at what point in research is random assignment used

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.

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Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

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

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

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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.

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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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.

Materio / Getty Images

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."

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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As previously mentioned, one of the characteristics of a true experiment is that researchers use a random process to decide which participants are tested under which conditions. Random assignation is a powerful research technique that addresses the assumption of pre-test equivalence – that the experimental and control group are equal in all respects before the administration of the independent variable (Palys & Atchison, 2014).

Random assignation is the primary way that researchers attempt to control extraneous variables across conditions. Random assignation is associated with experimental research methods. In its strictest sense, random assignment should meet two criteria.  One is that each participant has an equal chance of being assigned to each condition (e.g., a 50% chance of being assigned to each of two conditions). The second is that each participant is assigned to a condition independently of other participants. Thus, one way to assign participants to two conditions would be to flip a coin for each one. If the coin lands on the heads side, the participant is assigned to Condition A, and if it lands on the tails side, the participant is assigned to Condition B. For three conditions, one could use a computer to generate a random integer from 1 to 3 for each participant. If the integer is 1, the participant is assigned to Condition A; if it is 2, the participant is assigned to Condition B; and, if it is 3, the participant is assigned to Condition C. In practice, a full sequence of conditions—one for each participant expected to be in the experiment—is usually created ahead of time, and each new participant is assigned to the next condition in the sequence as he or she is tested.

However, one problem with coin flipping and other strict procedures for random assignment is that they are likely to result in unequal sample sizes in the different conditions. Unequal sample sizes are generally not a serious problem, and you should never throw away data you have already collected to achieve equal sample sizes. However, for a fixed number of participants, it is statistically most efficient to divide them into equal-sized groups. It is standard practice, therefore, to use a kind of modified random assignment that keeps the number of participants in each group as similar as possible.

One approach is block randomization. In block randomization, all the conditions occur once in the sequence before any of them is repeated. Then they all occur again before any of them is repeated again. Within each of these “blocks,” the conditions occur in a random order. Again, the sequence of conditions is usually generated before any participants are tested, and each new participant is assigned to the next condition in the sequence. When the procedure is computerized, the computer program often handles the random assignment, which is obviously much easier. You can also find programs online to help you randomize your random assignation. For example, the Research Randomizer website will generate block randomization sequences for any number of participants and conditions ( Research Randomizer ).

Random assignation is not guaranteed to control all extraneous variables across conditions. It is always possible that, just by chance, the participants in one condition might turn out to be substantially older, less tired, more motivated, or less depressed on average than the participants in another condition. However, there are some reasons that this may not be a major concern. One is that random assignment works better than one might expect, especially for large samples. Another is that the inferential statistics that researchers use to decide whether a difference between groups reflects a difference in the population take the “fallibility” of random assignment into account. Yet another reason is that even if random assignment does result in a confounding variable and therefore produces misleading results, this confound is likely to be detected when the experiment is replicated. The upshot is that random assignment to conditions—although not infallible in terms of controlling extraneous variables—is always considered a strength of a research design. Note: Do not confuse random assignation with random sampling. Random sampling is a method for selecting a sample from a population; we will talk about this in Chapter 7.

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Chapter 6: Experimental Research

6.2 experimental design, learning objectives.

• Explain the difference between between-subjects and within-subjects experiments, list some of the pros and cons of each approach, and decide which approach to use to answer a particular research question.
• Define random assignment, distinguish it from random sampling, explain its purpose in experimental research, and use some simple strategies to implement it.
• Define what a control condition is, explain its purpose in research on treatment effectiveness, and describe some alternative types of control conditions.
• Define several types of carryover effect, give examples of each, and explain how counterbalancing helps to deal with them.

In this section, we look at some different ways to design an experiment. The primary distinction we will make is between approaches in which each participant experiences one level of the independent variable and approaches in which each participant experiences all levels of the independent variable. The former are called between-subjects experiments and the latter are called within-subjects experiments.

Between-Subjects Experiments

In a between-subjects experiment , each participant is tested in only one condition. For example, a researcher with a sample of 100 college students might assign half of them to write about a traumatic event and the other half write about a neutral event. Or a researcher with a sample of 60 people with severe agoraphobia (fear of open spaces) might assign 20 of them to receive each of three different treatments for that disorder. It is essential in a between-subjects experiment that the researcher assign participants to conditions so that the different groups are, on average, highly similar to each other. Those in a trauma condition and a neutral condition, for example, should include a similar proportion of men and women, and they should have similar average intelligence quotients (IQs), similar average levels of motivation, similar average numbers of health problems, and so on. This is a matter of controlling these extraneous participant variables across conditions so that they do not become confounding variables.

Random Assignment

The primary way that researchers accomplish this kind of control of extraneous variables across conditions is called random assignment , which means using a random process to decide which participants are tested in which conditions. Do not confuse random assignment with random sampling. Random sampling is a method for selecting a sample from a population, and it is rarely used in psychological research. Random assignment is a method for assigning participants in a sample to the different conditions, and it is an important element of all experimental research in psychology and other fields too.

In its strictest sense, random assignment should meet two criteria. One is that each participant has an equal chance of being assigned to each condition (e.g., a 50% chance of being assigned to each of two conditions). The second is that each participant is assigned to a condition independently of other participants. Thus one way to assign participants to two conditions would be to flip a coin for each one. If the coin lands heads, the participant is assigned to Condition A, and if it lands tails, the participant is assigned to Condition B. For three conditions, one could use a computer to generate a random integer from 1 to 3 for each participant. If the integer is 1, the participant is assigned to Condition A; if it is 2, the participant is assigned to Condition B; and if it is 3, the participant is assigned to Condition C. In practice, a full sequence of conditions—one for each participant expected to be in the experiment—is usually created ahead of time, and each new participant is assigned to the next condition in the sequence as he or she is tested. When the procedure is computerized, the computer program often handles the random assignment.

One problem with coin flipping and other strict procedures for random assignment is that they are likely to result in unequal sample sizes in the different conditions. Unequal sample sizes are generally not a serious problem, and you should never throw away data you have already collected to achieve equal sample sizes. However, for a fixed number of participants, it is statistically most efficient to divide them into equal-sized groups. It is standard practice, therefore, to use a kind of modified random assignment that keeps the number of participants in each group as similar as possible. One approach is block randomization . In block randomization, all the conditions occur once in the sequence before any of them is repeated. Then they all occur again before any of them is repeated again. Within each of these “blocks,” the conditions occur in a random order. Again, the sequence of conditions is usually generated before any participants are tested, and each new participant is assigned to the next condition in the sequence. Table 6.2 “Block Randomization Sequence for Assigning Nine Participants to Three Conditions” shows such a sequence for assigning nine participants to three conditions. The Research Randomizer website ( http://www.randomizer.org ) will generate block randomization sequences for any number of participants and conditions. Again, when the procedure is computerized, the computer program often handles the block randomization.

Table 6.2 Block Randomization Sequence for Assigning Nine Participants to Three Conditions

Random assignment is not guaranteed to control all extraneous variables across conditions. It is always possible that just by chance, the participants in one condition might turn out to be substantially older, less tired, more motivated, or less depressed on average than the participants in another condition. However, there are some reasons that this is not a major concern. One is that random assignment works better than one might expect, especially for large samples. Another is that the inferential statistics that researchers use to decide whether a difference between groups reflects a difference in the population takes the “fallibility” of random assignment into account. Yet another reason is that even if random assignment does result in a confounding variable and therefore produces misleading results, this is likely to be detected when the experiment is replicated. The upshot is that random assignment to conditions—although not infallible in terms of controlling extraneous variables—is always considered a strength of a research design.

Treatment and Control Conditions

Between-subjects experiments are often used to determine whether a treatment works. In psychological research, a treatment is any intervention meant to change people’s behavior for the better. This includes psychotherapies and medical treatments for psychological disorders but also interventions designed to improve learning, promote conservation, reduce prejudice, and so on. To determine whether a treatment works, participants are randomly assigned to either a treatment condition , in which they receive the treatment, or a control condition , in which they do not receive the treatment. If participants in the treatment condition end up better off than participants in the control condition—for example, they are less depressed, learn faster, conserve more, express less prejudice—then the researcher can conclude that the treatment works. In research on the effectiveness of psychotherapies and medical treatments, this type of experiment is often called a randomized clinical trial .

There are different types of control conditions. In a no-treatment control condition , participants receive no treatment whatsoever. One problem with this approach, however, is the existence of placebo effects. A placebo is a simulated treatment that lacks any active ingredient or element that should make it effective, and a placebo effect is a positive effect of such a treatment. Many folk remedies that seem to work—such as eating chicken soup for a cold or placing soap under the bedsheets to stop nighttime leg cramps—are probably nothing more than placebos. Although placebo effects are not well understood, they are probably driven primarily by people’s expectations that they will improve. Having the expectation to improve can result in reduced stress, anxiety, and depression, which can alter perceptions and even improve immune system functioning (Price, Finniss, & Benedetti, 2008).

Placebo effects are interesting in their own right (see Note 6.28 “The Powerful Placebo” ), but they also pose a serious problem for researchers who want to determine whether a treatment works. Figure 6.2 “Hypothetical Results From a Study Including Treatment, No-Treatment, and Placebo Conditions” shows some hypothetical results in which participants in a treatment condition improved more on average than participants in a no-treatment control condition. If these conditions (the two leftmost bars in Figure 6.2 “Hypothetical Results From a Study Including Treatment, No-Treatment, and Placebo Conditions” ) were the only conditions in this experiment, however, one could not conclude that the treatment worked. It could be instead that participants in the treatment group improved more because they expected to improve, while those in the no-treatment control condition did not.

Figure 6.2 Hypothetical Results From a Study Including Treatment, No-Treatment, and Placebo Conditions

Fortunately, there are several solutions to this problem. One is to include a placebo control condition , in which participants receive a placebo that looks much like the treatment but lacks the active ingredient or element thought to be responsible for the treatment’s effectiveness. When participants in a treatment condition take a pill, for example, then those in a placebo control condition would take an identical-looking pill that lacks the active ingredient in the treatment (a “sugar pill”). In research on psychotherapy effectiveness, the placebo might involve going to a psychotherapist and talking in an unstructured way about one’s problems. The idea is that if participants in both the treatment and the placebo control groups expect to improve, then any improvement in the treatment group over and above that in the placebo control group must have been caused by the treatment and not by participants’ expectations. This is what is shown by a comparison of the two outer bars in Figure 6.2 “Hypothetical Results From a Study Including Treatment, No-Treatment, and Placebo Conditions” .

Of course, the principle of informed consent requires that participants be told that they will be assigned to either a treatment or a placebo control condition—even though they cannot be told which until the experiment ends. In many cases the participants who had been in the control condition are then offered an opportunity to have the real treatment. An alternative approach is to use a waitlist control condition , in which participants are told that they will receive the treatment but must wait until the participants in the treatment condition have already received it. This allows researchers to compare participants who have received the treatment with participants who are not currently receiving it but who still expect to improve (eventually). A final solution to the problem of placebo effects is to leave out the control condition completely and compare any new treatment with the best available alternative treatment. For example, a new treatment for simple phobia could be compared with standard exposure therapy. Because participants in both conditions receive a treatment, their expectations about improvement should be similar. This approach also makes sense because once there is an effective treatment, the interesting question about a new treatment is not simply “Does it work?” but “Does it work better than what is already available?”

The Powerful Placebo

Many people are not surprised that placebos can have a positive effect on disorders that seem fundamentally psychological, including depression, anxiety, and insomnia. However, placebos can also have a positive effect on disorders that most people think of as fundamentally physiological. These include asthma, ulcers, and warts (Shapiro & Shapiro, 1999). There is even evidence that placebo surgery—also called “sham surgery”—can be as effective as actual surgery.

Medical researcher J. Bruce Moseley and his colleagues conducted a study on the effectiveness of two arthroscopic surgery procedures for osteoarthritis of the knee (Moseley et al., 2002). The control participants in this study were prepped for surgery, received a tranquilizer, and even received three small incisions in their knees. But they did not receive the actual arthroscopic surgical procedure. The surprising result was that all participants improved in terms of both knee pain and function, and the sham surgery group improved just as much as the treatment groups. According to the researchers, “This study provides strong evidence that arthroscopic lavage with or without débridement [the surgical procedures used] is not better than and appears to be equivalent to a placebo procedure in improving knee pain and self-reported function” (p. 85).

Research has shown that patients with osteoarthritis of the knee who receive a “sham surgery” experience reductions in pain and improvement in knee function similar to those of patients who receive a real surgery.

Army Medicine – Surgery – CC BY 2.0.

Within-Subjects Experiments

In a within-subjects experiment , each participant is tested under all conditions. Consider an experiment on the effect of a defendant’s physical attractiveness on judgments of his guilt. Again, in a between-subjects experiment, one group of participants would be shown an attractive defendant and asked to judge his guilt, and another group of participants would be shown an unattractive defendant and asked to judge his guilt. In a within-subjects experiment, however, the same group of participants would judge the guilt of both an attractive and an unattractive defendant.

The primary advantage of this approach is that it provides maximum control of extraneous participant variables. Participants in all conditions have the same mean IQ, same socioeconomic status, same number of siblings, and so on—because they are the very same people. Within-subjects experiments also make it possible to use statistical procedures that remove the effect of these extraneous participant variables on the dependent variable and therefore make the data less “noisy” and the effect of the independent variable easier to detect. We will look more closely at this idea later in the book.

Carryover Effects and Counterbalancing

The primary disadvantage of within-subjects designs is that they can result in carryover effects. A carryover effect is an effect of being tested in one condition on participants’ behavior in later conditions. One type of carryover effect is a practice effect , where participants perform a task better in later conditions because they have had a chance to practice it. Another type is a fatigue effect , where participants perform a task worse in later conditions because they become tired or bored. Being tested in one condition can also change how participants perceive stimuli or interpret their task in later conditions. This is called a context effect . For example, an average-looking defendant might be judged more harshly when participants have just judged an attractive defendant than when they have just judged an unattractive defendant. Within-subjects experiments also make it easier for participants to guess the hypothesis. For example, a participant who is asked to judge the guilt of an attractive defendant and then is asked to judge the guilt of an unattractive defendant is likely to guess that the hypothesis is that defendant attractiveness affects judgments of guilt. This could lead the participant to judge the unattractive defendant more harshly because he thinks this is what he is expected to do. Or it could make participants judge the two defendants similarly in an effort to be “fair.”

Carryover effects can be interesting in their own right. (Does the attractiveness of one person depend on the attractiveness of other people that we have seen recently?) But when they are not the focus of the research, carryover effects can be problematic. Imagine, for example, that participants judge the guilt of an attractive defendant and then judge the guilt of an unattractive defendant. If they judge the unattractive defendant more harshly, this might be because of his unattractiveness. But it could be instead that they judge him more harshly because they are becoming bored or tired. In other words, the order of the conditions is a confounding variable. The attractive condition is always the first condition and the unattractive condition the second. Thus any difference between the conditions in terms of the dependent variable could be caused by the order of the conditions and not the independent variable itself.

There is a solution to the problem of order effects, however, that can be used in many situations. It is counterbalancing , which means testing different participants in different orders. For example, some participants would be tested in the attractive defendant condition followed by the unattractive defendant condition, and others would be tested in the unattractive condition followed by the attractive condition. With three conditions, there would be six different orders (ABC, ACB, BAC, BCA, CAB, and CBA), so some participants would be tested in each of the six orders. With counterbalancing, participants are assigned to orders randomly, using the techniques we have already discussed. Thus random assignment plays an important role in within-subjects designs just as in between-subjects designs. Here, instead of randomly assigning to conditions, they are randomly assigned to different orders of conditions. In fact, it can safely be said that if a study does not involve random assignment in one form or another, it is not an experiment.

There are two ways to think about what counterbalancing accomplishes. One is that it controls the order of conditions so that it is no longer a confounding variable. Instead of the attractive condition always being first and the unattractive condition always being second, the attractive condition comes first for some participants and second for others. Likewise, the unattractive condition comes first for some participants and second for others. Thus any overall difference in the dependent variable between the two conditions cannot have been caused by the order of conditions. A second way to think about what counterbalancing accomplishes is that if there are carryover effects, it makes it possible to detect them. One can analyze the data separately for each order to see whether it had an effect.

When 9 Is “Larger” Than 221

Researcher Michael Birnbaum has argued that the lack of context provided by between-subjects designs is often a bigger problem than the context effects created by within-subjects designs. To demonstrate this, he asked one group of participants to rate how large the number 9 was on a 1-to-10 rating scale and another group to rate how large the number 221 was on the same 1-to-10 rating scale (Birnbaum, 1999). Participants in this between-subjects design gave the number 9 a mean rating of 5.13 and the number 221 a mean rating of 3.10. In other words, they rated 9 as larger than 221! According to Birnbaum, this is because participants spontaneously compared 9 with other one-digit numbers (in which case it is relatively large) and compared 221 with other three-digit numbers (in which case it is relatively small).

Simultaneous Within-Subjects Designs

So far, we have discussed an approach to within-subjects designs in which participants are tested in one condition at a time. There is another approach, however, that is often used when participants make multiple responses in each condition. Imagine, for example, that participants judge the guilt of 10 attractive defendants and 10 unattractive defendants. Instead of having people make judgments about all 10 defendants of one type followed by all 10 defendants of the other type, the researcher could present all 20 defendants in a sequence that mixed the two types. The researcher could then compute each participant’s mean rating for each type of defendant. Or imagine an experiment designed to see whether people with social anxiety disorder remember negative adjectives (e.g., “stupid,” “incompetent”) better than positive ones (e.g., “happy,” “productive”). The researcher could have participants study a single list that includes both kinds of words and then have them try to recall as many words as possible. The researcher could then count the number of each type of word that was recalled. There are many ways to determine the order in which the stimuli are presented, but one common way is to generate a different random order for each participant.

Between-Subjects or Within-Subjects?

Almost every experiment can be conducted using either a between-subjects design or a within-subjects design. This means that researchers must choose between the two approaches based on their relative merits for the particular situation.

Between-subjects experiments have the advantage of being conceptually simpler and requiring less testing time per participant. They also avoid carryover effects without the need for counterbalancing. Within-subjects experiments have the advantage of controlling extraneous participant variables, which generally reduces noise in the data and makes it easier to detect a relationship between the independent and dependent variables.

A good rule of thumb, then, is that if it is possible to conduct a within-subjects experiment (with proper counterbalancing) in the time that is available per participant—and you have no serious concerns about carryover effects—this is probably the best option. If a within-subjects design would be difficult or impossible to carry out, then you should consider a between-subjects design instead. For example, if you were testing participants in a doctor’s waiting room or shoppers in line at a grocery store, you might not have enough time to test each participant in all conditions and therefore would opt for a between-subjects design. Or imagine you were trying to reduce people’s level of prejudice by having them interact with someone of another race. A within-subjects design with counterbalancing would require testing some participants in the treatment condition first and then in a control condition. But if the treatment works and reduces people’s level of prejudice, then they would no longer be suitable for testing in the control condition. This is true for many designs that involve a treatment meant to produce long-term change in participants’ behavior (e.g., studies testing the effectiveness of psychotherapy). Clearly, a between-subjects design would be necessary here.

Remember also that using one type of design does not preclude using the other type in a different study. There is no reason that a researcher could not use both a between-subjects design and a within-subjects design to answer the same research question. In fact, professional researchers often do exactly this.

Key Takeaways

• Experiments can be conducted using either between-subjects or within-subjects designs. Deciding which to use in a particular situation requires careful consideration of the pros and cons of each approach.
• Random assignment to conditions in between-subjects experiments or to orders of conditions in within-subjects experiments is a fundamental element of experimental research. Its purpose is to control extraneous variables so that they do not become confounding variables.
• Experimental research on the effectiveness of a treatment requires both a treatment condition and a control condition, which can be a no-treatment control condition, a placebo control condition, or a waitlist control condition. Experimental treatments can also be compared with the best available alternative.

Discussion: For each of the following topics, list the pros and cons of a between-subjects and within-subjects design and decide which would be better.

• You want to test the relative effectiveness of two training programs for running a marathon.
• Using photographs of people as stimuli, you want to see if smiling people are perceived as more intelligent than people who are not smiling.
• In a field experiment, you want to see if the way a panhandler is dressed (neatly vs. sloppily) affects whether or not passersby give him any money.
• You want to see if concrete nouns (e.g., dog ) are recalled better than abstract nouns (e.g., truth ).
• Discussion: Imagine that an experiment shows that participants who receive psychodynamic therapy for a dog phobia improve more than participants in a no-treatment control group. Explain a fundamental problem with this research design and at least two ways that it might be corrected.

Birnbaum, M. H. (1999). How to show that 9 > 221: Collect judgments in a between-subjects design. Psychological Methods, 4 , 243–249.

Moseley, J. B., O’Malley, K., Petersen, N. J., Menke, T. J., Brody, B. A., Kuykendall, D. H., … Wray, N. P. (2002). A controlled trial of arthroscopic surgery for osteoarthritis of the knee. The New England Journal of Medicine, 347 , 81–88.

Price, D. D., Finniss, D. G., & Benedetti, F. (2008). A comprehensive review of the placebo effect: Recent advances and current thought. Annual Review of Psychology, 59 , 565–590.

Shapiro, A. K., & Shapiro, E. (1999). The powerful placebo: From ancient priest to modern physician . Baltimore, MD: Johns Hopkins University Press.

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Random Assignment in Psychology (Intro for Students)

Random assignment is a research procedure used to randomly assign participants to different experimental conditions (or ‘groups’). This introduces the element of chance, ensuring that each participant has an equal likelihood of being placed in any condition group for the study.

It is absolutely essential that the treatment condition and the control condition are the same in all ways except for the variable being manipulated.

Using random assignment to place participants in different conditions helps to achieve this.

It ensures that those conditions are the same in regards to all potential confounding variables and extraneous factors .

Why Researchers Use Random Assignment

Researchers use random assignment to control for confounds in research.

Confounds refer to unwanted and often unaccounted-for variables that might affect the outcome of a study. These confounding variables can skew the results, rendering the experiment unreliable.

For example, below is a study with two groups. Note how there are more ‘red’ individuals in the first group than the second:

There is likely a confounding variable in this experiment explaining why more red people ended up in the treatment condition and less in the control condition. The red people might have self-selected, for example, leading to a skew of them in one group over the other.

Ideally, we’d want a more even distribution, like below:

To achieve better balance in our two conditions, we use randomized sampling.

Fact File: Experiments 101

Random assignment is used in the type of research called the experiment.

An experiment involves manipulating the level of one variable and examining how it affects another variable. These are the independent and dependent variables :

• Independent Variable: The variable manipulated is called the independent variable (IV)
• Dependent Variable: The variable that it is expected to affect is called the dependent variable (DV).

The most basic form of the experiment involves two conditions: the treatment and the control .

• The Treatment Condition: The treatment condition involves the participants being exposed to the IV.
• The Control Condition: The control condition involves the absence of the IV. Therefore, the IV has two levels: zero and some quantity.

Researchers utilize random assignment to determine which participants go into which conditions.

Methods of Random Assignment

There are several procedures that researchers can use to randomly assign participants to different conditions.

1. Random number generator

There are several websites that offer computer-generated random numbers. Simply indicate how many conditions are in the experiment and then click. If there are 4 conditions, the program will randomly generate a number between 1 and 4 each time it is clicked.

2. Flipping a coin

If there are two conditions in an experiment, then the simplest way to implement random assignment is to flip a coin for each participant. Heads means being assigned to the treatment and tails means being assigned to the control (or vice versa).

3. Rolling a die

Rolling a single die is another way to randomly assign participants. If the experiment has three conditions, then numbers 1 and 2 mean being assigned to the control; numbers 3 and 4 mean treatment condition one; and numbers 5 and 6 mean treatment condition two.

4. Condition names in a hat

In some studies, the researcher will write the name of the treatment condition(s) or control on slips of paper and place them in a hat. If there are 4 conditions and 1 control, then there are 5 slips of paper.

The researcher closes their eyes and selects one slip for each participant. That person is then assigned to one of the conditions in the study and that slip of paper is placed back in the hat. Repeat as necessary.

There are other ways of trying to ensure that the groups of participants are equal in all ways with the exception of the IV. However, random assignment is the most often used because it is so effective at reducing confounds.

Read About More Methods and Examples of Random Assignment Here

Potential Confounding Effects

Random assignment is all about minimizing confounding effects.

Here are six types of confounds that can be controlled for using random assignment:

• Individual Differences: Participants in a study will naturally vary in terms of personality, intelligence, mood, prior knowledge, and many other characteristics. If one group happens to have more people with a particular characteristic, this could affect the results. Random assignment ensures that these individual differences are spread out equally among the experimental groups, making it less likely that they will unduly influence the outcome.
• Temporal or Time-Related Confounds: Events or situations that occur at a particular time can influence the outcome of an experiment. For example, a participant might be tested after a stressful event, while another might be tested after a relaxing weekend. Random assignment ensures that such effects are equally distributed among groups, thus controlling for their potential influence.
• Order Effects: If participants are exposed to multiple treatments or tests, the order in which they experience them can influence their responses. Randomly assigning the order of treatments for different participants helps control for this.
• Location or Environmental Confounds: The environment in which the study is conducted can influence the results. One group might be tested in a noisy room, while another might be in a quiet room. Randomly assigning participants to different locations can control for these effects.
• Instrumentation Confounds: These occur when there are variations in the calibration or functioning of measurement instruments across conditions. If one group’s responses are being measured using a slightly different tool or scale, it can introduce a confound. Random assignment can ensure that any such potential inconsistencies in instrumentation are equally distributed among groups.
• Experimenter Effects: Sometimes, the behavior or expectations of the person administering the experiment can unintentionally influence the participants’ behavior or responses. For instance, if an experimenter believes one treatment is superior, they might unconsciously communicate this belief to participants. Randomly assigning experimenters or using a double-blind procedure (where neither the participant nor the experimenter knows the treatment being given) can help control for this.

Random assignment helps balance out these and other potential confounds across groups, ensuring that any observed differences are more likely due to the manipulated independent variable rather than some extraneous factor.

Limitations of the Random Assignment Procedure

Although random assignment is extremely effective at eliminating the presence of participant-related confounds, there are several scenarios in which it cannot be used.

• Ethics: The most obvious scenario is when it would be unethical. For example, if wanting to investigate the effects of emotional abuse on children, it would be unethical to randomly assign children to either received abuse or not.  Even if a researcher were to propose such a study, it would not receive approval from the Institutional Review Board (IRB) which oversees research by university faculty.
• Practicality: Other scenarios involve matters of practicality. For example, randomly assigning people to specific types of diet over a 10-year period would be interesting, but it would be highly unlikely that participants would be diligent enough to make the study valid. This is why examining these types of subjects has to be carried out through observational studies . The data is correlational, which is informative, but falls short of the scientist’s ultimate goal of identifying causality.
• Small Sample Size: The smaller the sample size being assigned to conditions, the more likely it is that the two groups will be unequal. For example, if you flip a coin many times in a row then you will notice that sometimes there will be a string of heads or tails that come up consecutively. This means that one condition may have a build-up of participants that share the same characteristics. However, if you continue flipping the coin, over the long-term, there will be a balance of heads and tails. Unfortunately, how large a sample size is necessary has been the subject of considerable debate (Bloom, 2006; Shadish et al., 2002).

“It is well known that larger sample sizes reduce the probability that random assignment will result in conditions that are unequal” (Goldberg, 2019, p. 2).

Applications of Random Assignment

The importance of random assignment has been recognized in a wide range of scientific and applied disciplines (Bloom, 2006).

Random assignment began as a tool in agricultural research by Fisher (1925, 1935). After WWII, it became extensively used in medical research to test the effectiveness of new treatments and pharmaceuticals (Marks, 1997).

Today it is widely used in industrial engineering (Box, Hunter, and Hunter, 2005), educational research (Lindquist, 1953; Ong-Dean et al., 2011)), psychology (Myers, 1972), and social policy studies (Boruch, 1998; Orr, 1999).

One of the biggest obstacles to the validity of an experiment is the confound. If the group of participants in the treatment condition are substantially different from the group in the control condition, then it is impossible to determine if the IV has an affect or if the confound has an effect.

Thankfully, random assignment is highly effective at eliminating confounds that are known and unknown. Because each participant has an equal chance of being placed in each condition, they are equally distributed.

There are several ways of implementing random assignment, including flipping a coin or using a random number generator.

Random assignment has become an essential procedure in research in a wide range of subjects such as psychology, education, and social policy.

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Bloom, H. S. (2008). The core analytics of randomized experiments for social research. The SAGE Handbook of Social Research Methods , 115-133.

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Fisher, R.A. (1925). Statistical methods for research workers (11th ed. rev.). Oliver and Boyd: Edinburgh.

Fisher, R. A. (1935). The Design of Experiments. Edinburgh: Oliver and Boyd.

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Purpose and Limitations of Random Assignment

In an experimental study, random assignment is a process by which participants are assigned, with the same chance, to either a treatment or a control group. The goal is to assure an unbiased assignment of participants to treatment options.

Random assignment is considered the gold standard for achieving comparability across study groups, and therefore is the best method for inferring a causal relationship between a treatment (or intervention or risk factor) and an outcome.

Random assignment of participants produces comparable groups regarding the participants’ initial characteristics, thereby any difference detected in the end between the treatment and the control group will be due to the effect of the treatment alone.

How does random assignment produce comparable groups?

1. random assignment prevents selection bias.

Randomization works by removing the researcher’s and the participant’s influence on the treatment allocation. So the allocation can no longer be biased since it is done at random, i.e. in a non-predictable way.

This is in contrast with the real world, where for example, the sickest people are more likely to receive the treatment.

2. Random assignment prevents confounding

A confounding variable is one that is associated with both the intervention and the outcome, and thus can affect the outcome in 2 ways:

Either directly:

Or indirectly through the treatment:

This indirect relationship between the confounding variable and the outcome can cause the treatment to appear to have an influence on the outcome while in reality the treatment is just a mediator of that effect (as it happens to be on the causal pathway between the confounder and the outcome).

Random assignment eliminates the influence of the confounding variables on the treatment since it distributes them at random between the study groups, therefore, ruling out this alternative path or explanation of the outcome.

3. Random assignment also eliminates other threats to internal validity

By distributing all threats (known and unknown) at random between study groups, participants in both the treatment and the control group become equally subject to the effect of any threat to validity. Therefore, comparing the outcome between the 2 groups will bypass the effect of these threats and will only reflect the effect of the treatment on the outcome.

These threats include:

• History: This is any event that co-occurs with the treatment and can affect the outcome.
• Maturation: This is the effect of time on the study participants (e.g. participants becoming wiser, hungrier, or more stressed with time) which might influence the outcome.
• Regression to the mean: This happens when the participants’ outcome score is exceptionally good on a pre-treatment measurement, so the post-treatment measurement scores will naturally regress toward the mean — in simple terms, regression happens since an exceptional performance is hard to maintain. This effect can bias the study since it represents an alternative explanation of the outcome.

Note that randomization does not prevent these effects from happening, it just allows us to control them by reducing their risk of being associated with the treatment.

What if random assignment produced unequal groups?

Question: What should you do if after randomly assigning participants, it turned out that the 2 groups still differ in participants’ characteristics? More precisely, what if randomization accidentally did not balance risk factors that can be alternative explanations between the 2 groups? (For example, if one group includes more male participants, or sicker, or older people than the other group).

Short answer: This is perfectly normal, since randomization only assures an unbiased assignment of participants to groups, i.e. it produces comparable groups, but it does not guarantee the equality of these groups.

A more complete answer: Randomization will not and cannot create 2 equal groups regarding each and every characteristic. This is because when dealing with randomization there is still an element of luck. If you want 2 perfectly equal groups, you better match them manually as is done in a matched pairs design (for more information see my article on matched pairs design ).

This is similar to throwing a die: If you throw it 10 times, the chance of getting a specific outcome will not be 1/6. But it will approach 1/6 if you repeat the experiment a very large number of times and calculate the average number of times the specific outcome turned up.

So randomization will not produce perfectly equal groups for each specific study, especially if the study has a small sample size. But do not forget that scientific evidence is a long and continuous process, and the groups will tend to be equal in the long run when a meta-analysis aggregates the results of a large number of randomized studies.

So for each individual study, differences between the treatment and control group will exist and will influence the study results. This means that the results of a randomized trial will sometimes be wrong, and this is absolutely okay.

BOTTOM LINE:

Although the results of a particular randomized study are unbiased, they will still be affected by a sampling error due to chance. But the real benefit of random assignment will be when data is aggregated in a meta-analysis.

Limitations of random assignment

Randomized designs can suffer from:

1. Ethical issues:

Randomization is ethical only if the researcher has no evidence that one treatment is superior to the other.

Also, it would be unethical to randomly assign participants to harmful exposures such as smoking or dangerous chemicals.

2. Low external validity:

With random assignment, external validity (i.e. the generalizability of the study results) is compromised because the results of a study that uses random assignment represent what would happen under “ideal” experimental conditions, which is in general very different from what happens at the population level.

In the real world, people who take the treatment might be very different from those who don’t – so the assignment of participants is not a random event, but rather under the influence of all sort of external factors.

External validity can be also jeopardized in cases where not all participants are eligible or willing to accept the terms of the study.

3. Higher cost of implementation:

An experimental design with random assignment is typically more expensive than observational studies where the investigator’s role is just to observe events without intervening.

Experimental designs also typically take a lot of time to implement, and therefore are less practical when a quick answer is needed.

4. Impracticality when answering non-causal questions:

A randomized trial is our best bet when the question is to find the causal effect of a treatment or a risk factor.

Sometimes however, the researcher is just interested in predicting the probability of an event or a disease given some risk factors. In this case, the causal relationship between these variables is not important, making observational designs more suitable for such problems.

5. Impracticality when studying the effect of variables that cannot be manipulated:

The usual objective of studying the effects of risk factors is to propose recommendations that involve changing the level of exposure to these factors.

However, some risk factors cannot be manipulated, and so it does not make any sense to study them in a randomized trial. For example it would be impossible to randomly assign participants to age categories, gender, or genetic factors.

6. Difficulty to control participants:

These difficulties include:

• Participants refusing to receive the assigned treatment.
• Participants not adhering to recommendations.
• Differential loss to follow-up between those who receive the treatment and those who don’t.

All of these issues might occur in a randomized trial, but might not affect an observational study.

• Shadish WR, Cook TD, Campbell DT. Experimental and Quasi-Experimental Designs for Generalized Causal Inference . 2nd edition. Cengage Learning; 2001.
• Friedman LM, Furberg CD, DeMets DL, Reboussin DM, Granger CB. Fundamentals of Clinical Trials . 5th ed. 2015 edition. Springer; 2015.

Further reading

• Posttest-Only Control Group Design
• Pretest-Posttest Control Group Design
• Randomized Block Design

Random Assignment

• First Online: 17 May 2019

Cite this chapter

• Gideon J. Mellenbergh 2  

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A substantial part of behavioral research is aimed at the testing of substantive hypotheses. In general, a hypothesis testing study investigates the causal influence of an independent variable (IV) on a dependent variable (DV) . The discussion is restricted to IVs that can be manipulated by the researcher, such as, experimental (E- ) and control (C- ) conditions. Association between IV and DV does not imply that the IV has a causal influence on the DV . The association can be spurious because it is caused by an other variable (OV). OVs that cause spurious associations come from the (1) participant, (2) research situation, and (3) reactions of the participants to the research situation. If participants select their own (E- or C- ) condition or others select a condition for them, the assignment to conditions is usually biased (e.g., males prefer the E-condition and females the C-condition), and participant variables (e.g., participants’ sex) may cause a spurious association between the IV and DV . This selection bias is a systematic error of a design. It is counteracted by random assignment of participants to conditions. Random assignment guarantees that all participant variables are related to the IV by chance, and turns systematic error into random error. Random errors decrease the precision of parameter estimates. Random error variance is reduced by including auxiliary variables into the randomized design. A randomized block design includes an auxiliary variable to divide the participants into relatively homogeneous blocks, and randomly assigns participants to the conditions per block. A covariate is an auxiliary variable that is used in the statistical analysis of the data to reduce the error variance. Cluster randomization randomly assigns clusters (e.g., classes of students) to conditions, which yields specific problems. Random assignment should not be confused with random selection. Random assignment controls for selection bias , whereas random selection makes possible to generalize study results of a sample to the population.

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Mellenbergh, G.J. (2019). Random Assignment. In: Counteracting Methodological Errors in Behavioral Research. Springer, Cham. https://doi.org/10.1007/978-3-030-12272-0_4

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Module 3: Elements of Research - Section 5

Section 5: Random Assignment

The benefit of using random assignment is that it "evens the playing field." This means that the groups will differ only in the program or treatment to which they are assigned. If both groups are equivalent except for the program or treatment that they receive, then any change that is observed after comparing information collected about individuals at the beginning of the study and again at the end of the study can be attributed to the program or treatment. This way, the researcher has more confidence that any changes that might have occurred are due to the treatment under study and not to the characteristics of the group.

Definition : Random assignment is a procedure used in experiments to create study groups with similar characteristics so that the groups are equivalent at the beginning of the study.

Case Example for Random Assignment

In a study to help individuals quit smoking, investigators randomly assigned participants to one of two groups. In Group A, participants took a class to quit smoking. The classes took place each week for 10-weeks and included information about the benefits of quitting smoking. In addition, participants in the class received strong social support from mentors or "buddies." In the Group B, participants read a 3-page pamphlet created by the American Cancer Association that explains the benefits of quitting smoking. The investigator randomly assigned participants to one of the two groups. It was found that those who participated in the class and received support from their buddies were more likely to quit smoking compared to those in the other group that received only the pamphlet.

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Chapter 6: Experimental Research

Experimental Design

Learning Objectives

• Explain the difference between between-subjects and within-subjects experiments, list some of the pros and cons of each approach, and decide which approach to use to answer a particular research question.
• Define random assignment, distinguish it from random sampling, explain its purpose in experimental research, and use some simple strategies to implement it.
• Define what a control condition is, explain its purpose in research on treatment effectiveness, and describe some alternative types of control conditions.
• Define several types of carryover effect, give examples of each, and explain how counterbalancing helps to deal with them.

In this section, we look at some different ways to design an experiment. The primary distinction we will make is between approaches in which each participant experiences one level of the independent variable and approaches in which each participant experiences all levels of the independent variable. The former are called between-subjects experiments and the latter are called within-subjects experiments.

Between-Subjects Experiments

In a  between-subjects experiment , each participant is tested in only one condition. For example, a researcher with a sample of 100 university  students might assign half of them to write about a traumatic event and the other half write about a neutral event. Or a researcher with a sample of 60 people with severe agoraphobia (fear of open spaces) might assign 20 of them to receive each of three different treatments for that disorder. It is essential in a between-subjects experiment that the researcher assign participants to conditions so that the different groups are, on average, highly similar to each other. Those in a trauma condition and a neutral condition, for example, should include a similar proportion of men and women, and they should have similar average intelligence quotients (IQs), similar average levels of motivation, similar average numbers of health problems, and so on. This matching is a matter of controlling these extraneous participant variables across conditions so that they do not become confounding variables.

Random Assignment

The primary way that researchers accomplish this kind of control of extraneous variables across conditions is called  random assignment , which means using a random process to decide which participants are tested in which conditions. Do not confuse random assignment with random sampling. Random sampling is a method for selecting a sample from a population, and it is rarely used in psychological research. Random assignment is a method for assigning participants in a sample to the different conditions, and it is an important element of all experimental research in psychology and other fields too.

In its strictest sense, random assignment should meet two criteria. One is that each participant has an equal chance of being assigned to each condition (e.g., a 50% chance of being assigned to each of two conditions). The second is that each participant is assigned to a condition independently of other participants. Thus one way to assign participants to two conditions would be to flip a coin for each one. If the coin lands heads, the participant is assigned to Condition A, and if it lands tails, the participant is assigned to Condition B. For three conditions, one could use a computer to generate a random integer from 1 to 3 for each participant. If the integer is 1, the participant is assigned to Condition A; if it is 2, the participant is assigned to Condition B; and if it is 3, the participant is assigned to Condition C. In practice, a full sequence of conditions—one for each participant expected to be in the experiment—is usually created ahead of time, and each new participant is assigned to the next condition in the sequence as he or she is tested. When the procedure is computerized, the computer program often handles the random assignment.

One problem with coin flipping and other strict procedures for random assignment is that they are likely to result in unequal sample sizes in the different conditions. Unequal sample sizes are generally not a serious problem, and you should never throw away data you have already collected to achieve equal sample sizes. However, for a fixed number of participants, it is statistically most efficient to divide them into equal-sized groups. It is standard practice, therefore, to use a kind of modified random assignment that keeps the number of participants in each group as similar as possible. One approach is block randomization . In block randomization, all the conditions occur once in the sequence before any of them is repeated. Then they all occur again before any of them is repeated again. Within each of these “blocks,” the conditions occur in a random order. Again, the sequence of conditions is usually generated before any participants are tested, and each new participant is assigned to the next condition in the sequence.  Table 6.2  shows such a sequence for assigning nine participants to three conditions. The Research Randomizer website will generate block randomization sequences for any number of participants and conditions. Again, when the procedure is computerized, the computer program often handles the block randomization.

Random assignment is not guaranteed to control all extraneous variables across conditions. It is always possible that just by chance, the participants in one condition might turn out to be substantially older, less tired, more motivated, or less depressed on average than the participants in another condition. However, there are some reasons that this possibility is not a major concern. One is that random assignment works better than one might expect, especially for large samples. Another is that the inferential statistics that researchers use to decide whether a difference between groups reflects a difference in the population takes the “fallibility” of random assignment into account. Yet another reason is that even if random assignment does result in a confounding variable and therefore produces misleading results, this confound is likely to be detected when the experiment is replicated. The upshot is that random assignment to conditions—although not infallible in terms of controlling extraneous variables—is always considered a strength of a research design.

Treatment and Control Conditions

Between-subjects experiments are often used to determine whether a treatment works. In psychological research, a  treatment  is any intervention meant to change people’s behaviour for the better. This  intervention  includes psychotherapies and medical treatments for psychological disorders but also interventions designed to improve learning, promote conservation, reduce prejudice, and so on. To determine whether a treatment works, participants are randomly assigned to either a  treatment condition , in which they receive the treatment, or a control condition , in which they do not receive the treatment. If participants in the treatment condition end up better off than participants in the control condition—for example, they are less depressed, learn faster, conserve more, express less prejudice—then the researcher can conclude that the treatment works. In research on the effectiveness of psychotherapies and medical treatments, this type of experiment is often called a randomized clinical trial .

There are different types of control conditions. In a  no-treatment control condition , participants receive no treatment whatsoever. One problem with this approach, however, is the existence of placebo effects. A  placebo  is a simulated treatment that lacks any active ingredient or element that should make it effective, and a  placebo effect  is a positive effect of such a treatment. Many folk remedies that seem to work—such as eating chicken soup for a cold or placing soap under the bedsheets to stop nighttime leg cramps—are probably nothing more than placebos. Although placebo effects are not well understood, they are probably driven primarily by people’s expectations that they will improve. Having the expectation to improve can result in reduced stress, anxiety, and depression, which can alter perceptions and even improve immune system functioning (Price, Finniss, & Benedetti, 2008) [1] .

Placebo effects are interesting in their own right (see  Note “The Powerful Placebo” ), but they also pose a serious problem for researchers who want to determine whether a treatment works.  Figure 6.2  shows some hypothetical results in which participants in a treatment condition improved more on average than participants in a no-treatment control condition. If these conditions (the two leftmost bars in  Figure 6.2 ) were the only conditions in this experiment, however, one could not conclude that the treatment worked. It could be instead that participants in the treatment group improved more because they expected to improve, while those in the no-treatment control condition did not.

Fortunately, there are several solutions to this problem. One is to include a placebo control condition , in which participants receive a placebo that looks much like the treatment but lacks the active ingredient or element thought to be responsible for the treatment’s effectiveness. When participants in a treatment condition take a pill, for example, then those in a placebo control condition would take an identical-looking pill that lacks the active ingredient in the treatment (a “sugar pill”). In research on psychotherapy effectiveness, the placebo might involve going to a psychotherapist and talking in an unstructured way about one’s problems. The idea is that if participants in both the treatment and the placebo control groups expect to improve, then any improvement in the treatment group over and above that in the placebo control group must have been caused by the treatment and not by participants’ expectations. This  difference  is what is shown by a comparison of the two outer bars in  Figure 6.2 .

Of course, the principle of informed consent requires that participants be told that they will be assigned to either a treatment or a placebo control condition—even though they cannot be told which until the experiment ends. In many cases the participants who had been in the control condition are then offered an opportunity to have the real treatment. An alternative approach is to use a waitlist control condition , in which participants are told that they will receive the treatment but must wait until the participants in the treatment condition have already received it. This disclosure allows researchers to compare participants who have received the treatment with participants who are not currently receiving it but who still expect to improve (eventually). A final solution to the problem of placebo effects is to leave out the control condition completely and compare any new treatment with the best available alternative treatment. For example, a new treatment for simple phobia could be compared with standard exposure therapy. Because participants in both conditions receive a treatment, their expectations about improvement should be similar. This approach also makes sense because once there is an effective treatment, the interesting question about a new treatment is not simply “Does it work?” but “Does it work better than what is already available?

The Powerful Placebo

Many people are not surprised that placebos can have a positive effect on disorders that seem fundamentally psychological, including depression, anxiety, and insomnia. However, placebos can also have a positive effect on disorders that most people think of as fundamentally physiological. These include asthma, ulcers, and warts (Shapiro & Shapiro, 1999) [2] . There is even evidence that placebo surgery—also called “sham surgery”—can be as effective as actual surgery.

Medical researcher J. Bruce Moseley and his colleagues conducted a study on the effectiveness of two arthroscopic surgery procedures for osteoarthritis of the knee (Moseley et al., 2002) [3] . The control participants in this study were prepped for surgery, received a tranquilizer, and even received three small incisions in their knees. But they did not receive the actual arthroscopic surgical procedure. The surprising result was that all participants improved in terms of both knee pain and function, and the sham surgery group improved just as much as the treatment groups. According to the researchers, “This study provides strong evidence that arthroscopic lavage with or without débridement [the surgical procedures used] is not better than and appears to be equivalent to a placebo procedure in improving knee pain and self-reported function” (p. 85).

Within-Subjects Experiments

In a within-subjects experiment , each participant is tested under all conditions. Consider an experiment on the effect of a defendant’s physical attractiveness on judgments of his guilt. Again, in a between-subjects experiment, one group of participants would be shown an attractive defendant and asked to judge his guilt, and another group of participants would be shown an unattractive defendant and asked to judge his guilt. In a within-subjects experiment, however, the same group of participants would judge the guilt of both an attractive and an unattractive defendant.

The primary advantage of this approach is that it provides maximum control of extraneous participant variables. Participants in all conditions have the same mean IQ, same socioeconomic status, same number of siblings, and so on—because they are the very same people. Within-subjects experiments also make it possible to use statistical procedures that remove the effect of these extraneous participant variables on the dependent variable and therefore make the data less “noisy” and the effect of the independent variable easier to detect. We will look more closely at this idea later in the book.  However, not all experiments can use a within-subjects design nor would it be desirable to.

Carryover Effects and Counterbalancing

The primary disad vantage of within-subjects designs is that they can result in carryover effects. A  carryover effect  is an effect of being tested in one condition on participants’ behaviour in later conditions. One type of carryover effect is a  practice effect , where participants perform a task better in later conditions because they have had a chance to practice it. Another type is a fatigue effect , where participants perform a task worse in later conditions because they become tired or bored. Being tested in one condition can also change how participants perceive stimuli or interpret their task in later conditions. This  type of effect  is called a  context effect . For example, an average-looking defendant might be judged more harshly when participants have just judged an attractive defendant than when they have just judged an unattractive defendant. Within-subjects experiments also make it easier for participants to guess the hypothesis. For example, a participant who is asked to judge the guilt of an attractive defendant and then is asked to judge the guilt of an unattractive defendant is likely to guess that the hypothesis is that defendant attractiveness affects judgments of guilt. This  knowledge  could lead the participant to judge the unattractive defendant more harshly because he thinks this is what he is expected to do. Or it could make participants judge the two defendants similarly in an effort to be “fair.”

Carryover effects can be interesting in their own right. (Does the attractiveness of one person depend on the attractiveness of other people that we have seen recently?) But when they are not the focus of the research, carryover effects can be problematic. Imagine, for example, that participants judge the guilt of an attractive defendant and then judge the guilt of an unattractive defendant. If they judge the unattractive defendant more harshly, this might be because of his unattractiveness. But it could be instead that they judge him more harshly because they are becoming bored or tired. In other words, the order of the conditions is a confounding variable. The attractive condition is always the first condition and the unattractive condition the second. Thus any difference between the conditions in terms of the dependent variable could be caused by the order of the conditions and not the independent variable itself.

There is a solution to the problem of order effects, however, that can be used in many situations. It is  counterbalancing , which means testing different participants in different orders. For example, some participants would be tested in the attractive defendant condition followed by the unattractive defendant condition, and others would be tested in the unattractive condition followed by the attractive condition. With three conditions, there would be six different orders (ABC, ACB, BAC, BCA, CAB, and CBA), so some participants would be tested in each of the six orders. With counterbalancing, participants are assigned to orders randomly, using the techniques we have already discussed. Thus random assignment plays an important role in within-subjects designs just as in between-subjects designs. Here, instead of randomly assigning to conditions, they are randomly assigned to different orders of conditions. In fact, it can safely be said that if a study does not involve random assignment in one form or another, it is not an experiment.

An efficient way of counterbalancing is through a Latin square design which randomizes through having equal rows and columns. For example, if you have four treatments, you must have four versions. Like a Sudoku puzzle, no treatment can repeat in a row or column. For four versions of four treatments, the Latin square design would look like:

There are two ways to think about what counterbalancing accomplishes. One is that it controls the order of conditions so that it is no longer a confounding variable. Instead of the attractive condition always being first and the unattractive condition always being second, the attractive condition comes first for some participants and second for others. Likewise, the unattractive condition comes first for some participants and second for others. Thus any overall difference in the dependent variable between the two conditions cannot have been caused by the order of conditions. A second way to think about what counterbalancing accomplishes is that if there are carryover effects, it makes it possible to detect them. One can analyze the data separately for each order to see whether it had an effect.

When 9 is “larger” than 221

Researcher Michael Birnbaum has argued that the lack of context provided by between-subjects designs is often a bigger problem than the context effects created by within-subjects designs. To demonstrate this problem, he asked participants to rate two numbers on how large they were on a scale of 1-to-10 where 1 was “very very small” and 10 was “very very large”.  One group of participants were asked to rate the number 9 and another group was asked to rate the number 221 (Birnbaum, 1999) [4] . Participants in this between-subjects design gave the number 9 a mean rating of 5.13 and the number 221 a mean rating of 3.10. In other words, they rated 9 as larger than 221! According to Birnbaum, this difference is because participants spontaneously compared 9 with other one-digit numbers (in which case it is relatively large) and compared 221 with other three-digit numbers (in which case it is relatively small) .

Simultaneous Within-Subjects Designs

So far, we have discussed an approach to within-subjects designs in which participants are tested in one condition at a time. There is another approach, however, that is often used when participants make multiple responses in each condition. Imagine, for example, that participants judge the guilt of 10 attractive defendants and 10 unattractive defendants. Instead of having people make judgments about all 10 defendants of one type followed by all 10 defendants of the other type, the researcher could present all 20 defendants in a sequence that mixed the two types. The researcher could then compute each participant’s mean rating for each type of defendant. Or imagine an experiment designed to see whether people with social anxiety disorder remember negative adjectives (e.g., “stupid,” “incompetent”) better than positive ones (e.g., “happy,” “productive”). The researcher could have participants study a single list that includes both kinds of words and then have them try to recall as many words as possible. The researcher could then count the number of each type of word that was recalled. There are many ways to determine the order in which the stimuli are presented, but one common way is to generate a different random order for each participant.

Between-Subjects or Within-Subjects?

Almost every experiment can be conducted using either a between-subjects design or a within-subjects design. This possibility means that researchers must choose between the two approaches based on their relative merits for the particular situation.

Between-subjects experiments have the advantage of being conceptually simpler and requiring less testing time per participant. They also avoid carryover effects without the need for counterbalancing. Within-subjects experiments have the advantage of controlling extraneous participant variables, which generally reduces noise in the data and makes it easier to detect a relationship between the independent and dependent variables.

A good rule of thumb, then, is that if it is possible to conduct a within-subjects experiment (with proper counterbalancing) in the time that is available per participant—and you have no serious concerns about carryover effects—this design is probably the best option. If a within-subjects design would be difficult or impossible to carry out, then you should consider a between-subjects design instead. For example, if you were testing participants in a doctor’s waiting room or shoppers in line at a grocery store, you might not have enough time to test each participant in all conditions and therefore would opt for a between-subjects design. Or imagine you were trying to reduce people’s level of prejudice by having them interact with someone of another race. A within-subjects design with counterbalancing would require testing some participants in the treatment condition first and then in a control condition. But if the treatment works and reduces people’s level of prejudice, then they would no longer be suitable for testing in the control condition. This difficulty is true for many designs that involve a treatment meant to produce long-term change in participants’ behaviour (e.g., studies testing the effectiveness of psychotherapy). Clearly, a between-subjects design would be necessary here.

Remember also that using one type of design does not preclude using the other type in a different study. There is no reason that a researcher could not use both a between-subjects design and a within-subjects design to answer the same research question. In fact, professional researchers often take exactly this type of mixed methods approach.

Key Takeaways

• Experiments can be conducted using either between-subjects or within-subjects designs. Deciding which to use in a particular situation requires careful consideration of the pros and cons of each approach.
• Random assignment to conditions in between-subjects experiments or to orders of conditions in within-subjects experiments is a fundamental element of experimental research. Its purpose is to control extraneous variables so that they do not become confounding variables.
• Experimental research on the effectiveness of a treatment requires both a treatment condition and a control condition, which can be a no-treatment control condition, a placebo control condition, or a waitlist control condition. Experimental treatments can also be compared with the best available alternative.
• You want to test the relative effectiveness of two training programs for running a marathon.
• Using photographs of people as stimuli, you want to see if smiling people are perceived as more intelligent than people who are not smiling.
• In a field experiment, you want to see if the way a panhandler is dressed (neatly vs. sloppily) affects whether or not passersby give him any money.
• You want to see if concrete nouns (e.g.,  dog ) are recalled better than abstract nouns (e.g.,  truth ).
• Discussion: Imagine that an experiment shows that participants who receive psychodynamic therapy for a dog phobia improve more than participants in a no-treatment control group. Explain a fundamental problem with this research design and at least two ways that it might be corrected.
• Price, D. D., Finniss, D. G., & Benedetti, F. (2008). A comprehensive review of the placebo effect: Recent advances and current thought. Annual Review of Psychology, 59 , 565–590. ↵
• Shapiro, A. K., & Shapiro, E. (1999). The powerful placebo: From ancient priest to modern physician . Baltimore, MD: Johns Hopkins University Press. ↵
• Moseley, J. B., O’Malley, K., Petersen, N. J., Menke, T. J., Brody, B. A., Kuykendall, D. H., … Wray, N. P. (2002). A controlled trial of arthroscopic surgery for osteoarthritis of the knee. The New England Journal of Medicine, 347 , 81–88. ↵
• Birnbaum, M.H. (1999). How to show that 9>221: Collect judgments in a between-subjects design. Psychological Methods, 4(3), 243-249. ↵

An experiment in which each participant is only tested in one condition.

A method of controlling extraneous variables across conditions by using a random process to decide which participants will be tested in the different conditions.

All the conditions of an experiment occur once in the sequence before any of them is repeated.

Any intervention meant to change people’s behaviour for the better.

A condition in a study where participants receive treatment.

A condition in a study that the other condition is compared to. This group does not receive the treatment or intervention that the other conditions do.

A type of experiment to research the effectiveness of psychotherapies and medical treatments.

A type of control condition in which participants receive no treatment.

A simulated treatment that lacks any active ingredient or element that should make it effective.

A positive effect of a treatment that lacks any active ingredient or element to make it effective.

Participants receive a placebo that looks like the treatment but lacks the active ingredient or element thought to be responsible for the treatment’s effectiveness.

Participants are told that they will receive the treatment but must wait until the participants in the treatment condition have already received it.

Each participant is tested under all conditions.

An effect of being tested in one condition on participants’ behaviour in later conditions.

Participants perform a task better in later conditions because they have had a chance to practice it.

Participants perform a task worse in later conditions because they become tired or bored.

Being tested in one condition can also change how participants perceive stimuli or interpret their task in later conditions.

Testing different participants in different orders.

Research Methods in Psychology - 2nd Canadian Edition Copyright © 2015 by Paul C. Price, Rajiv Jhangiani, & I-Chant A. Chiang is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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An overview of randomization techniques: an unbiased assessment of outcome in clinical research.

Department of Biostatics, National Institute of Animal Nutrition & Physiology (NIANP), Adugodi, Bangalore, India

Randomization as a method of experimental control has been extensively used in human clinical trials and other biological experiments. It prevents the selection bias and insures against the accidental bias. It produces the comparable groups and eliminates the source of bias in treatment assignments. Finally, it permits the use of probability theory to express the likelihood of chance as a source for the difference of end outcome. This paper discusses the different methods of randomization and use of online statistical computing web programming ( www.graphpad.com /quickcalcs or www.randomization.com ) to generate the randomization schedule. Issues related to randomization are also discussed in this paper.

INTRODUCTION

A good experiment or trial minimizes the variability of the evaluation and provides unbiased evaluation of the intervention by avoiding confounding from other factors, which are known and unknown. Randomization ensures that each patient has an equal chance of receiving any of the treatments under study, generate comparable intervention groups, which are alike in all the important aspects except for the intervention each groups receives. It also provides a basis for the statistical methods used in analyzing the data. The basic benefits of randomization are as follows: it eliminates the selection bias, balances the groups with respect to many known and unknown confounding or prognostic variables, and forms the basis for statistical tests, a basis for an assumption of free statistical test of the equality of treatments. In general, a randomized experiment is an essential tool for testing the efficacy of the treatment.

In practice, randomization requires generating randomization schedules, which should be reproducible. Generation of a randomization schedule usually includes obtaining the random numbers and assigning random numbers to each subject or treatment conditions. Random numbers can be generated by computers or can come from random number tables found in the most statistical text books. For simple experiments with small number of subjects, randomization can be performed easily by assigning the random numbers from random number tables to the treatment conditions. However, in the large sample size situation or if restricted randomization or stratified randomization to be performed for an experiment or if an unbalanced allocation ratio will be used, it is better to use the computer programming to do the randomization such as SAS, R environment etc.[ 1 – 6 ]

REASON FOR RANDOMIZATION

Researchers in life science research demand randomization for several reasons. First, subjects in various groups should not differ in any systematic way. In a clinical research, if treatment groups are systematically different, research results will be biased. Suppose that subjects are assigned to control and treatment groups in a study examining the efficacy of a surgical intervention. If a greater proportion of older subjects are assigned to the treatment group, then the outcome of the surgical intervention may be influenced by this imbalance. The effects of the treatment would be indistinguishable from the influence of the imbalance of covariates, thereby requiring the researcher to control for the covariates in the analysis to obtain an unbiased result.[ 7 , 8 ]

Second, proper randomization ensures no a priori knowledge of group assignment (i.e., allocation concealment). That is, researchers, subject or patients or participants, and others should not know to which group the subject will be assigned. Knowledge of group assignment creates a layer of potential selection bias that may taint the data.[ 9 ] Schul and Grimes stated that trials with inadequate or unclear randomization tended to overestimate treatment effects up to 40% compared with those that used proper randomization. The outcome of the research can be negatively influenced by this inadequate randomization.

Statistical techniques such as analysis of covariance (ANCOVA), multivariate ANCOVA, or both, are often used to adjust for covariate imbalance in the analysis stage of the clinical research. However, the interpretation of this post adjustment approach is often difficult because imbalance of covariates frequently leads to unanticipated interaction effects, such as unequal slopes among subgroups of covariates.[ 1 ] One of the critical assumptions in ANCOVA is that the slopes of regression lines are the same for each group of covariates. The adjustment needed for each covariate group may vary, which is problematic because ANCOVA uses the average slope across the groups to adjust the outcome variable. Thus, the ideal way of balancing covariates among groups is to apply sound randomization in the design stage of a clinical research (before the adjustment procedure) instead of post data collection. In such instances, random assignment is necessary and guarantees validity for statistical tests of significance that are used to compare treatments.

TYPES OF RANDOMIZATION

Many procedures have been proposed for the random assignment of participants to treatment groups in clinical trials. In this article, common randomization techniques, including simple randomization, block randomization, stratified randomization, and covariate adaptive randomization, are reviewed. Each method is described along with its advantages and disadvantages. It is very important to select a method that will produce interpretable and valid results for your study. Use of online software to generate randomization code using block randomization procedure will be presented.

Simple randomization

Randomization based on a single sequence of random assignments is known as simple randomization.[ 3 ] This technique maintains complete randomness of the assignment of a subject to a particular group. The most common and basic method of simple randomization is flipping a coin. For example, with two treatment groups (control versus treatment), the side of the coin (i.e., heads - control, tails - treatment) determines the assignment of each subject. Other methods include using a shuffled deck of cards (e.g., even - control, odd - treatment) or throwing a dice (e.g., below and equal to 3 - control, over 3 - treatment). A random number table found in a statistics book or computer-generated random numbers can also be used for simple randomization of subjects.

This randomization approach is simple and easy to implement in a clinical research. In large clinical research, simple randomization can be trusted to generate similar numbers of subjects among groups. However, randomization results could be problematic in relatively small sample size clinical research, resulting in an unequal number of participants among groups.

Block randomization

The block randomization method is designed to randomize subjects into groups that result in equal sample sizes. This method is used to ensure a balance in sample size across groups over time. Blocks are small and balanced with predetermined group assignments, which keeps the numbers of subjects in each group similar at all times.[ 1 , 2 ] The block size is determined by the researcher and should be a multiple of the number of groups (i.e., with two treatment groups, block size of either 4, 6, or 8). Blocks are best used in smaller increments as researchers can more easily control balance.[ 10 ]

After block size has been determined, all possible balanced combinations of assignment within the block (i.e., equal number for all groups within the block) must be calculated. Blocks are then randomly chosen to determine the patients’ assignment into the groups.

Although balance in sample size may be achieved with this method, groups may be generated that are rarely comparable in terms of certain covariates. For example, one group may have more participants with secondary diseases (e.g., diabetes, multiple sclerosis, cancer, hypertension, etc.) that could confound the data and may negatively influence the results of the clinical trial.[ 11 ] Pocock and Simon stressed the importance of controlling for these covariates because of serious consequences to the interpretation of the results. Such an imbalance could introduce bias in the statistical analysis and reduce the power of the study. Hence, sample size and covariates must be balanced in clinical research.

Stratified randomization

The stratified randomization method addresses the need to control and balance the influence of covariates. This method can be used to achieve balance among groups in terms of subjects’ baseline characteristics (covariates). Specific covariates must be identified by the researcher who understands the potential influence each covariate has on the dependent variable. Stratified randomization is achieved by generating a separate block for each combination of covariates, and subjects are assigned to the appropriate block of covariates. After all subjects have been identified and assigned into blocks, simple randomization is performed within each block to assign subjects to one of the groups.

The stratified randomization method controls for the possible influence of covariates that would jeopardize the conclusions of the clinical research. For example, a clinical research of different rehabilitation techniques after a surgical procedure will have a number of covariates. It is well known that the age of the subject affects the rate of prognosis. Thus, age could be a confounding variable and influence the outcome of the clinical research. Stratified randomization can balance the control and treatment groups for age or other identified covariates. Although stratified randomization is a relatively simple and useful technique, especially for smaller clinical trials, it becomes complicated to implement if many covariates must be controlled.[ 12 ] Stratified randomization has another limitation; it works only when all subjects have been identified before group assignment. However, this method is rarely applicable because clinical research subjects are often enrolled one at a time on a continuous basis. When baseline characteristics of all subjects are not available before assignment, using stratified randomization is difficult.[ 10 ]

Covariate adaptive randomization

One potential problem with small to moderate size clinical research is that simple randomization (with or without taking stratification of prognostic variables into account) may result in imbalance of important covariates among treatment groups. Imbalance of covariates is important because of its potential to influence the interpretation of a research results. Covariate adaptive randomization has been recommended by many researchers as a valid alternative randomization method for clinical research.[ 8 , 13 ] In covariate adaptive randomization, a new participant is sequentially assigned to a particular treatment group by taking into account the specific covariates and previous assignments of participants.[ 7 ] Covariate adaptive randomization uses the method of minimization by assessing the imbalance of sample size among several covariates.

Using the online randomization http://www.graphpad.com/quickcalcs/index.cfm , researcher can generate randomization plan for treatment assignment to patients. This online software is very simple and easy to implement. Up to 10 treatments can be allocated to patients and the replication of treatment can also be performed up to 9 times. The major limitations of this software is that once the randomization plan is generated, same randomization plan cannot be generated as this uses the seed point of local computer clock and is not displayed for further use. Other limitation of this online software Maximum of only 10 treatments can be assigned to patients. Entering the web address http://www.graphpad.com/quickcalcs/index.cfm on address bar of any browser, the page of graphpad appears with number of options. Select the option of “Random Numbers” and then press continue, Random Number Calculator with three options appears. Select the tab “Randomly assign subjects to groups” and press continue. In the next page, enter the number of subjects in each group in the tab “Assign” and select the number of groups from the tab “Subjects to each group” and keep number 1 in repeat tab if there is no replication in the study. For example, the total number of patients in a three group experimental study is 30 and each group will assigned to 10 patients. Type 10 in the “Assign” tab and select 3 in the tab “Subjects to each group” and then press “do it” button. The results is obtained as shown as below (partial output is presented)

Another randomization online software, which can be used to generate randomization plan is http://www.randomization.com . The seed for the random number generator[ 14 , 15 ] (Wichmann and Hill, 1982, as modified by McLeod, 1985) is obtained from the clock of the local computer and is printed at the bottom of the randomization plan. If a seed is included in the request, it overrides the value obtained from the clock and can be used to reproduce or verify a particular plan. Up to 20 treatments can be specified. The randomization plan is not affected by the order in which the treatments are entered or the particular boxes left blank if not all are needed. The program begins by sorting treatment names internally. The sorting is case sensitive, however, so the same capitalization should be used when recreating an earlier plan. Example of 10 patients allocating to two groups (each with 5 patients), first the enter the treatment labels in the boxes, and enter the total number of patients that is 10 in the tab “Number of subjects per block” and enter the 1 in the tab “Number of blocks” for simple randomization or more than one for Block randomization. The output of this online software is presented as follows.

The benefits of randomization are numerous. It ensures against the accidental bias in the experiment and produces comparable groups in all the respect except the intervention each group received. The purpose of this paper is to introduce the randomization, including concept and significance and to review several randomization techniques to guide the researchers and practitioners to better design their randomized clinical trials. Use of online randomization was effectively demonstrated in this article for benefit of researchers. Simple randomization works well for the large clinical trails ( n >100) and for small to moderate clinical trials ( n <100) without covariates, use of block randomization helps to achieve the balance. For small to moderate size clinical trials with several prognostic factors or covariates, the adaptive randomization method could be more useful in providing a means to achieve treatment balance.

Source of Support: Nil

Conflict of Interest: None declared.

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5.15: Drawing Conclusions from Statistics

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Learning Objectives

• Describe the role of random sampling and random assignment in drawing cause-and-effect conclusions

Generalizability

One limitation to the study mentioned previously about the babies choosing the “helper” toy is that the conclusion only applies to the 16 infants in the study. We don’t know much about how those 16 infants were selected. Suppose we want to select a subset of individuals (a sample ) from a much larger group of individuals (the population ) in such a way that conclusions from the sample can be generalized to the larger population. This is the question faced by pollsters every day.

Example 1 : The General Social Survey (GSS) is a survey on societal trends conducted every other year in the United States. Based on a sample of about 2,000 adult Americans, researchers make claims about what percentage of the U.S. population consider themselves to be “liberal,” what percentage consider themselves “happy,” what percentage feel “rushed” in their daily lives, and many other issues. The key to making these claims about the larger population of all American adults lies in how the sample is selected. The goal is to select a sample that is representative of the population, and a common way to achieve this goal is to select a random sample that gives every member of the population an equal chance of being selected for the sample. In its simplest form, random sampling involves numbering every member of the population and then using a computer to randomly select the subset to be surveyed. Most polls don’t operate exactly like this, but they do use probability-based sampling methods to select individuals from nationally representative panels.

In 2004, the GSS reported that 817 of 977 respondents (or 83.6%) indicated that they always or sometimes feel rushed. This is a clear majority, but we again need to consider variation due to random sampling . Fortunately, we can use the same probability model we did in the previous example to investigate the probable size of this error. (Note, we can use the coin-tossing model when the actual population size is much, much larger than the sample size, as then we can still consider the probability to be the same for every individual in the sample.) This probability model predicts that the sample result will be within 3 percentage points of the population value (roughly 1 over the square root of the sample size, the margin of error ). A statistician would conclude, with 95% confidence, that between 80.6% and 86.6% of all adult Americans in 2004 would have responded that they sometimes or always feel rushed.

The key to the margin of error is that when we use a probability sampling method, we can make claims about how often (in the long run, with repeated random sampling) the sample result would fall within a certain distance from the unknown population value by chance (meaning by random sampling variation) alone. Conversely, non-random samples are often suspect to bias, meaning the sampling method systematically over-represents some segments of the population and under-represents others. We also still need to consider other sources of bias, such as individuals not responding honestly. These sources of error are not measured by the margin of error.

Query \(\PageIndex{1}\)

Query \(\PageIndex{2}\)

Cause and Effect

In many research studies, the primary question of interest concerns differences between groups. Then the question becomes how were the groups formed (e.g., selecting people who already drink coffee vs. those who don’t). In some studies, the researchers actively form the groups themselves. But then we have a similar question—could any differences we observe in the groups be an artifact of that group-formation process? Or maybe the difference we observe in the groups is so large that we can discount a “fluke” in the group-formation process as a reasonable explanation for what we find?

Example 2 : A psychology study investigated whether people tend to display more creativity when they are thinking about intrinsic (internal) or extrinsic (external) motivations (Ramsey & Schafer, 2002, based on a study by Amabile, 1985). The subjects were 47 people with extensive experience with creative writing. Subjects began by answering survey questions about either intrinsic motivations for writing (such as the pleasure of self-expression) or extrinsic motivations (such as public recognition). Then all subjects were instructed to write a haiku, and those poems were evaluated for creativity by a panel of judges. The researchers conjectured beforehand that subjects who were thinking about intrinsic motivations would display more creativity than subjects who were thinking about extrinsic motivations. The creativity scores from the 47 subjects in this study are displayed in Figure 2, where higher scores indicate more creativity.

In this example, the key question is whether the type of motivation affects creativity scores. In particular, do subjects who were asked about intrinsic motivations tend to have higher creativity scores than subjects who were asked about extrinsic motivations?

Figure 2 reveals that both motivation groups saw considerable variability in creativity scores, and these scores have considerable overlap between the groups. In other words, it’s certainly not always the case that those with extrinsic motivations have higher creativity than those with intrinsic motivations, but there may still be a statistical tendency in this direction. (Psychologist Keith Stanovich (2013) refers to people’s difficulties with thinking about such probabilistic tendencies as “the Achilles heel of human cognition.”)

The mean creativity score is 19.88 for the intrinsic group, compared to 15.74 for the extrinsic group, which supports the researchers’ conjecture. Yet comparing only the means of the two groups fails to consider the variability of creativity scores in the groups. We can measure variability with statistics using, for instance, the standard deviation: 5.25 for the extrinsic group and 4.40 for the intrinsic group. The standard deviations tell us that most of the creativity scores are within about 5 points of the mean score in each group. We see that the mean score for the intrinsic group lies within one standard deviation of the mean score for extrinsic group. So, although there is a tendency for the creativity scores to be higher in the intrinsic group, on average, the difference is not extremely large.

We again want to consider possible explanations for this difference. The study only involved individuals with extensive creative writing experience. Although this limits the population to which we can generalize, it does not explain why the mean creativity score was a bit larger for the intrinsic group than for the extrinsic group. Maybe women tend to receive higher creativity scores? Here is where we need to focus on how the individuals were assigned to the motivation groups. If only women were in the intrinsic motivation group and only men in the extrinsic group, then this would present a problem because we wouldn’t know if the intrinsic group did better because of the different type of motivation or because they were women. However, the researchers guarded against such a problem by randomly assigning the individuals to the motivation groups. Like flipping a coin, each individual was just as likely to be assigned to either type of motivation. Why is this helpful? Because this random assignment tends to balance out all the variables related to creativity we can think of, and even those we don’t think of in advance, between the two groups. So we should have a similar male/female split between the two groups; we should have a similar age distribution between the two groups; we should have a similar distribution of educational background between the two groups; and so on. Random assignment should produce groups that are as similar as possible except for the type of motivation, which presumably eliminates all those other variables as possible explanations for the observed tendency for higher scores in the intrinsic group.

But does this always work? No, so by “luck of the draw” the groups may be a little different prior to answering the motivation survey. So then the question is, is it possible that an unlucky random assignment is responsible for the observed difference in creativity scores between the groups? In other words, suppose each individual’s poem was going to get the same creativity score no matter which group they were assigned to, that the type of motivation in no way impacted their score. Then how often would the random-assignment process alone lead to a difference in mean creativity scores as large (or larger) than 19.88 – 15.74 = 4.14 points?

We again want to apply to a probability model to approximate a p-value , but this time the model will be a bit different. Think of writing everyone’s creativity scores on an index card, shuffling up the index cards, and then dealing out 23 to the extrinsic motivation group and 24 to the intrinsic motivation group, and finding the difference in the group means. We (better yet, the computer) can repeat this process over and over to see how often, when the scores don’t change, random assignment leads to a difference in means at least as large as 4.41. Figure 3 shows the results from 1,000 such hypothetical random assignments for these scores.

Only 2 of the 1,000 simulated random assignments produced a difference in group means of 4.41 or larger. In other words, the approximate p-value is 2/1000 = 0.002. This small p-value indicates that it would be very surprising for the random assignment process alone to produce such a large difference in group means. Therefore, as with Example 2, we have strong evidence that focusing on intrinsic motivations tends to increase creativity scores, as compared to thinking about extrinsic motivations.

Notice that the previous statement implies a cause-and-effect relationship between motivation and creativity score; is such a strong conclusion justified? Yes, because of the random assignment used in the study. That should have balanced out any other variables between the two groups, so now that the small p-value convinces us that the higher mean in the intrinsic group wasn’t just a coincidence, the only reasonable explanation left is the difference in the type of motivation. Can we generalize this conclusion to everyone? Not necessarily—we could cautiously generalize this conclusion to individuals with extensive experience in creative writing similar the individuals in this study, but we would still want to know more about how these individuals were selected to participate.

Statistical thinking involves the careful design of a study to collect meaningful data to answer a focused research question, detailed analysis of patterns in the data, and drawing conclusions that go beyond the observed data. Random sampling is paramount to generalizing results from our sample to a larger population, and random assignment is key to drawing cause-and-effect conclusions. With both kinds of randomness, probability models help us assess how much random variation we can expect in our results, in order to determine whether our results could happen by chance alone and to estimate a margin of error.

So where does this leave us with regard to the coffee study mentioned previously (the Freedman, Park, Abnet, Hollenbeck, & Sinha, 2012 found that men who drank at least six cups of coffee a day had a 10% lower chance of dying (women 15% lower) than those who drank none)? We can answer many of the questions:

• This was a 14-year study conducted by researchers at the National Cancer Institute.
• The results were published in the June issue of the New England Journal of Medicine , a respected, peer-reviewed journal.
• The study reviewed coffee habits of more than 402,000 people ages 50 to 71 from six states and two metropolitan areas. Those with cancer, heart disease, and stroke were excluded at the start of the study. Coffee consumption was assessed once at the start of the study.
• About 52,000 people died during the course of the study.
• People who drank between two and five cups of coffee daily showed a lower risk as well, but the amount of reduction increased for those drinking six or more cups.
• The sample sizes were fairly large and so the p-values are quite small, even though percent reduction in risk was not extremely large (dropping from a 12% chance to about 10%–11%).
• Whether coffee was caffeinated or decaffeinated did not appear to affect the results.
• This was an observational study, so no cause-and-effect conclusions can be drawn between coffee drinking and increased longevity, contrary to the impression conveyed by many news headlines about this study. In particular, it’s possible that those with chronic diseases don’t tend to drink coffee.

This study needs to be reviewed in the larger context of similar studies and consistency of results across studies, with the constant caution that this was not a randomized experiment. Whereas a statistical analysis can still “adjust” for other potential confounding variables, we are not yet convinced that researchers have identified them all or completely isolated why this decrease in death risk is evident. Researchers can now take the findings of this study and develop more focused studies that address new questions.

Explore these outside resources to learn more about applied statistics:

• Video about p-values:  P-Value Extravaganza
• Interactive web applets for teaching and learning statistics
• Inter-university Consortium for Political and Social Research  where you can find and analyze data.
• The Consortium for the Advancement of Undergraduate Statistics

Think It Over

• Find a recent research article in your field and answer the following: What was the primary research question? How were individuals selected to participate in the study? Were summary results provided? How strong is the evidence presented in favor or against the research question? Was random assignment used? Summarize the main conclusions from the study, addressing the issues of statistical significance, statistical confidence, generalizability, and cause and effect. Do you agree with the conclusions drawn from this study, based on the study design and the results presented?
• Is it reasonable to use a random sample of 1,000 individuals to draw conclusions about all U.S. adults? Explain why or why not.

cause-and-effect: related to whether we say one variable is causing changes in the other variable, versus other variables that may be related to these two variables.

generalizability : related to whether the results from the sample can be generalized to a larger population.

margin of error : the expected amount of random variation in a statistic; often defined for 95% confidence level.

population : a larger collection of individuals that we would like to generalize our results to.

p-value : the probability of observing a particular outcome in a sample, or more extreme, under a conjecture about the larger population or process.

random assignment : using a probability-based method to divide a sample into treatment groups.

random sampling : using a probability-based method to select a subset of individuals for the sample from the population.

sample : the collection of individuals on which we collect data.

Licenses and Attributions

CC licensed content, Original

• Modification, adaptation, and original content. Authored by : Pat Carroll and Lumen Learning. Provided by : Lumen Learning. License : CC BY: Attribution
• Statistical Thinking. Authored by : Beth Chance and Allan Rossman, California Polytechnic State University, San Luis Obispo. Provided by : Noba. Located at : http://nobaproject.com/modules/statistical-thinking . License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
• The Replication Crisis. Authored by : Colin Thomas William. Provided by : Ivy Tech Community College. License : CC BY: Attribution

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