random assignment real life examples

Random Assignment in Psychology (Definition + 40 Examples)

Have you ever wondered how researchers discover new ways to help people learn, make decisions, or overcome challenges? A hidden hero in this adventure of discovery is a method called random assignment, a cornerstone in psychological research that helps scientists uncover the truths about the human mind and behavior.

Random Assignment is a process used in research where each participant has an equal chance of being placed in any group within the study. This technique is essential in experiments as it helps to eliminate biases, ensuring that the different groups being compared are similar in all important aspects.

By doing so, researchers can be confident that any differences observed are likely due to the variable being tested, rather than other factors.

In this article, we’ll explore the intriguing world of random assignment, diving into its history, principles, real-world examples, and the impact it has had on the field of psychology.

History of Random Assignment

Stepping back in time, we delve into the origins of random assignment, which finds its roots in the early 20th century.

The pioneering mind behind this innovative technique was Sir Ronald A. Fisher , a British statistician and biologist. Fisher introduced the concept of random assignment in the 1920s, aiming to improve the quality and reliability of experimental research .

His contributions laid the groundwork for the method's evolution and its widespread adoption in various fields, particularly in psychology.

Fisher’s groundbreaking work on random assignment was motivated by his desire to control for confounding variables – those pesky factors that could muddy the waters of research findings.

By assigning participants to different groups purely by chance, he realized that the influence of these confounding variables could be minimized, paving the way for more accurate and trustworthy results.

Early Studies Utilizing Random Assignment

Following Fisher's initial development, random assignment started to gain traction in the research community. Early studies adopting this methodology focused on a variety of topics, from agriculture (which was Fisher’s primary field of interest) to medicine and psychology.

The approach allowed researchers to draw stronger conclusions from their experiments, bolstering the development of new theories and practices.

One notable early study utilizing random assignment was conducted in the field of educational psychology. Researchers were keen to understand the impact of different teaching methods on student outcomes.

By randomly assigning students to various instructional approaches, they were able to isolate the effects of the teaching methods, leading to valuable insights and recommendations for educators.

Evolution of the Methodology

As the decades rolled on, random assignment continued to evolve and adapt to the changing landscape of research.

Advances in technology introduced new tools and techniques for implementing randomization, such as computerized random number generators, which offered greater precision and ease of use.

The application of random assignment expanded beyond the confines of the laboratory, finding its way into field studies and large-scale surveys.

Researchers across diverse disciplines embraced the methodology, recognizing its potential to enhance the validity of their findings and contribute to the advancement of knowledge.

From its humble beginnings in the early 20th century to its widespread use today, random assignment has proven to be a cornerstone of scientific inquiry.

Its development and evolution have played a pivotal role in shaping the landscape of psychological research, driving discoveries that have improved lives and deepened our understanding of the human experience.

Principles of Random Assignment

Delving into the heart of random assignment, we uncover the theories and principles that form its foundation.

The method is steeped in the basics of probability theory and statistical inference, ensuring that each participant has an equal chance of being placed in any group, thus fostering fair and unbiased results.

Basic Principles of Random Assignment

Understanding the core principles of random assignment is key to grasping its significance in research. There are three principles: equal probability of selection, reduction of bias, and ensuring representativeness.

The first principle, equal probability of selection , ensures that every participant has an identical chance of being assigned to any group in the study. This randomness is crucial as it mitigates the risk of bias and establishes a level playing field.

The second principle focuses on the reduction of bias . Random assignment acts as a safeguard, ensuring that the groups being compared are alike in all essential aspects before the experiment begins.

This similarity between groups allows researchers to attribute any differences observed in the outcomes directly to the independent variable being studied.

Lastly, ensuring representativeness is a vital principle. When participants are assigned randomly, the resulting groups are more likely to be representative of the larger population.

This characteristic is crucial for the generalizability of the study’s findings, allowing researchers to apply their insights broadly.

Theoretical Foundation

The theoretical foundation of random assignment lies in probability theory and statistical inference .

Probability theory deals with the likelihood of different outcomes, providing a mathematical framework for analyzing random phenomena. In the context of random assignment, it helps in ensuring that each participant has an equal chance of being placed in any group.

Statistical inference, on the other hand, allows researchers to draw conclusions about a population based on a sample of data drawn from that population. It is the mechanism through which the results of a study can be generalized to a broader context.

Random assignment enhances the reliability of statistical inferences by reducing biases and ensuring that the sample is representative.

Differentiating Random Assignment from Random Selection

It’s essential to distinguish between random assignment and random selection, as the two terms, while related, have distinct meanings in the realm of research.

Random assignment refers to how participants are placed into different groups in an experiment, aiming to control for confounding variables and help determine causes.

In contrast, random selection pertains to how individuals are chosen to participate in a study. This method is used to ensure that the sample of participants is representative of the larger population, which is vital for the external validity of the research.

While both methods are rooted in randomness and probability, they serve different purposes in the research process.

Understanding the theories, principles, and distinctions of random assignment illuminates its pivotal role in psychological research.

This method, anchored in probability theory and statistical inference, serves as a beacon of reliability, guiding researchers in their quest for knowledge and ensuring that their findings stand the test of validity and applicability.

Methodology of Random Assignment

Implementing random assignment in a study is a meticulous process that involves several crucial steps.

The initial step is participant selection, where individuals are chosen to partake in the study. This stage is critical to ensure that the pool of participants is diverse and representative of the population the study aims to generalize to.

Once the pool of participants has been established, the actual assignment process begins. In this step, each participant is allocated randomly to one of the groups in the study.

Researchers use various tools, such as random number generators or computerized methods, to ensure that this assignment is genuinely random and free from biases.

Monitoring and adjusting form the final step in the implementation of random assignment. Researchers need to continuously observe the groups to ensure that they remain comparable in all essential aspects throughout the study.

If any significant discrepancies arise, adjustments might be necessary to maintain the study’s integrity and validity.

Tools and Techniques Used

The evolution of technology has introduced a variety of tools and techniques to facilitate random assignment.

Random number generators, both manual and computerized, are commonly used to assign participants to different groups. These generators ensure that each individual has an equal chance of being placed in any group, upholding the principle of equal probability of selection.

In addition to random number generators, researchers often use specialized computer software designed for statistical analysis and experimental design.

These software programs offer advanced features that allow for precise and efficient random assignment, minimizing the risk of human error and enhancing the study’s reliability.

Ethical Considerations

The implementation of random assignment is not devoid of ethical considerations. Informed consent is a fundamental ethical principle that researchers must uphold.

Informed consent means that every participant should be fully informed about the nature of the study, the procedures involved, and any potential risks or benefits, ensuring that they voluntarily agree to participate.

Beyond informed consent, researchers must conduct a thorough risk and benefit analysis. The potential benefits of the study should outweigh any risks or harms to the participants.

Safeguarding the well-being of participants is paramount, and any study employing random assignment must adhere to established ethical guidelines and standards.

Conclusion of Methodology

The methodology of random assignment, while seemingly straightforward, is a multifaceted process that demands precision, fairness, and ethical integrity. From participant selection to assignment and monitoring, each step is crucial to ensure the validity of the study’s findings.

The tools and techniques employed, coupled with a steadfast commitment to ethical principles, underscore the significance of random assignment as a cornerstone of robust psychological research.

Benefits of Random Assignment in Psychological Research

The impact and importance of random assignment in psychological research cannot be overstated. It is fundamental for ensuring the study is accurate, allowing the researchers to determine if their study actually caused the results they saw, and making sure the findings can be applied to the real world.

Facilitating Causal Inferences

When participants are randomly assigned to different groups, researchers can be more confident that the observed effects are due to the independent variable being changed, and not other factors.

This ability to determine the cause is called causal inference .

This confidence allows for the drawing of causal relationships, which are foundational for theory development and application in psychology.

Ensuring Internal Validity

One of the foremost impacts of random assignment is its ability to enhance the internal validity of an experiment.

Internal validity refers to the extent to which a researcher can assert that changes in the dependent variable are solely due to manipulations of the independent variable , and not due to confounding variables.

By ensuring that each participant has an equal chance of being in any condition of the experiment, random assignment helps control for participant characteristics that could otherwise complicate the results.

Enhancing Generalizability

Beyond internal validity, random assignment also plays a crucial role in enhancing the generalizability of research findings.

When done correctly, it ensures that the sample groups are representative of the larger population, so can allow researchers to apply their findings more broadly.

This representative nature is essential for the practical application of research, impacting policy, interventions, and psychological therapies.

Limitations of Random Assignment

Potential for implementation issues.

While the principles of random assignment are robust, the method can face implementation issues.

One of the most common problems is logistical constraints. Some studies, due to their nature or the specific population being studied, find it challenging to implement random assignment effectively.

For instance, in educational settings, logistical issues such as class schedules and school policies might stop the random allocation of students to different teaching methods .

Ethical Dilemmas

Random assignment, while methodologically sound, can also present ethical dilemmas.

In some cases, withholding a potentially beneficial treatment from one of the groups of participants can raise serious ethical questions, especially in medical or clinical research where participants' well-being might be directly affected.

Researchers must navigate these ethical waters carefully, balancing the pursuit of knowledge with the well-being of participants.

Generalizability Concerns

Even when implemented correctly, random assignment does not always guarantee generalizable results.

The types of people in the participant pool, the specific context of the study, and the nature of the variables being studied can all influence the extent to which the findings can be applied to the broader population.

Researchers must be cautious in making broad generalizations from studies, even those employing strict random assignment.

Practical and Real-World Limitations

In the real world, many variables cannot be manipulated for ethical or practical reasons, limiting the applicability of random assignment.

For instance, researchers cannot randomly assign individuals to different levels of intelligence, socioeconomic status, or cultural backgrounds.

This limitation necessitates the use of other research designs, such as correlational or observational studies , when exploring relationships involving such variables.

Response to Critiques

In response to these critiques, people in favor of random assignment argue that the method, despite its limitations, remains one of the most reliable ways to establish cause and effect in experimental research.

They acknowledge the challenges and ethical considerations but emphasize the rigorous frameworks in place to address them.

The ongoing discussion around the limitations and critiques of random assignment contributes to the evolution of the method, making sure it is continuously relevant and applicable in psychological research.

While random assignment is a powerful tool in experimental research, it is not without its critiques and limitations. Implementation issues, ethical dilemmas, generalizability concerns, and real-world limitations can pose significant challenges.

However, the continued discourse and refinement around these issues underline the method's enduring significance in the pursuit of knowledge in psychology.

By being careful with how we do things and doing what's right, random assignment stays a really important part of studying how people act and think.

Real-World Applications and Examples

Random assignment has been employed in many studies across various fields of psychology, leading to significant discoveries and advancements.

Here are some real-world applications and examples illustrating the diversity and impact of this method:

• Medicine and Health Psychology: Randomized Controlled Trials (RCTs) are the gold standard in medical research. In these studies, participants are randomly assigned to either the treatment or control group to test the efficacy of new medications or interventions.
• Educational Psychology: Studies in this field have used random assignment to explore the effects of different teaching methods, classroom environments, and educational technologies on student learning and outcomes.
• Cognitive Psychology: Researchers have employed random assignment to investigate various aspects of human cognition, including memory, attention, and problem-solving, leading to a deeper understanding of how the mind works.
• Social Psychology: Random assignment has been instrumental in studying social phenomena, such as conformity, aggression, and prosocial behavior, shedding light on the intricate dynamics of human interaction.

Let's get into some specific examples. You'll need to know one term though, and that is "control group." A control group is a set of participants in a study who do not receive the treatment or intervention being tested , serving as a baseline to compare with the group that does, in order to assess the effectiveness of the treatment.

• Smoking Cessation Study: Researchers used random assignment to put participants into two groups. One group received a new anti-smoking program, while the other did not. This helped determine if the program was effective in helping people quit smoking.
• Math Tutoring Program: A study on students used random assignment to place them into two groups. One group received additional math tutoring, while the other continued with regular classes, to see if the extra help improved their grades.
• Exercise and Mental Health: Adults were randomly assigned to either an exercise group or a control group to study the impact of physical activity on mental health and mood.
• Diet and Weight Loss: A study randomly assigned participants to different diet plans to compare their effectiveness in promoting weight loss and improving health markers.
• Sleep and Learning: Researchers randomly assigned students to either a sleep extension group or a regular sleep group to study the impact of sleep on learning and memory.
• Classroom Seating Arrangement: Teachers used random assignment to place students in different seating arrangements to examine the effect on focus and academic performance.
• Music and Productivity: Employees were randomly assigned to listen to music or work in silence to investigate the effect of music on workplace productivity.
• Medication for ADHD: Children with ADHD were randomly assigned to receive either medication, behavioral therapy, or a placebo to compare treatment effectiveness.
• Mindfulness Meditation for Stress: Adults were randomly assigned to a mindfulness meditation group or a waitlist control group to study the impact on stress levels.
• Video Games and Aggression: A study randomly assigned participants to play either violent or non-violent video games and then measured their aggression levels.
• Online Learning Platforms: Students were randomly assigned to use different online learning platforms to evaluate their effectiveness in enhancing learning outcomes.
• Hand Sanitizers in Schools: Schools were randomly assigned to use hand sanitizers or not to study the impact on student illness and absenteeism.
• Caffeine and Alertness: Participants were randomly assigned to consume caffeinated or decaffeinated beverages to measure the effects on alertness and cognitive performance.
• Green Spaces and Well-being: Neighborhoods were randomly assigned to receive green space interventions to study the impact on residents’ well-being and community connections.
• Pet Therapy for Hospital Patients: Patients were randomly assigned to receive pet therapy or standard care to assess the impact on recovery and mood.
• Yoga for Chronic Pain: Individuals with chronic pain were randomly assigned to a yoga intervention group or a control group to study the effect on pain levels and quality of life.
• Flu Vaccines Effectiveness: Different groups of people were randomly assigned to receive either the flu vaccine or a placebo to determine the vaccine’s effectiveness.
• Reading Strategies for Dyslexia: Children with dyslexia were randomly assigned to different reading intervention strategies to compare their effectiveness.
• Physical Environment and Creativity: Participants were randomly assigned to different room setups to study the impact of physical environment on creative thinking.
• Laughter Therapy for Depression: Individuals with depression were randomly assigned to laughter therapy sessions or control groups to assess the impact on mood.
• Financial Incentives for Exercise: Participants were randomly assigned to receive financial incentives for exercising to study the impact on physical activity levels.
• Art Therapy for Anxiety: Individuals with anxiety were randomly assigned to art therapy sessions or a waitlist control group to measure the effect on anxiety levels.
• Natural Light in Offices: Employees were randomly assigned to workspaces with natural or artificial light to study the impact on productivity and job satisfaction.
• School Start Times and Academic Performance: Schools were randomly assigned different start times to study the effect on student academic performance and well-being.
• Horticulture Therapy for Seniors: Older adults were randomly assigned to participate in horticulture therapy or traditional activities to study the impact on cognitive function and life satisfaction.
• Hydration and Cognitive Function: Participants were randomly assigned to different hydration levels to measure the impact on cognitive function and alertness.
• Intergenerational Programs: Seniors and young people were randomly assigned to intergenerational programs to study the effects on well-being and cross-generational understanding.
• Therapeutic Horseback Riding for Autism: Children with autism were randomly assigned to therapeutic horseback riding or traditional therapy to study the impact on social communication skills.
• Active Commuting and Health: Employees were randomly assigned to active commuting (cycling, walking) or passive commuting to study the effect on physical health.
• Mindful Eating for Weight Management: Individuals were randomly assigned to mindful eating workshops or control groups to study the impact on weight management and eating habits.
• Noise Levels and Learning: Students were randomly assigned to classrooms with different noise levels to study the effect on learning and concentration.
• Bilingual Education Methods: Schools were randomly assigned different bilingual education methods to compare their effectiveness in language acquisition.
• Outdoor Play and Child Development: Children were randomly assigned to different amounts of outdoor playtime to study the impact on physical and cognitive development.
• Social Media Detox: Participants were randomly assigned to a social media detox or regular usage to study the impact on mental health and well-being.
• Therapeutic Writing for Trauma Survivors: Individuals who experienced trauma were randomly assigned to therapeutic writing sessions or control groups to study the impact on psychological well-being.
• Mentoring Programs for At-risk Youth: At-risk youth were randomly assigned to mentoring programs or control groups to assess the impact on academic achievement and behavior.
• Dance Therapy for Parkinson’s Disease: Individuals with Parkinson’s disease were randomly assigned to dance therapy or traditional exercise to study the effect on motor function and quality of life.
• Aquaponics in Schools: Schools were randomly assigned to implement aquaponics programs to study the impact on student engagement and environmental awareness.
• Virtual Reality for Phobia Treatment: Individuals with phobias were randomly assigned to virtual reality exposure therapy or traditional therapy to compare effectiveness.
• Gardening and Mental Health: Participants were randomly assigned to engage in gardening or other leisure activities to study the impact on mental health and stress reduction.

Each of these studies exemplifies how random assignment is utilized in various fields and settings, shedding light on the multitude of ways it can be applied to glean valuable insights and knowledge.

Real-world Impact of Random Assignment

Random assignment is like a key tool in the world of learning about people's minds and behaviors. It’s super important and helps in many different areas of our everyday lives. It helps make better rules, creates new ways to help people, and is used in lots of different fields.

Health and Medicine

In health and medicine, random assignment has helped doctors and scientists make lots of discoveries. It’s a big part of tests that help create new medicines and treatments.

By putting people into different groups by chance, scientists can really see if a medicine works.

This has led to new ways to help people with all sorts of health problems, like diabetes, heart disease, and mental health issues like depression and anxiety.

Schools and education have also learned a lot from random assignment. Researchers have used it to look at different ways of teaching, what kind of classrooms are best, and how technology can help learning.

This knowledge has helped make better school rules, develop what we learn in school, and find the best ways to teach students of all ages and backgrounds.

Workplace and Organizational Behavior

Random assignment helps us understand how people act at work and what makes a workplace good or bad.

Studies have looked at different kinds of workplaces, how bosses should act, and how teams should be put together. This has helped companies make better rules and create places to work that are helpful and make people happy.

Environmental and Social Changes

Random assignment is also used to see how changes in the community and environment affect people. Studies have looked at community projects, changes to the environment, and social programs to see how they help or hurt people’s well-being.

This has led to better community projects, efforts to protect the environment, and programs to help people in society.

Technology and Human Interaction

In our world where technology is always changing, studies with random assignment help us see how tech like social media, virtual reality, and online stuff affect how we act and feel.

This has helped make better and safer technology and rules about using it so that everyone can benefit.

The effects of random assignment go far and wide, way beyond just a science lab. It helps us understand lots of different things, leads to new and improved ways to do things, and really makes a difference in the world around us.

From making healthcare and schools better to creating positive changes in communities and the environment, the real-world impact of random assignment shows just how important it is in helping us learn and make the world a better place.

So, what have we learned? Random assignment is like a super tool in learning about how people think and act. It's like a detective helping us find clues and solve mysteries in many parts of our lives.

From creating new medicines to helping kids learn better in school, and from making workplaces happier to protecting the environment, it’s got a big job!

This method isn’t just something scientists use in labs; it reaches out and touches our everyday lives. It helps make positive changes and teaches us valuable lessons.

Whether we are talking about technology, health, education, or the environment, random assignment is there, working behind the scenes, making things better and safer for all of us.

In the end, the simple act of putting people into groups by chance helps us make big discoveries and improvements. It’s like throwing a small stone into a pond and watching the ripples spread out far and wide.

Thanks to random assignment, we are always learning, growing, and finding new ways to make our world a happier and healthier place for everyone!

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Random Assignment in Psychology: Definition & Examples

Julia Simkus

Editor at Simply Psychology

BA (Hons) Psychology, Princeton University

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

Learn about our Editorial Process

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

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

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

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

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

In psychology, random assignment refers to the practice of allocating participants to different experimental groups in a study in a completely unbiased way, ensuring each participant has an equal chance of being assigned to any group.

In experimental research, random assignment, or random placement, organizes participants from your sample into different groups using randomization. 

Random assignment uses chance procedures to ensure that each participant has an equal opportunity of being assigned to either a control or experimental group.

The control group does not receive the treatment in question, whereas the experimental group does receive the treatment.

When using random assignment, neither the researcher nor the participant can choose the group to which the participant is assigned. This ensures that any differences between and within the groups are not systematic at the onset of the study. 

In a study to test the success of a weight-loss program, investigators randomly assigned a pool of participants to one of two groups.

Group A participants participated in the weight-loss program for 10 weeks and took a class where they learned about the benefits of healthy eating and exercise.

Group B participants read a 200-page book that explains the benefits of weight loss. The investigator randomly assigned participants to one of the two groups.

The researchers found that those who participated in the program and took the class were more likely to lose weight than those in the other group that received only the book.

Importance 

Random assignment ensures that each group in the experiment is identical before applying the independent variable.

In experiments , researchers will manipulate an independent variable to assess its effect on a dependent variable, while controlling for other variables. Random assignment increases the likelihood that the treatment groups are the same at the onset of a study.

Thus, any changes that result from the independent variable can be assumed to be a result of the treatment of interest. This is particularly important for eliminating sources of bias and strengthening the internal validity of an experiment.

Random assignment is the best method for inferring a causal relationship between a treatment and an outcome.

Random Selection vs. Random Assignment 

Random selection (also called probability sampling or random sampling) is a way of randomly selecting members of a population to be included in your study.

On the other hand, random assignment is a way of sorting the sample participants into control and treatment groups. 

Random selection ensures that everyone in the population has an equal chance of being selected for the study. Once the pool of participants has been chosen, experimenters use random assignment to assign participants into groups. 

Random assignment is only used in between-subjects experimental designs, while random selection can be used in a variety of study designs.

Random Assignment vs Random Sampling

Random sampling refers to selecting participants from a population so that each individual has an equal chance of being chosen. This method enhances the representativeness of the sample.

Random assignment, on the other hand, is used in experimental designs once participants are selected. It involves allocating these participants to different experimental groups or conditions randomly.

This helps ensure that any differences in results across groups are due to manipulating the independent variable, not preexisting differences among participants.

When to Use Random Assignment

Random assignment is used in experiments with a between-groups or independent measures design.

In these research designs, researchers will manipulate an independent variable to assess its effect on a dependent variable, while controlling for other variables.

There is usually a control group and one or more experimental groups. Random assignment helps ensure that the groups are comparable at the onset of the study.

How to Use Random Assignment

There are a variety of ways to assign participants into study groups randomly. Here are a handful of popular methods: 

• Random Number Generator : Give each member of the sample a unique number; use a computer program to randomly generate a number from the list for each group.
• Lottery : Give each member of the sample a unique number. Place all numbers in a hat or bucket and draw numbers at random for each group.
• Flipping a Coin : Flip a coin for each participant to decide if they will be in the control group or experimental group (this method can only be used when you have just two groups) 
• Roll a Die : For each number on the list, roll a dice to decide which of the groups they will be in. For example, assume that rolling 1, 2, or 3 places them in a control group and rolling 3, 4, 5 lands them in an experimental group.

When is Random Assignment not used?

• When it is not ethically permissible: Randomization is only ethical if the researcher has no evidence that one treatment is superior to the other or that one treatment might have harmful side effects. 
• When answering non-causal questions : If the researcher is just interested in predicting the probability of an event, the causal relationship between the variables is not important and observational designs would be more suitable than random assignment. 
• When studying the effect of variables that cannot be manipulated: Some risk factors cannot be manipulated and so it would not make any sense to study them in a randomized trial. For example, we cannot randomly assign participants into categories based on age, gender, or genetic factors.

Drawbacks of Random Assignment

While randomization assures an unbiased assignment of participants to groups, it does not guarantee the equality of these groups. There could still be extraneous variables that differ between groups or group differences that arise from chance. Additionally, there is still an element of luck with random assignments.

Thus, researchers can not produce perfectly equal groups for each specific study. Differences between the treatment group and control group might still exist, and the results of a randomized trial may sometimes be wrong, but this is absolutely okay.

Scientific evidence is a long and continuous process, and the groups will tend to be equal in the long run when data is aggregated in a meta-analysis.

Additionally, external validity (i.e., the extent to which the researcher can use the results of the study to generalize to the larger population) is compromised with random assignment.

Random assignment is challenging to implement outside of controlled laboratory conditions and might not represent what would happen in the real world at the population level. 

Random assignment can also be more costly than simple observational studies, where an investigator is just observing events without intervening with the population.

Randomization also can be time-consuming and challenging, especially when participants refuse to receive the assigned treatment or do not adhere to recommendations. 

What is the difference between random sampling and random assignment?

Random sampling refers to randomly selecting a sample of participants from a population. Random assignment refers to randomly assigning participants to treatment groups from the selected sample.

Does random assignment increase internal validity?

Yes, random assignment ensures that there are no systematic differences between the participants in each group, enhancing the study’s internal validity .

Does random assignment reduce sampling error?

Yes, with random assignment, participants have an equal chance of being assigned to either a control group or an experimental group, resulting in a sample that is, in theory, representative of the population.

Random assignment does not completely eliminate sampling error because a sample only approximates the population from which it is drawn. However, random sampling is a way to minimize sampling errors. 

When is random assignment not possible?

Random assignment is not possible when the experimenters cannot control the treatment or independent variable.

For example, if you want to compare how men and women perform on a test, you cannot randomly assign subjects to these groups.

Participants are not randomly assigned to different groups in this study, but instead assigned based on their characteristics.

Does random assignment eliminate confounding variables?

Yes, random assignment eliminates the influence of any confounding variables on the treatment because it distributes them at random among the study groups. Randomization invalidates any relationship between a confounding variable and the treatment.

Why is random assignment of participants to treatment conditions in an experiment used?

Random assignment is used to ensure that all groups are comparable at the start of a study. This allows researchers to conclude that the outcomes of the study can be attributed to the intervention at hand and to rule out alternative explanations for study results.

Further Reading

• Bogomolnaia, A., & Moulin, H. (2001). A new solution to the random assignment problem .  Journal of Economic theory ,  100 (2), 295-328.
• Krause, M. S., & Howard, K. I. (2003). What random assignment does and does not do .  Journal of Clinical Psychology ,  59 (7), 751-766.

15 Random Assignment Examples

In research, random assignment refers to the process of randomly assigning research participants into groups (conditions) in order to minimize the influence of confounding variables or extraneous factors .

Ideally, through randomization, each research participant has an equal chance of ending up in either the control or treatment condition group.

For example, consider the following two groups under analysis. Under a model such as self-selection or snowball sampling, there may be a chance that the reds cluster themselves into one group (The reason for this would likely be that there is a confounding variable that the researchers have not controlled for):

To maximize the chances that the reds will be evenly split between groups, we could employ a random assignment method, which might produce the following more balanced outcome:

This process is considered a gold standard for experimental research and is generally expected of major studies that explore the effects of independent variables on dependent variables .

However, random assignment is not without its flaws – chief among them being the importance of a sufficiently sized sample which will allow for randomization to tend toward a mean (take, for example, the odds of 50/50 heads and tail after 100 coin flips being higher than 1/1 heads and tail after 2 coin flips). In fact, even in the above example where I randomized the colors, you can see that there are twice as many yellows in the treatment condition than the control condition, likely because of the low number of research participants.

Methods for Random Assignment of Participants

Randomly assigning research participants into controls is relatively easy. However, there is a range of ways to go about it, and each method has its own pros and cons.

For example, there are some strategies – like the matched-pair method – that can help you to control for confounds in interesting ways.

Here are some of the most common methods of random assignment, with explanations of when you might want to use each one:

1. Simple Random Assignment This is the most basic form of random assignment. All participants are pooled together and then divided randomly into groups using an equivalent chance process such as flipping a coin, drawing names from a hat, or using a random number generator. This method is straightforward and ensures each participant has an equal chance of being assigned to any group (Jamison, 2019; Nestor & Schutt, 2018).

2. Block Randomization In this method, the researcher divides the participants into “blocks” or batches of a pre-determined size, which is then randomized (Alferes, 2012). This technique ensures that the researcher will have evenly sized groups by the end of the randomization process. It’s especially useful in clinical trials where balanced and similar-sized groups are vital.

3. Stratified Random Assignment In stratified random assignment, the researcher categorizes the participants based on key characteristics (such as gender, age, ethnicity) before the random allocation process begins. Each stratum is then subjected to simple random assignment. This method is beneficial when the researcher aims to ensure that the groups are balanced with regard to certain characteristics or variables (Rosenberger & Lachin, 2015).

4. Cluster Random Assignment Here, pre-existing groups or clusters, such as schools, households, or communities, are randomly assigned to different conditions of a research study. It’s ideal when individual random assignment is not feasible, or when the treatment is naturally delivered at the group or community level (Blair, Coppock & Humphreys, 2023).

5. Matched-Pair Random Assignment In this method, participants are first paired based on a particular characteristic or set of characteristics that are relevant to the research study, such as age, gender, or a specific health condition. Each pair is then split randomly into different research conditions or groups. This can help control for the influence of specific variables and increase the likelihood that the groups will be comparable, thereby increasing the validity of the results (Nestor & Schutt, 2018).

Random Assignment Examples

1. Pharmaceutical Efficacy Study In this type of research, consider a scenario where a pharmaceutical company wishes to test the potency of two different versions of a medication, Medication A and Medication B. The researcher recruits a group of volunteers and randomly assigns them to receive either Medication A or Medication B. This method ensures that each participant has an equal chance of being given either option, mitigating potential bias from the investigator’s side. It’s an expectation, for example, for FDA approval pre-trials (Rosenberger & Lachin, 2015).

2. Educational Techniques Study In this approach, an educator looking to evaluate a new teaching technique may randomly assign their students into two distinct classrooms. In one classroom, the new teaching technique will be implemented, while in the other, traditional methods will be utilized. The students’ performance will then be analyzed to determine if the new teaching strategy yields better results. To ensure the class cohorts are randomly assigned, we need to make sure there is no interference from parents, administrators, or others.

3. Website Usability Test In this digital-oriented example, a web designer could be researching the most effective layout for a website. Participants would be randomly assigned to use websites with a different layout and their navigation and satisfaction would be subsequently measured. This technique helps identify which design is user-friendlier based on the measured outcomes.

4. Physical Fitness Research For an investigator looking to evaluate the effectiveness of different exercise routines for weight loss, they could randomly assign participants to either a High-Intensity Interval Training (HIIT) or an endurance-based running program. By studying the participants’ weight changes across a specified time, a conclusion can be drawn on which exercise regime produces better weight loss results.

5. Environmental Psychology Study In this illustration, imagine a psychologist wanting to understand how office settings influence employees’ productivity. He could randomly assign employees to work in one of two offices: one with windows and natural light, the other windowless. The psychologist would then measure their work output to gauge if the environmental conditions impact productivity.

6. Dietary Research Test In this case, a dietician, striving to determine the efficacy of two diets on heart health, might randomly assign participants to adhere to either a Mediterranean diet or a low-fat diet. The dietician would then track cholesterol levels, blood pressure, and other heart health indicators over a determined period to discern which diet benefits heart health the most.

7. Mental Health Study In examining the IMPACT (Improving Mood-Promoting Access to Collaborative Treatment) model, a mental health researcher could randomly assign patients to receive either standard depression treatment or the IMPACT model treatment. Here, the purpose is to cross-compare recovery rates to gauge the effectiveness of the IMPACT model against the standard treatment.

8. Marketing Research A company intending to validate the effectiveness of different marketing strategies could randomly assign customers to receive either email marketing materials or social media marketing materials. Customer response and engagement rates would then be measured to evaluate which strategy is more beneficial and drives better engagement.

9. Sleep Study Research Suppose a researcher wants to investigate the effects of different levels of screen time on sleep quality. The researcher may randomly assign participants to varying amounts of nightly screen time, then compare sleep quality metrics (such as total sleep time, sleep latency, and awakenings during the night).

10. Workplace Productivity Experiment Let’s consider an HR professional who aims to evaluate the efficacy of open office and closed office layouts on employee productivity. She could randomly assign a group of employees to work in either environment and measure metrics such as work completed, attention to detail, and number of errors made to determine which office layout promotes higher productivity.

11. Child Development Study Suppose a developmental psychologist wants to investigate the effect of different learning tools on children’s development. The psychologist could randomly assign children to use either digital learning tools or traditional physical learning tools, such as books, for a fixed period. Subsequently, their development and learning progression would be tracked to determine which tool fosters more effective learning.

12. Traffic Management Research In an urban planning study, researchers could randomly assign streets to implement either traditional stop signs or roundabouts. The researchers, over a predetermined period, could then measure accident rates, traffic flow, and average travel times to identify which traffic management method is safer and more efficient.

13. Energy Consumption Study In a research project comparing the effectiveness of various energy-saving strategies, residents could be randomly assigned to implement either energy-saving light bulbs or regular bulbs in their homes. After a specific duration, their energy consumption would be compared to evaluate which measure yields better energy conservation.

14. Product Testing Research In a consumer goods case, a company looking to launch a new dishwashing detergent could randomly assign the new product or the existing best seller to a group of consumers. By analyzing their feedback on cleaning capabilities, scent, and product usage, the company can find out if the new detergent is an improvement over the existing one Nestor & Schutt, 2018.

15. Physical Therapy Research A physical therapist might be interested in comparing the effectiveness of different treatment regimens for patients with lower back pain. They could randomly assign patients to undergo either manual therapy or exercise therapy for a set duration and later evaluate pain levels and mobility.

Random assignment is effective, but not infallible. Nevertheless, it does help us to achieve greater control over our experiments and minimize the chances that confounding variables are undermining the direct correlation between independent and dependent variables within a study. Over time, when a sufficient number of high-quality and well-designed studies are conducted, with sufficient sample sizes and sufficient generalizability, we can gain greater confidence in the causation between a treatment and its effects.

Read Next: Types of Research Design

Alferes, V. R. (2012). Methods of randomization in experimental design . Sage Publications.

Blair, G., Coppock, A., & Humphreys, M. (2023). Research Design in the Social Sciences: Declaration, Diagnosis, and Redesign. New Jersey: Princeton University Press.

Jamison, J. C. (2019). The entry of randomized assignment into the social sciences. Journal of Causal Inference , 7 (1), 20170025.

Nestor, P. G., & Schutt, R. K. (2018). Research Methods in Psychology: Investigating Human Behavior. New York: SAGE Publications.

Rosenberger, W. F., & Lachin, J. M. (2015). Randomization in Clinical Trials: Theory and Practice. London: Wiley.

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What Is Random Assignment in Psychology?

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Random assignment means that every participant has the same chance of being chosen for the experimental or control group. It involves using procedures that rely on chance to assign participants to groups. Doing this means that every participant in a study has an equal opportunity to be assigned to any group.

For example, in a psychology experiment, participants might be assigned to either a control or experimental group. Some experiments might only have one experimental group, while others may have several treatment variations.

Using random assignment means that each participant has the same chance of being assigned to any of these groups.

Table of Contents

How to Use Random Assignment

So what type of procedures might psychologists utilize for random assignment? Strategies can include:

• Flipping a coin
• Assigning random numbers
• Rolling dice
• Drawing names out of a hat

How Does Random Assignment Work?

A psychology experiment aims to determine if changes in one variable lead to changes in another variable. Researchers will first begin by coming up with a hypothesis. Once researchers have an idea of what they think they might find in a population, they will come up with an experimental design and then recruit participants for their study.

Once they have a pool of participants representative of the population they are interested in looking at, they will randomly assign the participants to their groups.

• Control group : Some participants will end up in the control group, which serves as a baseline and does not receive the independent variables.
• Experimental group : Other participants will end up in the experimental groups that receive some form of the independent variables.

By using random assignment, the researchers make it more likely that the groups are equal at the start of the experiment. Since the groups are the same on other variables, it can be assumed that any changes that occur are the result of varying the independent variables.

After a treatment has been administered, the researchers will then collect data in order to determine if the independent variable had any impact on the dependent variable.

Random Assignment vs. Random Selection

It is important to remember that random assignment is not the same thing as random selection , also known as random sampling.

Random selection instead involves how people are chosen to be in a study. Using random selection, every member of a population stands an equal chance of being chosen for a study or experiment.

So random sampling affects how participants are chosen for a study, while random assignment affects how participants are then assigned to groups.

Examples of Random Assignment

Imagine that a psychology researcher is conducting an experiment to determine if getting adequate sleep the night before an exam results in better test scores.

Forming a Hypothesis

They hypothesize that participants who get 8 hours of sleep will do better on a math exam than participants who only get 4 hours of sleep.

Obtaining Participants

The researcher starts by obtaining a pool of participants. They find 100 participants from a local university. Half of the participants are female, and half are male.

Randomly Assign Participants to Groups

The researcher then assigns random numbers to each participant and uses a random number generator to randomly assign each number to either the 4-hour or 8-hour sleep groups.

Conduct the Experiment

Those in the 8-hour sleep group agree to sleep for 8 hours that night, while those in the 4-hour group agree to wake up after only 4 hours. The following day, all of the participants meet in a classroom.

Collect and Analyze Data

Everyone takes the same math test. The test scores are then compared to see if the amount of sleep the night before had any impact on test scores.

Why Is Random Assignment Important in Psychology Research?

Random assignment is important in psychology research because it helps improve a study’s internal validity. This means that the researchers are sure that the study demonstrates a cause-and-effect relationship between an independent and dependent variable.

Random assignment improves the internal validity by minimizing the risk that there are systematic differences in the participants who are in each group.

Key Points to Remember About Random Assignment

• Random assignment in psychology involves each participant having an equal chance of being chosen for any of the groups, including the control and experimental groups.
• It helps control for potential confounding variables, reducing the likelihood of pre-existing differences between groups.
• This method enhances the internal validity of experiments, allowing researchers to draw more reliable conclusions about cause-and-effect relationships.
• Random assignment is crucial for creating comparable groups and increasing the scientific rigor of psychological studies.

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The Definition of Random Assignment According to Psychology

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Emily is a board-certified science editor who has worked with top digital publishing brands like Voices for Biodiversity, Study.com, GoodTherapy, Vox, and Verywell.

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Random assignment refers to the use of chance procedures in psychology experiments to ensure that each participant has the same opportunity to be assigned to any given group in a study to eliminate any potential bias in the experiment at the outset. Participants are randomly assigned to different groups, such as the treatment group versus the control group. In clinical research, randomized clinical trials are known as the gold standard for meaningful results.

Simple random assignment techniques might involve tactics such as flipping a coin, drawing names out of a hat, rolling dice, or assigning random numbers to a list of participants. It is important to note that random assignment differs from random selection .

While random selection refers to how participants are randomly chosen from a target population as representatives of that population, random assignment refers to how those chosen participants are then assigned to experimental groups.

Random Assignment In Research

To determine if changes in one variable will cause changes in another variable, psychologists must perform an experiment. Random assignment is a critical part of the experimental design that helps ensure the reliability of the study outcomes.

Researchers often begin by forming a testable hypothesis predicting that one variable of interest will have some predictable impact on another variable.

The variable that the experimenters will manipulate in the experiment is known as the independent variable , while the variable that they will then measure for different outcomes is known as the dependent variable. While there are different ways to look at relationships between variables, an experiment is the best way to get a clear idea if there is a cause-and-effect relationship between two or more variables.

Once researchers have formulated a hypothesis, conducted background research, and chosen an experimental design, it is time to find participants for their experiment. How exactly do researchers decide who will be part of an experiment? As mentioned previously, this is often accomplished through something known as random selection.

Random Selection

In order to generalize the results of an experiment to a larger group, it is important to choose a sample that is representative of the qualities found in that population. For example, if the total population is 60% female and 40% male, then the sample should reflect those same percentages.

Choosing a representative sample is often accomplished by randomly picking people from the population to be participants in a study. Random selection means that everyone in the group stands an equal chance of being chosen to minimize any bias. Once a pool of participants has been selected, it is time to assign them to groups.

By randomly assigning the participants into groups, the experimenters can be fairly sure that each group will have the same characteristics before the independent variable is applied.

Participants might be randomly assigned to the control group , which does not receive the treatment in question. The control group may receive a placebo or receive the standard treatment. Participants may also be randomly assigned to the experimental group , which receives the treatment of interest. In larger studies, there can be multiple treatment groups for comparison.

There are simple methods of random assignment, like rolling the die. However, there are more complex techniques that involve random number generators to remove any human error.

There can also be random assignment to groups with pre-established rules or parameters. For example, if you want to have an equal number of men and women in each of your study groups, you might separate your sample into two groups (by sex) before randomly assigning each of those groups into the treatment group and control group.

Random assignment is essential because it increases the likelihood that the groups are the same at the outset. With all characteristics being equal between groups, other than the application of the independent variable, any differences found between group outcomes can be more confidently attributed to the effect of the intervention.

Example of Random Assignment

Imagine that a researcher is interested in learning whether or not drinking caffeinated beverages prior to an exam will improve test performance. After randomly selecting a pool of participants, each person is randomly assigned to either the control group or the experimental group.

The participants in the control group consume a placebo drink prior to the exam that does not contain any caffeine. Those in the experimental group, on the other hand, consume a caffeinated beverage before taking the test.

Participants in both groups then take the test, and the researcher compares the results to determine if the caffeinated beverage had any impact on test performance.

A Word From Verywell

Random assignment plays an important role in the psychology research process. Not only does this process help eliminate possible sources of bias, but it also makes it easier to generalize the results of a tested sample of participants to a larger population.

Random assignment helps ensure that members of each group in the experiment are the same, which means that the groups are also likely more representative of what is present in the larger population of interest. Through the use of this technique, psychology researchers are able to study complex phenomena and contribute to our understanding of the human mind and behavior.

Lin Y, Zhu M, Su Z. The pursuit of balance: An overview of covariate-adaptive randomization techniques in clinical trials . Contemp Clin Trials. 2015;45(Pt A):21-25. doi:10.1016/j.cct.2015.07.011

Sullivan L. Random assignment versus random selection . In: The SAGE Glossary of the Social and Behavioral Sciences. SAGE Publications, Inc.; 2009. doi:10.4135/9781412972024.n2108

Alferes VR. Methods of Randomization in Experimental Design . SAGE Publications, Inc.; 2012. doi:10.4135/9781452270012

Nestor PG, Schutt RK. Research Methods in Psychology: Investigating Human Behavior. (2nd Ed.). SAGE Publications, Inc.; 2015.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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Random Assignment: Psychology Definition, History & Examples

Random assignment is a foundational concept in experimental psychology, serving as a core methodological strategy to ensure the validity of research findings. By randomly allocating participants to different groups, researchers aim to control for extraneous variables, thereby enhancing the internal validity of their studies.

Historically, this technique has its roots in the field’s evolution towards more rigorous scientific methodologies, progressively refining the ways in which psychological phenomena are empirically tested. Various hallmark experiments across cognitive, social, and clinical psychology have employed random assignment to demonstrate causal relationships between variables.

Such examples underscore the significance of the method in disentangling complex behavioral dynamics. This introduction provides an overview of random assignment, tracing its development and illustrating its application through pertinent examples within psychological research.

Table of Contents

Random assignment in psychology refers to the process of randomly assigning participants to different groups in an experiment . This helps ensure that each group is similar and reduces bias, making the study’s results more reliable.

It allows researchers to attribute the effects observed to the independent variable being tested, rather than other factors, increasing the study’s validity.

Historical Background of Random Assignment in Psychology

Random assignment, a fundamental methodology in psychological research, originated in the early 20th century and has since played a crucial role in advancing the field. This approach was developed to enhance the rigor and validity of experimental design by ensuring unbiased distribution of extraneous variables across treatment and control groups.

The concept of random assignment was influenced by the refinement of the scientific method and the desire for objectivity and replicability in psychological studies. Key figures associated with its development include eminent psychologists such as Charles Sanders Peirce, Ronald A. Fisher, and Jerzy Neyman.

One significant event that contributed to the evolution of random assignment was the advent of experimental psychology in the late 19th century. This marked a shift away from relying solely on introspection and subjective methods towards a more rigorous and empirical approach. As psychologists increasingly sought to establish causality in their research, random assignment emerged as a powerful tool to control for potential confounding factors.

In the early 20th century, Fisher and Neyman independently developed statistical techniques that further solidified the importance of random assignment. Fisher’s work on the design of experiments and the analysis of variance, along with Neyman’s contributions to mathematical statistics, laid the foundation for the widespread adoption of random assignment in psychological research.

Significant studies also played a role in shaping the prominence of random assignment. For example, the Stanford Prison Experiment conducted by Philip Zimbardo in 1971 utilized random assignment to assign participants to the roles of prisoners and guards. This study highlighted the ethical considerations and psychological effects of random assignment, sparking discussions and further refinements in its application.

Random assignment is a concept in psychology that is used in everyday life to ensure fairness and eliminate bias. For example, imagine you are organizing a game of dodgeball. To make the teams fair, you could use random assignment by drawing names out of a hat to determine which players will be on each team. This way, everyone has an equal chance of being on either team, and it helps prevent any advantages or disadvantages based on personal abilities.

Another real-life example of random assignment can be found in product testing. Let’s say a company wants to test the effectiveness of a new face cream. They would use random assignment to assign participants to two groups: one group would use the new face cream, and the other group would use a placebo cream. By randomly assigning participants to each group, the researchers can ensure that any differences in results between the two groups are due to the face cream itself and not other factors like age or skin type.

In education, random assignment can also be seen in the allocation of classroom seating. Teachers often use a random assignment method to assign students to different seats at the beginning of the school year. This helps create a fair and balanced learning environment , as students have an equal chance of being seated next to different classmates and forming new relationships.

These examples demonstrate how random assignment is applied in various real-life situations to ensure fairness, eliminate bias, and obtain reliable results. By using random assignment, researchers, organizers, and educators can make more accurate conclusions and decisions based on data that is free from confounding variables.

Related Terms

Several related terms are essential to understand when discussing random assignment in psychological research, including variables, control groups, and random sampling. These terms are closely linked as they all play crucial roles in the design and implementation of experiments.

Variables are the elements that researchers aim to measure, manipulate, or control in their study. They can be classified into independent variables, which are the presumed causes, and dependent variables, which are the observed effects. For example, in a study investigating the effects of a new medication on anxiety , the independent variable would be the medication, while the dependent variable would be the level of anxiety.

Control groups, on the other hand, serve as a standard or baseline for comparison against the experimental group. They do not receive the experimental treatment, allowing researchers to determine whether the treatment has a genuine effect. In the medication study mentioned earlier, the control group would receive a placebo or an existing medication for anxiety, while the experimental group would receive the new medication.

Random sampling is another important term in psychological research, although it is distinct from random assignment. Random sampling refers to the process of selecting participants from a larger population to be included in the study. It aims to ensure that the sample is representative of the population and that the findings can be generalized.

Random assignment, on the other hand, deals with how participants are then allocated to different groups within the experiment. It ensures that participants have an equal chance of being assigned to either the control or experimental group, minimizing the influence of confounding variables.

In understanding the concept of random assignment in psychology, it is essential to consult reputable sources, studies, and publications that have contributed knowledge to this field. These academically credible references provide a solid foundation for further reading and contribute to a comprehensive understanding of random assignment.

Scholarly journals, such as the Journal of Experimental Psychology: General, the Journal of Personality and Social Psychology, and the Journal of Abnormal Psychology, often publish research articles that explore the application and importance of random assignment in psychological research. These articles undergo rigorous peer-review processes, ensuring that the information presented is of high quality and meets academic standards.

Seminal research articles, such as those by Fisher (1935) and Neyman (1923), have made significant contributions to the understanding and use of random assignment in experimental design. These articles provide historical perspectives and methodological insights that have shaped the field of psychology and continue to inform current research practices.

Authoritative texts, like ‘Experimental and Quasi-Experimental Designs for Generalized Causal Inference’ by Shadish, Cook, and Campbell (2002), offer comprehensive overviews of experimental design, including random assignment. These texts provide in-depth explanations, theoretical frameworks, and practical guidelines for implementing random assignment in psychological research.

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Random Assignment – A Simple Introduction with Examples

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Completing a research or thesis paper is more work than most students imagine. For instance, you must conduct experiments before coming up with conclusions. Random assignment, a key methodology in academic research, ensures every participant has an equal chance of being placed in any group within an experiment. In experimental studies, the random assignment of participants is a vital element, which this article will discuss.

Inhaltsverzeichnis

• 1 Random Assignment – In a Nutshell
• 2 Definition: Random assignment
• 3 Importance of random assignment
• 4 Random assignment vs. random sampling
• 5 How to use random assignment
• 6 When random assignment is not used

Random Assignment – In a Nutshell

• Random assignment is where you randomly place research participants into specific groups.
• This method eliminates bias in the results by ensuring that all participants have an equal chance of getting into either group.
• Random assignment is usually used in independent measures or between-group experiment designs.

Definition: Random assignment

Pearson Correlation is a descriptive statistical procedure that describes the measure of linear dependence between two variables. It entails a sample, control group , experimental design , and randomized design. In this statistical procedure, random assignment is used. Random assignment is the random placement of participants into different groups in experimental research.

Importance of random assignment

Random assessment is essential for strengthening the internal validity of experimental research. Internal validity helps make a casual relationship’s conclusions reliable and trustworthy.

In experimental research, researchers isolate independent variables and manipulate them as they assess the impact while managing other variables. To achieve this, an independent variable for diverse member groups is vital. This experimental design is called an independent or between-group design.

Example: Different levels of independent variables

• In a medical study, you can research the impact of nutrient supplements on the immune (nutrient supplements = independent variable, immune = dependent variable)

Three independent participant levels are applicable here:

• Control group (given 0 dosages of iron supplements)
• The experimental group (low dosage)
• The second experimental group (high dosage)

This assignment technique in experiments ensures no bias in the treatment sets at the beginning of the trials. Therefore, if you do not use this technique, you won’t be able to exclude any alternate clarifications for your findings.

In the research experiment above, you can recruit participants randomly by handing out flyers at public spaces like gyms, cafés, and community centers. Then:

• Place the group from cafés in the control group
• Community center group in the low prescription trial group
• Gym group in the high-prescription group

Even with random participant assignment, other extraneous variables may still create bias in experiment results. However, these variations are usually low, hence should not hinder your research. Therefore, using random placement in experiments is highly necessary, especially where it is ethically required or makes sense for your research subject.

Random assignment vs. random sampling

Simple random sampling is a method of choosing the participants for a study. On the other hand, the random assignment involves sorting the participants selected through random sampling. Another difference between random sampling and random assignment is that the former is used in several types of studies, while the latter is only applied in between-subject experimental designs.

Your study researches the impact of technology on productivity in a specific company.

In such a case, you have contact with the entire staff. So, you can assign each employee a quantity and apply a random number generator to pick a specific sample.

For instance, from 500 employees, you can pick 200. So, the full sample is 200.

Random sampling enhances external validity, as it guarantees that the study sample is unbiased, and that an entire population is represented. This way, you can conclude that the results of your studies can be accredited to the autonomous variable.

After determining the full sample, you can break it down into two groups using random assignment. In this case, the groups are:

• The control group (does get access to technology)
• The experimental group (gets access to technology)

Using random assignment assures you that any differences in the productivity results for each group are not biased and will help the company make a decision.

How to use random assignment

Firstly, give each participant a unique number as an identifier. Then, use a specific tool to simplify assigning the participants to the sample groups. Some tools you can use are:

Random member assignment is a prevailing technique for placing participants in specific groups because each person has a fair opportunity of being put in either group.

Random assignment in block experimental designs

In complex experimental designs , you must group your participants into blocks before using the random assignment technique.

You can create participant blocks depending on demographic variables, working hours, or scores. However, the blocks imply that you will require a bigger sample to attain high statistical power.

After grouping the participants in blocks, you can use random assignments inside each block to allocate the members to a specific treatment condition. Doing this will help you examine if quality impacts the result of the treatment.

Depending on their unique characteristics, you can also use blocking in experimental matched designs before matching the participants in each block. Then, you can randomly allot each partaker to one of the treatments in the research and examine the results.

When random assignment is not used

As powerful a tool as it is, random assignment does not apply in all situations. Like the following:

Comparing different groups

When the purpose of your study is to assess the differences between the participants, random member assignment may not work.

If you want to compare teens and the elderly with and without specific health conditions, you must ensure that the participants have specific characteristics. Therefore, you cannot pick them randomly.

In such a study, the medical condition (quality of interest) is the independent variable, and the participants are grouped based on their ages (different levels). Also, all partakers are tried similarly to ensure they have the medical condition, and their outcomes are tested per group level.

No ethical justifiability

Another situation where you cannot use random assignment is if it is ethically not permitted.

If your study involves unhealthy or dangerous behaviors or subjects, such as drug use. Instead of assigning random partakers to sets, you can conduct quasi-experimental research.

When using a quasi-experimental design , you examine the conclusions of pre-existing groups you have no control over, such as existing drug users. While you cannot randomly assign them to groups, you can use variables like their age, years of drug use, or socioeconomic status to group the participants.

What is the definition of random assignment?

It is an experimental research technique that involves randomly placing participants from your samples into different groups. It ensures that every sample member has the same opportunity of being in whichever group (control or experimental group).

When is random assignment applicable?

You can use this placement technique in experiments featuring an independent measures design. It helps ensure that all your sample groups are comparable.

What is the importance of random assignment?

It can help you enhance your study’s validity . This technique also helps ensure that every sample has an equal opportunity of being assigned to a control or trial group.

When should you NOT use random assignment

You should not use this technique if your study focuses on group comparisons or if it is not legally ethical.

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• Knowledge Base
• Methodology
• Random Assignment in Experiments | Introduction & Examples

Random Assignment in Experiments | Introduction & Examples

Published on 6 May 2022 by Pritha Bhandari . Revised on 13 February 2023.

In experimental research, random assignment is a way of placing participants from your sample into different treatment groups using randomisation.

With simple random assignment, every member of the sample has a known or equal chance of being placed in a control group or an experimental group. Studies that use simple random assignment are also called completely randomised designs .

Random assignment is a key part of experimental design . It helps you ensure that all groups are comparable at the start of a study: any differences between them are due to random factors.

Table of contents

Why does random assignment matter, random sampling vs random assignment, how do you use random assignment, when is random assignment not used, frequently asked questions about random assignment.

Random assignment is an important part of control in experimental research, because it helps strengthen the internal validity of an experiment.

In experiments, researchers manipulate an independent variable to assess its effect on a dependent variable, while controlling for other variables. To do so, they often use different levels of an independent variable for different groups of participants.

This is called a between-groups or independent measures design.

You use three groups of participants that are each given a different level of the independent variable:

• A control group that’s given a placebo (no dosage)
• An experimental group that’s given a low dosage
• A second experimental group that’s given a high dosage

Random assignment to helps you make sure that the treatment groups don’t differ in systematic or biased ways at the start of the experiment.

If you don’t use random assignment, you may not be able to rule out alternative explanations for your results.

• Participants recruited from pubs are placed in the control group
• Participants recruited from local community centres are placed in the low-dosage experimental group
• Participants recruited from gyms are placed in the high-dosage group

With this type of assignment, it’s hard to tell whether the participant characteristics are the same across all groups at the start of the study. Gym users may tend to engage in more healthy behaviours than people who frequent pubs or community centres, and this would introduce a healthy user bias in your study.

Although random assignment helps even out baseline differences between groups, it doesn’t always make them completely equivalent. There may still be extraneous variables that differ between groups, and there will always be some group differences that arise from chance.

Most of the time, the random variation between groups is low, and, therefore, it’s acceptable for further analysis. This is especially true when you have a large sample. In general, you should always use random assignment in experiments when it is ethically possible and makes sense for your study topic.

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Random sampling and random assignment are both important concepts in research, but it’s important to understand the difference between them.

Random sampling (also called probability sampling or random selection) is a way of selecting members of a population to be included in your study. In contrast, random assignment is a way of sorting the sample participants into control and experimental groups.

While random sampling is used in many types of studies, random assignment is only used in between-subjects experimental designs.

Some studies use both random sampling and random assignment, while others use only one or the other.

Random sampling enhances the external validity or generalisability of your results, because it helps to ensure that your sample is unbiased and representative of the whole population. This allows you to make stronger statistical inferences .

You use a simple random sample to collect data. Because you have access to the whole population (all employees), you can assign all 8,000 employees a number and use a random number generator to select 300 employees. These 300 employees are your full sample.

Random assignment enhances the internal validity of the study, because it ensures that there are no systematic differences between the participants in each group. This helps you conclude that the outcomes can be attributed to the independent variable .

• A control group that receives no intervention
• An experimental group that has a remote team-building intervention every week for a month

You use random assignment to place participants into the control or experimental group. To do so, you take your list of participants and assign each participant a number. Again, you use a random number generator to place each participant in one of the two groups.

To use simple random assignment, you start by giving every member of the sample a unique number. Then, you can use computer programs or manual methods to randomly assign each participant to a group.

• Random number generator: Use a computer program to generate random numbers from the list for each group.
• Lottery method: Place all numbers individually into a hat or a bucket, and draw numbers at random for each group.
• Flip a coin: When you only have two groups, for each number on the list, flip a coin to decide if they’ll be in the control or the experimental group.
• Use a dice: When you have three groups, for each number on the list, roll a die to decide which of the groups they will be in. For example, assume that rolling 1 or 2 lands them in a control group; 3 or 4 in an experimental group; and 5 or 6 in a second control or experimental group.

This type of random assignment is the most powerful method of placing participants in conditions, because each individual has an equal chance of being placed in any one of your treatment groups.

Random assignment in block designs

In more complicated experimental designs, random assignment is only used after participants are grouped into blocks based on some characteristic (e.g., test score or demographic variable). These groupings mean that you need a larger sample to achieve high statistical power .

For example, a randomised block design involves placing participants into blocks based on a shared characteristic (e.g., college students vs graduates), and then using random assignment within each block to assign participants to every treatment condition. This helps you assess whether the characteristic affects the outcomes of your treatment.

In an experimental matched design , you use blocking and then match up individual participants from each block based on specific characteristics. Within each matched pair or group, you randomly assign each participant to one of the conditions in the experiment and compare their outcomes.

Sometimes, it’s not relevant or ethical to use simple random assignment, so groups are assigned in a different way.

When comparing different groups

Sometimes, differences between participants are the main focus of a study, for example, when comparing children and adults or people with and without health conditions. Participants are not randomly assigned to different groups, but instead assigned based on their characteristics.

In this type of study, the characteristic of interest (e.g., gender) is an independent variable, and the groups differ based on the different levels (e.g., men, women). All participants are tested the same way, and then their group-level outcomes are compared.

When it’s not ethically permissible

When studying unhealthy or dangerous behaviours, it’s not possible to use random assignment. For example, if you’re studying heavy drinkers and social drinkers, it’s unethical to randomly assign participants to one of the two groups and ask them to drink large amounts of alcohol for your experiment.

When you can’t assign participants to groups, you can also conduct a quasi-experimental study . In a quasi-experiment, you study the outcomes of pre-existing groups who receive treatments that you may not have any control over (e.g., heavy drinkers and social drinkers).

These groups aren’t randomly assigned, but may be considered comparable when some other variables (e.g., age or socioeconomic status) are controlled for.

In experimental research, random assignment is a way of placing participants from your sample into different groups using randomisation. With this method, every member of the sample has a known or equal chance of being placed in a control group or an experimental group.

Random selection, or random sampling , is a way of selecting members of a population for your study’s sample.

In contrast, random assignment is a way of sorting the sample into control and experimental groups.

Random sampling enhances the external validity or generalisability of your results, while random assignment improves the internal validity of your study.

Random assignment is used in experiments with a between-groups or independent measures design. In this research design, there’s usually a control group and one or more experimental groups. Random assignment helps ensure that the groups are comparable.

In general, you should always use random assignment in this type of experimental design when it is ethically possible and makes sense for your study topic.

To implement random assignment , assign a unique number to every member of your study’s sample .

Then, you can use a random number generator or a lottery method to randomly assign each number to a control or experimental group. You can also do so manually, by flipping a coin or rolling a die to randomly assign participants to groups.

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3 Real-World Examples of Using Instrumental Variables

The instrumental variable approach is a method to identify the causal effect of a treatment on an outcome of interest by controlling for unobserved confounding between them.

A valid instrumental variable, Z, is one that influences the outcome, Y, through the treatment, X, without being related to the confounding variable, C, as shown in the following diagram:

Therefore, the effect of the instrumental variable Z on the outcome Y can be used to estimate the effect of the treatment X on the outcome Y bypassing the confounding effect of C.

For more details, see: 7 Different Ways to Control for Confounding .

Example 1: Measuring the effect of smoking during pregnancy on birth weight

Smoking during pregnancy is correlated with low birth weight. But this association is confounded by all sort of unobserved (and hard to measure) maternal characteristics that complicate the relationship between smoking and low birth weight.

Evans and Ringel used cigarette taxes as an instrumental variable to study the causal effect of smoking on birth weight, as shown in the diagram below:

Cigarette taxes is a valid instrumental variable since:

• Cigarette taxes alter the smoking behavior of pregnant women (the instrumental variable Z affects the treatment X).
• Cigarettes taxes can only affect birth weight through the change in the smoking behavior of pregnant women (Z has no direct influence on the outcome Y).
• Cigarette taxes are not affected by the characteristics of the pregnant women (Z is not caused by the confounder C).

Therefore, cigarette taxes can be considered as a source of exogenous variation in the smoking behavior of pregnant women, resembling random assignment of pregnant women to either smoking or not.

Study results:

The authors concluded that an increase in the cigarette tax rates has a beneficial impact on birth weight.

Their estimate of the effect of smoking during pregnancy on birth weight was close to that of a randomized controlled trial, and larger in magnitude than the estimates obtained from other observational studies that used more classical methods of confounding control.

Example 2: Measuring the effect of smoking cessation on weight gain

In order to measure the effect of smoking cessation on weight gain, studies typically compare the average weight gain of quitters to that of continuing smokers while controlling for confounding factors such as age, gender, and initial body weight.

These studies, however, may still be biased since the relationship between smoking cessation and weight gain could be confounded by a long list of unmeasurable and unknown factors.

Eisenberg and Quinn used the instrumental variable approach on data from a randomized controlled trial that randomized smokers to either receive a smoking cessation intervention or not.

Here’s a causal diagram that represents relationships between variables in their study:

Random assignment of smokers to the intervention is a valid instrumental variable since:

• This random assignment affects the probability of quitting smoking (Z affects X).
• This random assignment can only affect weight gain through smoking cessation (Z has no direct influence on Y).
• This random assignment is not affected by any type of confounding (Z is not caused by C).

Therefore, random assignment of smokers to a smoking cessation intervention can be considered as a source of exogenous variation in smoking cessation, allowing us to study the effect of the latter on weight gain bypassing any confounding effect.

Study results

The authors concluded that smoking cessation caused twice the increase in weight as estimated by other studies using suboptimal methods to control confounding.

Example 3: Measuring the effect of heart attack treatment intensity on survival

Patients with a heart attack receive different treatments according to their health status (such as: the presence of other diseases, the severity of the case, etc.). So, if we want to study the causal effect of heart attack treatment intensity on survival we will have to face confounding by all kinds of patient characteristics.

Controlling for all these observable and unobservable characteristics is a real pain that can be avoided by using the instrumental variable approach.

In their study, McClellan and colleagues used the patient proximity to different types of hospitals as an instrumental variable to study the effect of treatment intensity on survival, as shown in the following diagram:

Patient proximity to hospitals is a valid instrumental variable since:

• The patient proximity to a certain type of hospital determines the type and intensity of the received treatment (Z affects X).
• The patient proximity to a certain type of hospital affects the outcome only through the treatment received. In other words, it does not have a direct effect on survival (Z affects Y only through X).
• The patient proximity to a certain type of hospital is not affected by the health status of the patient (Z is not related to C).

So, differential distances approximately randomize patients to receive different intensities of treatments, and therefore can be used to estimate the causal effect of the treatment intensity on survival.

The authors concluded that, when it comes to heart attacks, using a more aggressive treatment is not as efficacious as the timing of that treatment.

Further reading

• 7 Different Ways to Control for Confounding
• Front-Door Criterion to Adjust for Unmeasured Confounding
• 5 Real-World Examples of Confounding [With References]
• 8 Types of Treatment Effects Explained (with Examples)
• List of All Biases in Research (Sorted by Popularity)

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• Knowledge Base

Methodology

• Simple Random Sampling | Definition, Steps & Examples

Simple Random Sampling | Definition, Steps & Examples

Published on August 28, 2020 by Lauren Thomas . Revised on December 18, 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.

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 randomization, any research performed on this sample should have high internal and external validity, and be at a lower risk for research biases like sampling bias and selection bias .

Table of contents

When to use simple random sampling, how to perform simple random sampling, other interesting articles, 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 : randomization 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 4 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.

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 .

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 is 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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Statistics Made Easy

10 Examples of Random Variables in Real Life

A random variable is a variable whose possible values are outcomes of a random process.

There are two types of random variables:

• Discrete : Can take on only a countable number of distinct values like 0, 1, 2, 3, 50, 100, etc.
• Continuous : Can take on an infinite number of possible values like 0.03, 1.2374553, etc.

In this article we share 10 examples of random variables in different real-life situations.

Example 1: Number of Items Sold (Discrete)

One example of a discrete random variable is the number of items sold at a store on a certain day.

Using historical sales data, a store could create a probability distribution that shows how likely it is that they sell a certain number of items in a day.

For example:

The probability that they sell 0 items is .004, the probability that they sell 1 item is .023, etc.

Example 2: Number of Customers (Discrete)

Another example of a discrete random variable is the number of customers that enter a shop on a given day.

Using historical data, a shop could create a probability distribution that shows how likely it is that a certain number of customers enter the store.

Example 3: Number of Defective Products (Discrete)

Another example of a discrete random variable is the number of defective products produced per batch by a certain manufacturing plant.

Using historical data on defective products, a plant could create a probability distribution that shows how likely it is that a certain number of products will be defective in a given batch.

Example 4: Number of Traffic Accidents (Discrete)

Another example of a discrete random variable is the number of traffic accidents that occur in a specific city on a given day.

Using historical data, a police department could create a probability distribution that shows how likely it is that a certain number of accidents occur on a given day.

Example 5: Number of Home Runs (Discrete)

Another example of a discrete random variable is the number of home runs hit by a certain baseball team in a game.

Using historical data, sports analysts could create a probability distribution that shows how likely it is that the team hits a certain number of home runs in a given game.

Example 6: Marathon Time (Continuous)

One example of a continuous random variable is the marathon time of a given runner.

This is an example of a continuous random variable because it can take on an infinite number of values.

For example, a runner might complete the marathon in 3 hours 20 minutes 12.0003433 seconds. Or they may complete the marathon in 4 hours 6 minutes 2.28889 seconds, etc.

In this scenario, we could use historical marathon times to create a probability distribution that tells us the probability that a given runner finishes between a certain time interval.

Example 7: Interest Rate (Continuous)

Another example of a continuous random variable is the interest rate of loans in a certain country.

This is a continuous random variable because it can take on an infinite number of values. For example, a loan could have an interest rate of 3.5%, 3.765555%, 4.00095%, etc.

In this scenario, we could use historical interest rates to create a probability distribution that tells us the probability that a loan will have an interest rate within a certain interval.

Example 8: Animal Weight (Continuous)

Another example of a continuous random variable is the weight of a certain animal like a dog.

This is a continuous random variable because it can take on an infinite number of values. For example, a dog might weigh 30.333 pounds, 50.340999 pounds, 60.5 pounds, etc.

In this case, we could collect data on the weight of dogs and create a probability distribution that tells us the probability that a randomly selected dog weighs between two different amounts.

Example 9: Plant Height (Continuous)

Another example of a continuous random variable is the height of a certain species of plant.

This is a continuous random variable because it can take on an infinite number of values. For example, a plant might have a height of 6.5555 inches, 8.95 inches, 12.32426 inches, etc.

In this case, we could collect data on the height of this species of plant and create a probability distribution that tells us the probability that a randomly selected plant has a height between two different values.

Example 10: Distance Traveled (Continuous)

Another example of a continuous random variable is the distance traveled by a certain wolf during migration season.

This is a continuous random variable because it can take on an infinite number of values. For example, a wolf may travel 40.335 miles, 80.5322 miles, 105.59 miles, etc.

In this scenario, we could collect data on the distance traveled by wolves and create a probability distribution that tells us the probability that a randomly selected wolf will travel within a certain distance interval.

Additional Resources

The following tutorials provide additional information about variables in statistics:

Introduction to Random Variables What Are i.i.d. Random Variables? What Are Levels of an Independent Variable?

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10 Examples of Random Variables in Real Life

A random variable is a variable whose possible values are outcomes of a random process.

There are two types of random variables:

• Discrete : Can take on only a countable number of distinct values like 0, 1, 2, 3, 50, 100, etc.
• Continuous : Can take on an infinite number of possible values like 0.03, 1.2374553, etc.

In this article we share 10 examples of random variables in different real-life situations.

Example 1: Number of Items Sold (Discrete)

One example of a discrete random variable is the number of items sold at a store on a certain day.

Using historical sales data, a store could create a probability distribution that shows how likely it is that they sell a certain number of items in a day.

For example:

The probability that they sell 0 items is .004, the probability that they sell 1 item is .023, etc.

Example 2: Number of Customers (Discrete)

Another example of a discrete random variable is the number of customers that enter a shop on a given day.

Using historical data, a shop could create a probability distribution that shows how likely it is that a certain number of customers enter the store.

Example 3: Number of Defective Products (Discrete)

Another example of a discrete random variable is the number of defective products produced per batch by a certain manufacturing plant.

Using historical data on defective products, a plant could create a probability distribution that shows how likely it is that a certain number of products will be defective in a given batch.

Example 4: Number of Traffic Accidents (Discrete)

Another example of a discrete random variable is the number of traffic accidents that occur in a specific city on a given day.

Using historical data, a police department could create a probability distribution that shows how likely it is that a certain number of accidents occur on a given day.

Example 5: Number of Home Runs (Discrete)

Another example of a discrete random variable is the number of home runs hit by a certain baseball team in a game.

Using historical data, sports analysts could create a probability distribution that shows how likely it is that the team hits a certain number of home runs in a given game.

Example 6: Marathon Time (Continuous)

One example of a continuous random variable is the marathon time of a given runner.

This is an example of a continuous random variable because it can take on an infinite number of values.

For example, a runner might complete the marathon in 3 hours 20 minutes 12.0003433 seconds. Or they may complete the marathon in 4 hours 6 minutes 2.28889 seconds, etc.

In this scenario, we could use historical marathon times to create a probability distribution that tells us the probability that a given runner finishes between a certain time interval.

Example 7: Interest Rate (Continuous)

Another example of a continuous random variable is the interest rate of loans in a certain country.

This is a continuous random variable because it can take on an infinite number of values. For example, a loan could have an interest rate of 3.5%, 3.765555%, 4.00095%, etc.

In this scenario, we could use historical interest rates to create a probability distribution that tells us the probability that a loan will have an interest rate within a certain interval.

Example 8: Animal Weight (Continuous)

Another example of a continuous random variable is the weight of a certain animal like a dog.

This is a continuous random variable because it can take on an infinite number of values. For example, a dog might weigh 30.333 pounds, 50.340999 pounds, 60.5 pounds, etc.

In this case, we could collect data on the weight of dogs and create a probability distribution that tells us the probability that a randomly selected dog weighs between two different amounts.

Example 9: Plant Height (Continuous)

Another example of a continuous random variable is the height of a certain species of plant.

This is a continuous random variable because it can take on an infinite number of values. For example, a plant might have a height of 6.5555 inches, 8.95 inches, 12.32426 inches, etc.

In this case, we could collect data on the height of this species of plant and create a probability distribution that tells us the probability that a randomly selected plant has a height between two different values.

Example 10: Distance Traveled (Continuous)

Another example of a continuous random variable is the distance traveled by a certain wolf during migration season.

This is a continuous random variable because it can take on an infinite number of values. For example, a wolf may travel 40.335 miles, 80.5322 miles, 105.59 miles, etc.

In this scenario, we could collect data on the distance traveled by wolves and create a probability distribution that tells us the probability that a randomly selected wolf will travel within a certain distance interval.

Additional Resources

The following tutorials provide additional information about variables in statistics:

Introduction to Random Variables What Are i.i.d. Random Variables? What Are Levels of an Independent Variable?

How to Create a Stacked Bar Plot in Seaborn (Step-by-Step)

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