Right, now that we’ve looked at a few probability-based sampling methods, let’s look at three non-probability methods :

Again, this is not an exhaustive list of all possible sampling methods, so be sure to explore further if you’re interested in adopting a non-probability sampling approach.

First up, we’ve got purposive sampling – also known as judgment , selective or subjective sampling. Again, the name provides some clues, as this method involves the researcher selecting participants using his or her own judgement , based on the purpose of the study (i.e., the research aims).

For example, suppose your research aims were to understand the perceptions of hyper-loyal customers of a particular retail store. In that case, you could use your judgement to engage with frequent shoppers, as well as rare or occasional shoppers, to understand what judgements drive the two behavioural extremes .

Purposive sampling is often used in studies where the aim is to gather information from a small population (especially rare or hard-to-find populations), as it allows the researcher to target specific individuals who have unique knowledge or experience . Naturally, this sampling method is quite prone to researcher bias and judgement error, and it’s unlikely to produce generalisable results, so it’s best suited to studies where the aim is to go deep rather than broad .

Next up, we have convenience sampling. As the name suggests, with this method, participants are selected based on their availability or accessibility . In other words, the sample is selected based on how convenient it is for the researcher to access it, as opposed to using a defined and objective process.

Naturally, convenience sampling provides a quick and easy way to gather data, as the sample is selected based on the individuals who are readily available or willing to participate. This makes it an attractive option if you’re particularly tight on resources and/or time. However, as you’d expect, this sampling method is unlikely to produce a representative sample and will of course be vulnerable to researcher bias , so it’s important to approach it with caution.

Last but not least, we have the snowball sampling method. This method relies on referrals from initial participants to recruit additional participants. In other words, the initial subjects form the first (small) snowball and each additional subject recruited through referral is added to the snowball, making it larger as it rolls along .

Snowball sampling is often used in research contexts where it’s difficult to identify and access a particular population. For example, people with a rare medical condition or members of an exclusive group. It can also be useful in cases where the research topic is sensitive or taboo and people are unlikely to open up unless they’re referred by someone they trust.

Simply put, snowball sampling is ideal for research that involves reaching hard-to-access populations . But, keep in mind that, once again, it’s a sampling method that’s highly prone to researcher bias and is unlikely to produce a representative sample. So, make sure that it aligns with your research aims and questions before adopting this method.

How to choose a sampling method

Now that we’ve looked at a few popular sampling methods (both probability and non-probability based), the obvious question is, “ how do I choose the right sampling method for my study?”. When selecting a sampling method for your research project, you’ll need to consider two important factors: your research aims and your resources .

As with all research design and methodology choices, your sampling approach needs to be guided by and aligned with your research aims, objectives and research questions – in other words, your golden thread. Specifically, you need to consider whether your research aims are primarily concerned with producing generalisable findings (in which case, you’ll likely opt for a probability-based sampling method) or with achieving rich , deep insights (in which case, a non-probability-based approach could be more practical). Typically, quantitative studies lean toward the former, while qualitative studies aim for the latter, so be sure to consider your broader methodology as well.

The second factor you need to consider is your resources and, more generally, the practical constraints at play. If, for example, you have easy, free access to a large sample at your workplace or university and a healthy budget to help you attract participants, that will open up multiple options in terms of sampling methods. Conversely, if you’re cash-strapped, short on time and don’t have unfettered access to your population of interest, you may be restricted to convenience or referral-based methods.

In short, be ready for trade-offs – you won’t always be able to utilise the “perfect” sampling method for your study, and that’s okay. Much like all the other methodological choices you’ll make as part of your study, you’ll often need to compromise and accept practical trade-offs when it comes to sampling. Don’t let this get you down though – as long as your sampling choice is well explained and justified, and the limitations of your approach are clearly articulated, you’ll be on the right track.

Let’s recap…

In this post, we’ve covered the basics of sampling within the context of a typical research project.

• Sampling refers to the process of defining a subgroup (sample) from the larger group of interest (population).
• The two overarching approaches to sampling are probability sampling (random) and non-probability sampling .
• Common probability-based sampling methods include simple random sampling, stratified random sampling, cluster sampling and systematic sampling.
• Common non-probability-based sampling methods include purposive sampling, convenience sampling and snowball sampling.
• When choosing a sampling method, you need to consider your research aims , objectives and questions, as well as your resources and other practical constraints .

If you’d like to see an example of a sampling strategy in action, be sure to check out our research methodology chapter sample .

Last but not least, if you need hands-on help with your sampling (or any other aspect of your research), take a look at our 1-on-1 coaching service , where we guide you through each step of the research process, at your own pace.

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This post was based on one of our popular Research Bootcamps . If you're working on a research project, you'll definitely want to check this out ...

Excellent and helpful. Best site to get a full understanding of Research methodology. I’m nolonger as “clueless “..😉

Excellent and helpful for junior researcher!

Grad Coach tutorials are excellent – I recommend them to everyone doing research. I will be working with a sample of imprisoned women and now have a much clearer idea concerning sampling. Thank you to all at Grad Coach for generously sharing your expertise with students.

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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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• 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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Simple Random Sample: Definition and Examples

What is a random sample.

A random sample is a sample that is chosen randomly. It could be more accurately called a randomly chosen sample. Random samples are used to avoid bias and other unwanted effects. Of course, it isn’t quite as simple as it seems: choosing a random sample isn’t as simple as just picking 100 people from 10,000 people. You have to be sure that your random sample is truly random!

Note that the word “random” in random sample doesn’t exactly fit the dictionary definition of the word. If you Google “define:random” then you’ll read that it means:

made, done, happening, or chosen without method or conscious decision. “a random sample of 100 households”

It isn’t true that a random sample is chosen “without method of conscious decision.” Simple random sampling is one way to choose a random sample.

What is a Simple Random Sample?

A simple random sample is often mentioned in elementary statistics classes, but it’s actually one of the least used techniques. In theory, it’s easy to understand. However, in practice it’s tough to perform.

Technically, a simple random sample is a set of n objects in a population of N objects where all possible samples are equally likely to happen. Here’s a basic example of how to get a simple random sample: put 100 numbered bingo balls into a bowl (this is the population N). Select 10 balls from the bowl without looking (this is your sample n). Note that it’s important not to look as you could (unknowingly) bias the sample. While the “lottery bowl” method can work fine for smaller populations, in reality you’ll be dealing with much larger populations.

Imagine the people illustrated in the image above are game pieces. Place the 12 game pieces in a bowl and (again, without looking) choose 3. This is simple random sampling.

How to Perform Simple Random Sampling: Example

A larger population might be “All people who have had strokes in the United States.” That list of participants would be extremely hard to obtain. Where would you get such a list in the first place? You could contact individual hospitals (of which there are thousands and thousands…) and ask for a list of patients (would they even supply you with that information? If you could somehow obtain this list then you will end up with a list of 800,000 people which you then have to put into a “bowl” of some sort and choose random people for your sample. This type of situation is the type of real-life situation you’ll come across and is what makes getting a simple random sample so hard to undertake.

Example question: Outline the steps for obtaining a simple random sample for outcomes of strokes in U.S. trauma hospitals.

Step 1: Make a list of all the trauma hospitals in the U.S. (there are several hundred: the CDC keeps a list).

Step 2: Assign a sequential number to each trauma center (1,2,3…n). This is your sampling frame (the list from which you draw your simple random sample).

Step 3: Figure out what your sample size is going to be . See: ( Sample size ) (how to find one).

Step 4: Use a random number generator to select the sample , using your sampling frame (population size) from Step 2 and your sample size from Step 3. For example, if your sample size is 50 and your population is 500, generate 50 random numbers between 1 and 500.

Warning : If you compromise (say, by not including ALL trauma centers in your sampling frame), it could open your results to bias.

Simple Random Sample vs. Random Sample

A simple random sample is similar to a random sample. The difference between the two is that with a simple random sample, each object in the population has an equal chance of being chosen. With random sampling, each object does not necessarily have an equal chance of being chosen. Unequal probability sampling isn’t usually addressed in basic statistics courses.

Square Root Biased Sampling

Square root biased sampling isn’t a technique that’s widely used, and it’s doubtful that you’ll be tested on it in any elementary statistics or AP statistics class. That said it is an interesting technique that attempts to address the problem of profiling at airport screenings.

I get selected for “extra screening” every time I travel by plane. I’m guessing it’s because I have dreadlocks, but I really have no idea. All I know is something about me is causing security to pull me aside every time. As well as it not being fair, it’s also taking up resources that could be better spent looking at other people who might actually be up to terrorist activities!

Statisticians strive to choose random people for surveys and experiments. This random sampling doesn’t happen at airport screenings, presumably because people who “look” a certain way are more likely to be terrorists. This is a problem William H. Press attempts to address with square root biased sampling. He states:

“…resources are wasted on the repeated screening of higher probability, but innocent, individuals.”

In other words, profiling by ethnicity, having the same name as someone on a watch list (or in my case, having dreadlocks) isn’t a mathematically sound way to catch a terrorist.

Square root biased sampling adds simple random sampling to profiling. Simple random sampling is where individuals are chosen completely by chance from a population. The addition of SRS increases the chance a guilty person will be found. It should also mean innocent travelers are more likely to breeze through security. The system works by assigning the same profiling. Instead of a profiled passenger being selected for screening every time, they may be pulled aside less frequently. For example, if a person is 10 times more likely to be a terrorist, the current system would pull them aside ten times more often than a non-profiled passenger. This basically means every time that profiled person travels they will be pulled aside. The addition of SRS means that the passenger will only be pulled aside three times as often.

Other ways to get a random sample: Stratified random sample Single-stage cluster sampling

Agresti A. (1990) Categorical Data Analysis. John Wiley and Sons, New York. Dodge, Y. (2008). The Concise Encyclopedia of Statistics . Springer. Gonick, L. (1993). The Cartoon Guide to Statistics . HarperPerennial. William Press .

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What Is a Simple Random Sample?

• How It Works
• Conducting a Simple Random Sample

Random Sampling Techniques

• Simple Random vs. Other Methods
• Pros and Cons
• Simple Random Sample FAQs

The Bottom Line

• Corporate Finance
• Financial Analysis

Simple Random Sampling: 6 Basic Steps With Examples

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and behavioral finance. Adam received his master's in economics from The New School for Social Research and his Ph.D. from the University of Wisconsin-Madison in sociology. He is a CFA charterholder as well as holding FINRA Series 7, 55 & 63 licenses. He currently researches and teaches economic sociology and the social studies of finance at the Hebrew University in Jerusalem.

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. A simple random sample is meant to be an unbiased representation of a group.

Key Takeaways

• A simple random sample takes a small, random portion of the entire population to represent the entire data set, where each member has an equal probability of being chosen.
• Researchers can create a simple random sample using methods such as lotteries or random draws.
• A sampling error can occur with a simple random sample if the sample does not end up accurately reflecting the population it is supposed to represent.
• Simple random samples are determined by assigning sequential values to each item within a population, then randomly selecting those values.
• Systematic sampling, stratified sampling, and cluster sampling are other types of sampling approaches that may be used instead of simple random sampling.

Investopedia / Madelyn Goodnight

Understanding a Simple Random Sample

Researchers can create a simple random sample using a couple of methods. With a lottery method, each member of the population is assigned a number, and numbers are then selected at random.

An example of a simple random sample would be to choose the names of 25 employees out of a hat from a company of 250 employees. In this case the population is all 250 employees, and the sample is random because each employee has an equal chance of being chosen. Random sampling is used in science to conduct randomized control tests or for blinded experiments.

The example in which the names of 25 employees out of 250 are chosen out of a hat is an example of the lottery method at work. Each of the 250 employees would be assigned a number between one and 250, after which 25 of those numbers would be chosen at random.

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.

A manual lottery method can be quite onerous for larger populations. Selecting a random sample from a large population usually requires a computer-generated process. The same methodology as the lottery method is used, only the number assignments and subsequent selections are performed by computers, not humans.

Room for Error

With a simple random sample, there has to be room for error represented by a plus and minus variance ( sampling error ). For example, if a survey is taken to determine how many students are left-handed in a high school of 1,000 students, random sampling can determine that eight out of the 100 sampled are left-handed. The conclusion would then be that 8% of the student population of the high school are left-handed, when in fact the global average would be closer to 10%.

The same is true regardless of the subject matter. A survey on the percentage of the student population that has green eyes or a physical disability would result in a mathematical probability based on a simple random survey, but always with a plus or minus variance. The only way to have 100% accuracy rate would be to survey all 1,000 students which, while possible, would be impractical.

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.

How to Conduct a Simple Random Sample

The simple random sampling process entails six steps, each performed in sequential order.

Step 1: Define the Population

The starting point of statistical analysis is to determine the population base. This is the group about which you wish to learn more, confirm a hypothesis , or determine a statistical outcome. This step is simply to identify what that population base is and ensure that the group will adequately cover the outcome you are trying to ascertain.

Example: You want to learn how the stocks of the largest companies in the United States have performed over the past 20 years. Your population would be the largest companies in the United States as determined by the S&P 500.

Step 2: Choose the Sample Size

Before picking the units within a population, we need to determine how many to select. This sample size may be constrained by the amount of time, capital rationing , or other resources available to analyze the sample. However, be mindful to pick a sample size large enough to be genuinely representative of the population. In the example above, there are constraints in analyzing the performance for every stock in the S&P 500, so we only want to analyze a subset of this population.

Example: Your sample size will be 20 companies from the S&P 500.

Step 3: Determine Population Units

In our example the items within the population are easy to determine, as they've already been identified for us (i.e., the companies listed within the S&P 500). However, imagine analyzing the students currently enrolled at a university or food products being sold at a grocery store. This step entails crafting the entire list of all items within your population.

Example: Using exchange information, you copy the companies comprising the S&P 500 into an Excel spreadsheet.

Step 4: Assign Numerical Values

The simple random sample process calls for every unit within the population to receive an unrelated numerical value. This is often assigned based on how the data may be filtered. For example, you could assign the numbers one to 500 to the companies based on market cap , alphabetical order, or company formation date. How the values are assigned isn’t relevant; all that matters is that each value is sequential and has an equal chance of being selected.

Example: You assign the numbers one through 500 to the companies in the S&P 500 based on alphabetical order of the current CEO's surname, with the first company receiving the value one and the last company receiving the value 500.

Step 5: Select Random Values

In step 2 we chose 20 as the number of items we wanted to analyze within our population. We now randomly select 20 number values out of the 500. There are multiple ways to do this, as discussed later in this article.

Example: Using a random number table (see below), you select the numbers 2, 7, 17, 67, 68, 75, 77, 87, 92, 101, 145, 201, 222, 232, 311, 333, 376, 401, 478, and 489.

Step 6: Identify the Sample

Each of the random variables selected in the prior step corresponds to an item within our population. The group sample is selected by identifying which random values were chosen and which population items those values match.

Example: Your sample consists of the companies that correspond to the values chosen in step 5.

There is no single method for determining the random values to be selected in step 5. The analyst can’t choose completely random numbers on their own, as there may be factors influencing their decision. For example, the analyst’s wedding anniversary may be the 24th, so they may consciously (or subconsciously) pick the random value 24. Instead, the analyst may choose one of the following methods:

• Random lottery : Each population number receives an equivalent item, say a ping pong ball or slip of paper, on which it is written, and those items are stored in a box. Random numbers are then selected by pulling items from the container without looking at them.
• Physical methods : Simple, early methods of random selection may use dice, flipping coins, or spinning wheels. Each outcome is assigned a value or outcome relating to the population.
• Random number table : Many statistics and research books contain sample tables with randomized numbers.
• Online random number generator : Many online tools exist where an analyst inputs first the population size and then the sample size to be selected.
• Random numbers from Excel : Numbers can be selected in Excel using the =RANDBETWEEN formula. A cell containing =RANDBETWEEN(1,5) will select a single random number between one and 5.

When pulling together a sample, consider getting assistance from a colleague or an independent person. They may be able to identify biases or discrepancies of which you may not be aware.

Simple Random vs. Other Sampling Methods

Simple random vs. stratified random sample.

A simple random sample is used to represent the entire data population. A stratified random sample divides the population into smaller groups, known as “strata,” based on shared characteristics.

Unlike simple random samples, stratified random samples are used with populations that can be easily broken into different subgroups or subsets. These groups are based on certain criteria, then elements from each are randomly chosen in proportion to the group’s size versus the population. In our example above, S&P 500 companies could have subsets defined by type of industry or geographical region of the company’s headquarters.

This method of sampling means there will be selections from each different group—the size of which is based on its proportion to the entire population. Researchers must ensure that the strata do not overlap. Every point in the population must only belong to one stratum, because they should be  mutually exclusive . Overlapping strata would increase the likelihood that some data are included, thus skewing the sample.

Simple Random vs. Systematic Sampling

Systematic sampling entails selecting a single random variable that determines the interval of how the population items are selected. For example, if the number 37 was chosen, the 37th company on the list sorted by last name of the CEO would be selected by the sample. Then, the 74th (i.e., the next 37th) and the 111st (i.e. the next 37th after that) would be added as well.

Simple random sampling does not have a starting point; therefore, there is the risk that the population items selected at random may cluster. In our example there may be an abundance of CEOs with a last name that starts with the letter 'F.' Systematic sampling strives to even further reduce bias by ensuring that these clusters do not happen.

Simple Random vs. Cluster Sampling

Cluster sampling (also known as “multistage random sampling”) can occur as a one-stage or two-stage cluster. In the former, items within a population are put into comparable groupings (using our example, companies are grouped by year formed), then sampling occurs within these clusters.

Two-stage cluster sampling occurs when clusters are formed through random selection. The population is not clustered with other similar items. Sample items are then randomly selected within each cluster.

Simple random sampling does not cluster any population sets. Clustering (especially two-stage clustering) can enhance the randomness of sample items. In addition, cluster sampling may provide a deeper analysis on a specific snapshot of a population, which may or may not enhance the analysis.

Advantages and Disadvantages of Simple Random Samples

While simple random samples are easy to use, they do come with key disadvantages that can render the data useless.

Advantages of a Simple Random Sample

Ease of use represents the biggest advantage of simple random sampling. Unlike more complicated sampling methods, such as stratified random sampling and probability sampling, there is no need to divide the population into subpopulations or take any other additional steps before selecting members of the population at random.

A simple random sample is meant to be an unbiased representation of a group. It is considered a fair way to select a sample from a larger population, as every member of the population has an equal chance of getting selected. Therefore, it has less chance of sampling bias.

Disadvantages of a Simple Random Sample

A sampling error can occur with a simple random sample if the sample does not end up accurately reflecting the population it is supposed to represent. For example, in a simple random sample of 25 employees, it would be possible to draw 25 men even if the population consisted of 125 women, 125 men, and 125 nonbinary people.

For this reason simple random sampling is more commonly used when the researcher knows little about the population. If the researcher knows more, it is better to use a different sampling technique, such as stratified random sampling, which helps to account for the differences within the population, such as age, race, or gender.

Other disadvantages include the fact that for sampling from large populations, the process can be time-consuming and costly compared with other methods. Researchers may find that a project not worth the endeavor of its cost-benefit analysis does not generate positive results.

As every unit has to be assigned an identifying or sequential number prior to the selection process, this task may be difficult based on the method of data collection or size of the data set.

Simple Random Sampling

Each item within a population has an equal chance of being selected.

There is less of a chance of sampling bias, as every item is randomly selected.

It is easy and convenient for data sets already listed or digitally stored.

Incomplete population demographics may exclude certain groups from being sampled.

Random selection means the sample may not be truly representative of the population.

Depending on the data set size and format, random sampling may be a time-intensive process.

Why Is a Simple Random Sample Simple?

No easier method exists to extract a research sample from a larger population than simple random sampling. Selecting enough subjects completely at random from the larger population also yields a sample that can be representative of the group being studied.

What Are Some Drawbacks of a Simple Random Sample?

Among the disadvantages of this technique are difficulty gaining access to respondents that can be drawn from the larger population, greater time, greater costs, and the fact that bias can still occur under certain circumstances.

What Is a Stratified Random Sample?

A stratified random sample first divides the population into smaller groups, or strata, based on shared characteristics. Therefore, a stratified sampling strategy will ensure that members from each subgroup are included in the data analysis. Stratified sampling is used to highlight differences among groups in a population, as opposed to simple random sampling, which treats all members of a population as equal, with an equal likelihood of being sampled.

How Are Random Samples Used?

Using simple random sampling allows researchers to make generalizations about a specific population and leave out any bias. Using statistical techniques, inferences and predictions can be made about the population without having to survey or collect data from every individual in that population.

Simple random sampling is the most basic form of analyzing a population, allowing every item within it to have the same probability of being selected. There are also more complicated sampling methods that attempt to correct for possible shortcomings in the simple method. However, they don’t match the ease of simple random sampling for smaller populations.

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Methodology

Systematic Sampling | A Step-by-Step Guide with Examples

Published on October 2, 2020 by Lauren Thomas . Revised on December 18, 2023.

Systematic sampling is a probability sampling method in which researchers select members of the population at a regular interval (or k ) determined in advance.

If the population order is random or random-like (e.g., alphabetical), then this method will give you a representative sample that can be used to draw conclusions about your population of interest.

Table of contents

When to use systematic sampling, step 1: define your population, step 2: decide on your sample size, step 3: calculate sampling interval k, step 4: select the sample and collect data, other interesting articles, frequently asked questions about systematic sampling.

Systematic sampling is a method that imitates many of the randomization benefits of simple random sampling , but is slightly easier to conduct.

You can use systematic sampling with a list of the entire population , like you would in simple random sampling. However, unlike with simple random sampling, you can also use this method when you’re unable to access a list of your population in advance.

Order of the population

When using systematic sampling with a population list, it’s essential to consider the order in which your population is listed to ensure that your sample is valid .

If your population is in ascending or descending order, using systematic sampling should still give you a fairly representative sample, as it will include participants from both the bottom and top ends of the population.

For example, if you are sampling from a list of individuals ordered by age, systematic sampling will result in a population drawn from the entire age spectrum. If you instead used simple random sampling, it is possible (although unlikely) that you would end up with only younger or older individuals.

You should not use systematic sampling if your population is ordered cyclically or periodically, as your resulting sample cannot be guaranteed to be representative.

Systematic sampling without a population list

You can use systematic sampling to imitate the randomization of simple random sampling when you don’t have access to a full list of the population in advance.

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Like other methods of sampling, you must decide upon the population that you are studying.

In systematic sampling, you have two choices for data collection :

• You can select your sample ahead of time from a list and then approach the selected subjects to collect data, or
• You can approach every k th member of your target population to ask them to participate in your study.

Listing the population in advance

Ensure that your list contains the entire population and is not in a periodic or cyclic order. Ideally, it should be in a random or random-like (such as alphabetical) order, which will allow you to imitate the randomization benefits of simple random sampling .

Selecting your sample on the spot

If you cannot access a list in advance, but you are able to physically observe the population, you can also use systematic sampling to select subjects at the moment of data collection.

In this case, ensure that the timing and location of your sampling procedure covers the full population to avoid bias in the results.

Before you choose your interval, you must first decide on your sample size. It’s important to choose a representative number in order to avoid sampling bias . There are several different ways to choose a sample size, but one of the most common involves using a sample size calculator .

Once you have chosen your desired margin of error and confidence level , estimated total size of the population, and the standard deviation of the variables you are attempting to measure, this calculator will provide you with the sample size you should aim for.

When you know your target sample size, you can calculate your interval, k , by dividing your total estimated population size by your sample size. This can be a rough estimate rather than an exact calculation.

If you already have a list of your population, randomly select a starting point on your list, and from there, select every k th member of the population to include in your sample.

If you don’t have a list, you choose every k th member of the population for your sample at the same time as collecting the data for your study.

As in simple random sampling , you should try to make sure every individual you have chosen for your sample actually participates in your study. If those who decide to participate do so for reasons connected with the variables that you are collecting, this could cause research bias to affect your study.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Student’s  t -distribution
• Normal distribution
• Null and Alternative Hypotheses
• Chi square tests
• Confidence interval
• Quartiles & Quantiles
• Cluster sampling
• Stratified sampling
• Data cleansing
• Reproducibility vs Replicability
• Peer review
• Prospective cohort study

Research bias

• Implicit bias
• Cognitive bias
• Placebo effect
• Hawthorne effect
• Hindsight bias
• Affect heuristic
• Social desirability bias

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 .

Systematic sampling is a probability sampling method where researchers select members of the population at a regular interval – for example, by selecting every 15th person on a list of the population. If the population is in a random order, this can imitate the benefits of simple random sampling .

There are three key steps in systematic sampling :

• Define and list your population , ensuring that it is not ordered in a cyclical or periodic order.
• Decide on your sample size and calculate your interval, k , by dividing your population by your target sample size.
• Choose every k th member of the population as your sample.

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