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Random Assignment in Experiments | Introduction & Examples

Published on March 8, 2021 by Pritha Bhandari . Revised on June 22, 2023.

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

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

Random assignment is a key part of experimental design . It helps you ensure that all groups are comparable at the start of a study: any differences between them are due to random factors, not research biases like sampling bias or selection bias .

Table of contents

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

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

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

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

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

  • a control group that’s given a placebo (no dosage, to control for a placebo effect ),
  • an experimental group that’s given a low dosage,
  • a second experimental group that’s given a high dosage.

Random assignment to helps you make sure that the treatment groups don’t differ in systematic ways at the start of the experiment, as this can seriously affect (and even invalidate) your work.

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

  • participants recruited from cafes are placed in the control group ,
  • participants recruited from local community centers are placed in the low dosage experimental group,
  • participants recruited from gyms are placed in the high dosage group.

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

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

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

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

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

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

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

Random sample vs random assignment

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

You use a simple random sample to collect data. Because you have access to the whole population (all employees), you can assign all 8000 employees a number and use a random number generator to select 300 employees. These 300 employees are your full sample.

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

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

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

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

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

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

Random assignment in block designs

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

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

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

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

When comparing different groups

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

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

When it’s not ethically permissible

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

When you can’t assign participants to groups, you can also conduct a quasi-experimental study . In a quasi-experiment, you study the outcomes of pre-existing groups who receive treatments that you may not have any control over (e.g., heavy drinkers and social drinkers). These groups aren’t randomly assigned, but may be considered comparable when some other variables (e.g., age or socioeconomic status) are controlled for.

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

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

Research bias

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

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

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

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

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

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

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

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

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

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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."

power of random assignment

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.

power of random assignment

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

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

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

Random Assignment In Research

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

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

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

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

Random Selection

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

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

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

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

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

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

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

Example of Random Assignment

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

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

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

A Word From Verywell

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

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

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

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

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

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

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

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

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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.

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Random Assignment in Psychology (Definition + 40 Examples)

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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

two women in different conditions

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

woman sleeping with a brain monitor

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

man on a treadmill

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

old lady gardening

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!

Related posts:

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  • Cluster Sampling vs Stratified Sampling
  • 41+ White Collar Job Examples (Salary + Path)
  • 47+ Blue Collar Job Examples (Salary + Path)
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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.

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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 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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Statistical primer: sample size and power calculations—why, when and how? †

Graeme l hickey.

1 Department of Biostatistics, Institute of Translational Medicine, University of Liverpool, Liverpool, UK

Stuart W Grant

2 Department of Academic Surgery, University of Manchester, Manchester, UK

Joel Dunning

3 Department of Cardiothoracic Surgery, James Cook University Hospital, Middlesbrough, UK

Matthias Siepe

4 Department of Cardiovascular Surgery, University Heart Centre, Freiburg, Germany

When designing a clinical study, a fundamental aspect is the sample size. In this article, we describe the rationale for sample size calculations, when it should be calculated and describe the components necessary to calculate it. For simple studies, standard formulae can be used; however, for more advanced studies, it is generally necessary to use specialized statistical software programs and consult a biostatistician. Sample size calculations for non-randomized studies are also discussed and two clinical examples are used for illustration.

INTRODUCTION

It is essential that clinical studies are well-designed. One key aspect of study design is the sample size, which is the number of patients (or experiment subjects/samples) required to detect a clinically relevant treatment effect. Even for simple studies, there are several things to consider when calculating the required sample size. These include the type of study, type of outcome, variance of the outcome, the significance level and power of the test and the minimal clinically relevant difference. For more complex studies, there might be additional considerations that make the calculation more complex. As sample size calculations are frequently included in medical studies and are crucial to the interpretation of the study, a thorough understanding of the process underlying the calculation is necessary. In this article, we provide an overview of the rationale, methodology, implementation and reporting of sample size calculations specifically for cardiothoracic surgeons.

METHODOLOGY

Why and when.

The sample size calculation is generally required at the study design stage, before patient enrolment has begun [ 1 ]. There are several reasons for this [ 2 ]. Firstly, from a scientific perspective, testing too few might lead to failure to detect an important effect, whereas testing too many might lead to detecting a statistically significant yet clinically insignificant effect. Secondly, from an ethical viewpoint, testing too many subjects can lead to unnecessary harm or potentially unnecessary sacrifice in the case of animal studies. Conversely, testing too few is also unethical, as an underpowered study might not contribute to the evidence-based field of medicine. Thirdly, from an economical perspective, testing too many will lead to unnecessary costs and testing too few will be potentially wasteful if the trial is unable to address the scientific question of interest. For this reason, many funders and institutional review boards require an a priori sample size calculation, which is included in the study protocol. Adaptive trial designs, whereby prespecified modifications can be made to the trial after its inception, can potentially improve flexibility and efficiency [ 3 ].

There are four principal components required to calculate the sample size (Table ​ (Table1). 1 ). These components are specified via parameters. Working under a hypothesis testing framework, we assume a null hypothesis ( H 0 ) and an alternative hypothesis ( H 1 ). In practice, we do not know the ‘truth’, so we base our inferences on a statistical test applied to a random sample from the population. Two types of error can occur. The first is a Type I error, where the null hypothesis is true, but we incorrectly reject it. The second is a Type II error, where the null hypothesis is false, but we incorrectly fail to reject it. Specification of the Type I (denoted as α ) and Type II (denoted as β but more commonly reported as the complement: the power  = 1 -  β ) error rate parameters are required for the sample size calculation. Conventional choices are α =  0.05 and 0.01 (corresponding to a significance level of 5% and 1%, respectively) and β =  0.2 and 0.1 (corresponding to 80% and 90% power, respectively). However, there are situations in which these parameters might be increased or decreased, depending on the clinical context of the study [ 1 ].

Primary components required for a sample size calculation

The minimal clinically relevant difference is the smallest difference in outcome between the study groups, or effect size, that is of scientific interest to the investigator. For example, patients treated with a drug that lowers the mean systolic blood pressure by 7 mmHg compared to untreated hypertensive patients might be considered as clinically relevant (see Example 1). The statistician cannot decide this; it derives from clinical consideration. It is recognized that eliciting this minimal clinically relevant difference is difficult. A starting point is to ask: What results do you expect (or hope) to see? Typically, this question would be answered in terms of absolute effects, but relative effects can also be used. From the given response, the statistician and clinician can explore different scenarios about that choice. It is also useful to consider the individual benefit to the patient weighted against the potential inconvenience and adverse effects they might experience. The variance of the outcome is also required. This can generally be obtained from clinical knowledge; for example, if the clinician has historical similar data or if data have previously been published on the subject. In some cases, it is necessary to conduct a pilot study to gauge the variability of the outcome. Of course, in all cases, it must be considered whether the data used to determine the variance are reflective of the study sample in the planned study. If there are different eligibility criteria or outcome definitions, then this may not be the case.

Calculations

A simple example of a sample size calculation is that of comparing two means for a continuous outcome. Assume that the null hypothesis is H 0 : μ 1 =  μ 2 with an alternative hypothesis H 1 : μ 1  ≠  μ 2 , where μ 1 is the true population mean in the control population, and μ 2 the mean in the treated population. After collection of the data, a standard statistical test used to evaluate the hypothesis is the 2-tailed independent samples t -test. If the study investigators planned to have two groups of equal sample size n , then the following formula can be used, which is based on a normal approximation:

where σ 2 is the common population variance for both populations, and z 1- α /2 and z 1- β are the 100(1 -  α /2) and 100(1 -  β ) percentiles of the standard normal distribution, respectively. These values can be readily obtained using z -tables (Table ​ (Table2) 2 ) or statistical software with an example of this provided later in this article. Although other approximate formulae are sometimes used, a straightforward approximate formula [ 4 ] for comparing 2 proportions, p 1 and p 2 , between groups is

where p ¯ = ( p 1 + p 2 ) / 2 .

Conventional z -values for sample size calculations to use in Equations 1 and 2

Based on these formulae, some immediate deductions can be made. First, the sample size is inversely proportional to square of the absolute effect size; hence, halving the effect size would require quadrupling the sample size. Second, reducing α or increasing the power (equivalent to reducing β ) also increases the sample size required. Third, an increased variance leads to a larger necessary sample size. In the simple formula presented, the variance in each population was assumed to be identical. In practice, this may not hold, but adjustments are straightforward. It is clear, therefore, that slight changes in the factors that make up the sample size calculation (Table ​ (Table1) 1 ) can substantially alter the sample size. When there is doubt, it is generally advisable to err on the side of caution and choose the largest sample size of from the ensemble of scenarios. Although sample size formulae are frequently presented assuming 1:1 allocation between treatment and control groups, other allocation ratios can be accommodated using statistical software packages.

Dropouts, missing data and other study deviations

Patient dropouts, non-adherence (or non-compliance) and missing data are, unfortunately, a common occurrence in clinical studies. It is, therefore, essential to consider the potential impact of this at the study design phase, as deviations may lead to a failure to achieve the intended aims of the trial. If missing data are anticipated completely at random, then the determined sample size can simply be inflated. That is, if the sample size required is n subjects per arm, and it is expected that up to x % patients will drop out, then the final sample size ( n * ) can be inflated as n * = n / ( 1 - x 100 ) . Attention must always be given to the reasons and mechanisms for missing data. Moreover, designing trials to minimize missing data is always the best approach [ 5 ]. Non-compliance, for example, due to patients crossing over to other treatment arms can also affect the power of a trial if not appropriately considered during the study design. The Arterial Revascularization Trial (ART) is an example of this (see Example 2). When different deviations can affect a study, all to varying degrees, simulation is the best approach to assess the potential impacts. In practice, these can be coded using standard programming languages (e.g. R), or specialist software can be utilized (Table ​ (Table3 3 ).

Software for sample size calculations

When interest lies in estimation of a quantity, rather than hypothesis testing , then sample size calculations can be reframed to control the expected width of the confidence interval. For example, a surgeon might want to estimate—with a certain accuracy—the proportion, p , of patients undergoing cardiac surgery who would fail a preoperative cardiopulmonary exercise stress test. As cardiopulmonary exercise stress testing is expensive and time consuming to perform, the surgeon wants to estimate this proportion with a margin of error <5%. The estimated proportion will be p ^ = n u m b e r   o f   p a t i e n t s   t h a t   failed } / n , where n is the number of patients required to be tested. Standard mathematical approximations give a 95% confidence interval as

The term after the plus–minus sign is the margin of error, with the square root term denoting the standard error (SE). The surgeon does not know the value of p ^ yet and, therefore, does not know the SE, but a ‘worst case’ scenario can be mathematically determined based on p ^ = 0.5 . The margin of error is then approximately 1/ √ n , which the surgeon in the example above specified must be <5%; hence, it is required that n   is  ≥ 400 . If the surgeon has an estimate of the prevalence, then this sample size can potentially be reduced by refining the SE estimate.

There are a large number of software programmes available for performing sample size calculations (see Table ​ Table3 3 for a non-exhaustive list of available programmes) including stand-alone programmes, which might be preferable for those unfamiliar with general statistical software programmes. The capabilities of each vary from basic to complex calculations, but common trial designs are integrated into most. There are many online sample calculators and even some smartphone apps that can perform sample size calculations. Although such calculators can be useful, it should be noted that they are unlikely to have been validated, and it is generally advisable to use a validated software programme. Some potentially useful calculators can be found at http://homepage.stat.uiowa.edu/∼rlenth/Power/ , ‘Power and Sample Size’ ( http://powerandsamplesize.com ) and OpenEpi ( http://www.openepi.com ) [all accessed 11 April 2018]. There are also several specialist programs available to conduct simulation analyses to explore deviations (e.g. non-compliance, dropouts and adaptive designs).

It is essential that the details of the sample size calculation are reported in full. This demonstrates that the study has been well designed and establishes what the primary outcome is on which the calculation is based. It also enables reproducibility of the study. Reporting the calculation requires reporting of all parameters and assumptions used. In some cases, sample size formulae depend only on the standardized difference. However, it is preferable to report the individual components (expected effect size in each treatment group and variability). Details of inflation factors (e.g. due to expected dropouts) should also be reported. It is worthwhile noting that reporting of sample sizes is a requirement of the CONSORT Statement checklist [ 6 ]. The STROBE Statement checklist also asks for details on how the sample size was arrived at to be provided [ 7 ].

Non-randomized studies

Sample size formulae are generally presented for randomized clinical trials. In some cases, randomization is not feasible due to physical constraints, ethical issues or resource limitations. This leads to observational studies, whereby due to the presence of confounding variables, it is not appropriate to apply univariable comparison tests due to potential bias. In addition, there is potentially increased measurement error and unknown enrolment protocols. Consequently, sample size calculations in such studies are more complex. In some cases, analyses are based on large clinical (or administrative) registries. These can be very large, meaning that there is little concern about power. However, it is then important to consider whether the adjusted effect size is ‘clinically’ significant, regardless of ‘statistical’ significance. Another issue frequently encountered with non-randomized studies, particularly observational data studies, is the presence of missing data. In some cases, this can be substantial. Complete case analysis (i.e. excluding patients with any missing data) would likely lead to bias and larger SEs, whereas imputation techniques would need to account for the additional uncertainty from the imputed data [ 8 ].

A standard approach for adjusting for confounding is multivariable regression. In such models, we are typically interested in a single covariate (e.g. a binary treatment effect) and will include other covariates (i.e. the confounders) in the regression model. For multivariable linear regression, one approach is to apply a correction factor to the approximate formula (cf. Equation 1 ) [ 9 ]. Formulae for other regression models are also available, e.g. the Cox proportional hazards model [ 10 ] and the logistic [ 11 ] regression model. In the case of the former, it is a sample size formula for the number of ‘events’ required rather than the number of ‘subjects’. An alternative approach frequently used in non-randomized cardiothoracic surgery research studies is propensity score analysis using matching, covariance adjustment, inverse probability treatment weights or stratification [ 12 ]. Sample size calculations need to take account of the method used. For example, if 1-to-1 propensity score matching is used, then a sample size calculated assuming randomization must be inflated to account for patients who will not be matched based on the ratio of controls to treated patients and the degree of overlap of propensity score distributions [ 13 ]. In either case, the precision of the estimated treatment effect following adequate adjustment should be appropriately reported and interpreted.

When the sample size is not achievable

In some cases, achieving the determined sample size will not be feasible due to external factors; for example, time or resource limitations. This frequently happens in rare diseases, e.g. in congenital cardiac surgery. The immediate question is how to proceed in such a circumstance. One option is to inverse the problem and calculate the power that can be attained from the maximum permissible sample size. This power can then be evaluated against the study objectives. If the power is insufficient, then it might be used to gain additional funding to recruit further subjects.

If recruiting more subjects is not feasible, then other options include changing the primary outcome (e.g. using a composite outcome that increases the number of events) [ 14 ], pooling resources and sample populations with other centres and exploring means of reducing the variability (e.g. by limiting the scope of the patient population). Perhaps, the least desirable option is to simply not proceed with completing the study. In this case, data from the study might still be published, as there is a body of methodologists that consider underpowered trials to be acceptable [ 1 , 15 ]. The rationale for considering underpowered studies is that they can potentially be combined with other small studies in a meta-analysis framework. There is also a notion that some knowledge is better than no knowledge. Caveats exist in pursuing such an approach, which include the requirement of absolute transparency, and the rigorous minimization of potential sources of bias (e.g. due to inadequate randomization, blinding or retention) [ 1 ].

Example 1: watermelon treatment for hypertension

Following a pilot study by Figueroa et al. [ 16 ], a fictitious team of investigators want to design a study to test the effect of watermelon extract on systolic blood pressure among hypertensive patients. The investigators hypothesized that the L-citrulline present in watermelon, which naturally converts to L-arginine, will increase the production of endothelial nitric oxide and thus have a vasodilatory effect. Conventional choices of the Type I error rate ( α = 0.05 ) and power ( 1 -  β = 0.80 ) are proposed, yielding z -values of 1.96 and 0.84 (see Table ​ Table2), 2 ), respectively, in Equation 1 . The investigators plan to compare the systolic blood pressure at 6 weeks between placebo and daily watermelon treatment groups using an independent t -test. Based on previous knowledge, it was assumed that mean baseline systolic blood pressure would be 140 mmHg in the control group, and the researchers believed that a biologically plausible reduction of 5% systolic blood pressure (7 mmHg) in the treatment group would be of scientific interest. Assuming a common standard deviation of 10 mmHg in both treatment arms, the necessary sample size ( Equation 1 ) would be 33 subjects per treatment arm. Using a more accurate method (e.g. using a software package such as G*Power 3.1; Table ​ Table3), 3 ), we would be able to determine that a sample size of 34 subjects per group would be required, confirming the approximate formula ( Equation 1 ) as being sufficiently accurate for practical application.

Example 2: Arterial Revascularization Trial (ART)

The ART is a randomized controlled clinical trial initiated in 2004 with the primary objective to compare 10-year survival associated with using bilateral internal thoracic arteries versus the use of a single internal thoracic artery graft for coronary artery bypass surgery [ 17 ]. Following a systematic review, the investigators expected mortality of 25% in the single internal thoracic artery arm and 20% in the bilateral internal thoracic artery arm, conferring an absolute effect size of 5%. After specifying α = 0.05 and β = 0.10 (for 90% power), the authors estimated that a total sample size of 2928 patients ( n  =   1464 per treatment arm) would be required. This can be calculated by the sample size formula proposed by Freedman for comparing survival curves using the log-rank test [ 18 ]. Here, we used the ‘ssizeCT.default’ function in the R package powerSurvEpi (Table ​ (Table3; 3 ; in this case, the sample size calculated was n  = 1463 per arm). The authors subsequently rounded this up to 3000 patients ( n  =   1500 per treatment arm), with 3102 patients actually randomized. A limitation of the ART study is that there was substantial non-compliance (16.4% randomized to the bilateral internal thoracic artery did not receive this treatment, versus 3.9% randomized to single internal thoracic artery group who were non-compliant with treatment allocation). In addition, several patients were lost to follow-up, which will affect the overall power achieved [ 19 ].

The sample size calculation is a crucial element of study design. However, it is only one element of a well-designed protocol. For basic study designs and outcomes, several sample size formulae exist in medical statistics textbooks. For more advanced study designs or situations, there exist specialized textbooks [ 20 ] and accessible software programs (Table ​ (Table3). 3 ). In addition, for the most complex cases, experienced statisticians can use simulation methods to determine the sample size [ 21 ]. Nonetheless, we would generally advise the involvement of a statistician in all but the most basic trial designs. A fundamental requirement after the sample size calculation has been performed is the clear and transparent reporting of it [ 6 ]. A review of 6 high-impact journals found that 5% did not report any details and 43% did not report all the parameters necessary to reproduce the calculations [ 22 ].

There has been a perception that sample sizes of randomized controlled trials (RCT) in specialty fields such as cardiovascular medicine have increased over the years. The median sample size used in Circulation and the European Heart Journal in 1990 was 99 and 90, which rose to 630 and 935 in 2010, respectively [ 23 ]. One proposed explanation is that larger treatment effects have already been identified in historical studies, leaving only small effects to be discovered through more contemporary studies. Commensurate with increasing sample sizes are increased costs, study periods and resources. It is, therefore, necessary to not only consider sample size but also alternative study designs that can reduce these burdens. For example, (Bayesian) adaptive trials are one approach, whereby parameters specified in the trial protocol can be modified as observations are accumulated [ 24 ]. These adaptations must be specified in advance according to predefined rules and might include interim analyses with the aim of possibly stopping the trial early (e.g. due to success or futility), sample size re-estimation or changes to the randomization procedure.

Sample size calculations are sensitive to parameter choices and, hence, errors. Exploring a range of scenarios with regard to the sample size calculation can provide insight into the potential practical consequences. Sample size calculations should always be performed a priori since ‘ post hoc power calculations’ have no value once the study has concluded [ 1 ]. If the sample size was not calculated a priori , then this should be acknowledged, and the uncertainty in the treatment effect demonstrated should be represented via a confidence interval.

GLH was supported by the Medical Research Council (MRC) [MR/M013227/1 awarded to Dr Ruwanthi Kolamunnage-Dona (University of Liverpool)].

Conflicts of interest: none declared.

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Clinical trial basics: randomization in clinical trials, introduction.

Clinical trials represent a core pillar of advancing patient care and medical knowledge. Clinical trials are designed to thoroughly assess the effectiveness and safety of new drugs and treatments in the human population. There are 4 main phases of clinical trials, each with its own objectives and questions, and they can be designed in different ways depending on the study population, the treatment being tested, and the specific research hypotheses. The “gold standard” of clinical research are randomized controlled trials (RCTs), which aim to avoid bias by randomly assigning patients into different groups, which can then be compared to evaluate the new drug or treatment. The process of random assignment of patients to groups is called randomization.

Randomization in clinical trials is an essential concept for minimizing bias, ensuring fairness, and maximizing the statistical power of the study results. In this article, we will discuss the concept of randomization in clinical trials, why it is important, and go over some of the different randomization methods that are commonly used.

What does randomization mean in clinical trials?

Randomization in clinical trials involves assigning patients into two or more study groups according to a chosen randomization protocol (randomization method). Randomizing patients allows for directly comparing the outcomes between the different groups, thereby providing stronger evidence for any effects seen being a result of the treatment rather than due to chance or random variables.

What is the main purpose of randomization?

Randomization is considered a key element in clinical trials for ensuring unbiased treatment of patients and obtaining reliable, scientifically valuable results. [1] Randomization is important for generating comparable intervention groups and for ensuring that all patients have an equal chance of receiving the novel treatment under study. The systematic rule for the randomization process (known as “sequence generation”) reduces selection bias that could arise if researchers were to manually assign patients with better prognoses to specific study groups; steps must be taken to further ensure strict implementation of the sequence by preventing researchers and patients from knowing beforehand which group patients are destined for (known as “allocation sequence concealment”). [2]

Randomization also aims to remove the influence of external and prognostic variables to increase the statistical power of the results. Some researchers are opposed to randomization, instead supporting the use of statistical techniques such as analysis of covariance (ANCOVA) and multivariate ANCOVA to adjust for covariate imbalance after the study is completed, in the analysis stage. However, this post-adjustment approach might not be an ideal fit for every clinical trial because the researcher might be unaware of certain prognostic variables that could lead to unforeseen interaction effects and contaminate the data. Thus, the best way to avoid bias and the influence of external variables and thereby ensure the validity of statistical test results is to apply randomization in the clinical trial design stage.

Randomized controlled trials (RCTs): The ‘gold standard’

Randomized controlled trials, or RCTs, are considered the “gold standard” of clinical research because, by design, they feature minimized bias, high statistical power, and a strong ability to provide evidence that any clinical benefit observed results specifically from the study intervention (i.e., identifying cause-effect relationships between the intervention and the outcome).[3] A randomized controlled trial is one of the most effective studies for measuring the effectiveness of a new drug or intervention.

How are participants randomized? An introduction to randomization methods

Randomization includes a broad class of design techniques for clinical trials, and is not a single methodology. For randomization to be effective and reduce (rather than introduce) bias, a randomization schedule is required for assigning patients in an unbiased and systematic manner. Below is a brief overview of the main randomization techniques commonly used; further detail is given in the next sections.

Fixed vs. adaptive randomization

Randomization methods can be divided into fixed and adaptive randomization. Fixed randomization involves allocating patients to interventions using a fixed sequence that doesn’t change throughout the study. On the other hand, adaptive randomization involves assigning patients to groups in consideration of the characteristics of the patients already in the trial, and the randomization probabilities can change over the course of the study. Each of these techniques can be further subdivided:

Fixed allocation randomization methods:

  • Simple randomization : the simplest method of randomization, in which patient allocation is based on a single sequence of random assignments.
  • Block randomization : patients are first assigned to blocks of equal size, and then randomized within each block. This ensures balance in group sizes.

Stratified randomization : patients are first allocated to blocks (strata) designed to balance combinations of specific covariates (subject’s baseline characteristics), and then randomization is performed within each stratum.

Adaptive randomization methods:

  • Outcome-adaptive/results-adaptive randomization : involves allocating patients to study groups in consideration of other patients’ responses to the ongoing trial treatment. Minimization: involves minimizing imbalance amongst covariates by allocating new enrollments as a function of prior allocations

Below is a graphic summary of the breakdown we’ve just covered.

Randomization Methods

Fixed-allocation randomization in clinical trials

Here, we will discuss the three main fixed-allocation randomization types in more detail.

Simple Randomization

Simple randomization is the most commonly used method of fixed randomization, offering completely random patient allocation into the different study groups. It is based on a single sequence of random assignments and is not influenced by previous assignments. The benefits are that it is simple and it fulfills the allocation concealment requirement, ensuring that researchers, sponsors, and patients are unaware of which patient will be assigned to which treatment group. Simple randomization can be conceptualized, or even performed, by the following chance actions:

  • Flipping a coin (e.g., heads → control / tails → intervention)
  • Throwing a dice (e.g., 1-3 → control / 4-6 → intervention)
  • Using a deck of shuffled cards (e.g., red → control / black → intervention)
  • Using a computer-generated random number sequence
  • Using a random number table from a statistics textbook

There are certain disadvantages associated with simple randomization, namely that it does not take into consideration the influence of covariates, and it may lead to unequal sample sizes between groups. For clinical research studies with small sample sizes, the group sizes are more likely to be unequal.

Especially in smaller clinical trials, simple randomization can lead to covariate imbalance. It has been suggested that clinical trials enrolling at least 1,000 participants can essentially avoid random differences between treatment groups and minimize bias by using simple randomization. [4] On the other hand, the risks posed by imbalances in covariates and prognostic factors are more relevant in smaller clinical trials employing simple randomization, and thus, other methods such as blocking should be considered for such trials.

Block Randomization

Block randomization is a type of “constrained randomization” that is preferred for achieving balance in the sizes of treatment groups in smaller clinical trials. The first step is to select a block size. Blocks represent “subgroups” of participants who will be randomized in these subgroups, or blocks. Block size should be a multiple of the number of groups; for instance, if there are two groups, the block size can be 4, 6, 8, etc. Once block size is determined, then all possible different combinations (permutations) of assignment within the block are identified. Each block is then randomly assigned one of these permutations, and individuals in the block are allocated according to the specific pattern of the permuted block.[5]

Let’s consider a small clinical trial with two study groups (control and treatment) and 20 participants. In this situation, an allocation sequence based on blocked randomization would involve the following steps:

1. The researcher chooses block size: In this case, we will use a block size of 4 (which is a multiple of the number of study groups, 2).

2. All 6 possible balanced combinations of control (C) and treatment (T) allocations within each block are shown as follows:

3. These allocation sequences are randomly assigned to the blocks, which then determine the assignment of the 4 participants within each block. Let’s say the sequence TCCT is selected for block 1. The allocation would then be as follows:

  • Participant 1 → Treatment (T)
  • Participant 2 → Control (C)
  • Participant 3 → Control (C)
  • Participant 4 → Treatment (T)

We can see that blocked randomization ensures equal (or nearly equal, if for example enrollment is terminated early or the final target is not quite met) assignment to treatment groups.

There are disadvantages to blocked randomization. For one, if the investigators/researchers are not blinded (masked), then the condition of allocation concealment is not met, which could lead to selection bias. To illustrate this, let’s say that two of four participants have enrolled in block 2 of the above example, for which the randomly selected sequence is CCTT. In this case, the investigator would know that the next two participants for the current block would be assigned to the treatment group (T), which could influence his/her selection process. Keeping the investigator masked (blinded) or utilizing random block sizes are potential solutions for preventing this issue. Another drawback is that the determined blocks may still contain covariate imbalances. For instance, one block might have more participants with chronic or secondary illnesses.

Despite these drawbacks, block randomization is simple to implement and better than simple randomization for smaller clinical trials in that treatment groups will have an equal number of participants. Blinding researchers to block size or randomizing block size can reduce potential selection bias. [5]

Stratified Randomization

Stratified randomization aims to prevent imbalances amongst prognostic variables (or the patients’ baseline characteristics, also known as covariates) in the study groups. Stratified randomization is another type of constrained randomization, where participants are first grouped (“stratified”) into strata based on predetermined covariates, which could include such things as age, sex, comorbidities, etc. Block randomization is then applied within each of these strata separately, ensuring balance amongst prognostic variables as well as in group size.

The covariates of interest are determined by the researchers before enrollment begins, and are chosen based on the potential influence of each covariate on the dependent variable. Each covariate will have a given number of levels, and the product of the number of levels of all covariates determines the number of strata for the trial. For example, if two covariates are identified for a trial, each with two levels (let’s say age, divided into two levels [<50 and 50+], and height [<175 cm and 176+ cm]), a total of 4 strata will be created (2 x 2 = 4).

Patients are first assigned to the appropriate stratum according to these prognostic classifications, and then a randomization sequence is applied within each stratum. Block randomization is usually applied in order to guarantee balance between treatment groups in each stratum.

Stratified randomization can thus prevent covariate imbalance, which can be especially important in smaller clinical trials with few participants. [6] Nonetheless, stratification and imbalance control can become complex if too many covariates are considered, because an overly large number of strata can lead to imbalances in patient allocation due to small sample sizes within individual strata,. Thus, the number of strata should be kept to a minimum for the best results – in other words, only covariates with potentially important influences on study outcomes and results should be included. [6] Stratified randomization also reduces type I error, which describes “false positive” results, wherein differences in treatment outcomes are observed between groups despite the treatments being equal (for example, if the intervention group contained participants with overall better prognosis, it could be concluded that the intervention was effective, although in reality the effect was only due to their better initial prognosis and not the treatment). [5] Type II errors are also reduced, which describe “false negatives,” wherein actual differences in outcomes between groups are not noticed. The “power” of a trial to identify treatment effects is inversely related to these errors, which are related to variance between groups being compared; stratification reduces variance between groups and thus theoretically increases power. The required sample size decreases as power increases, which can also be used to explain why stratification is relatively more impactful with smaller sample sizes.

A major drawback of stratified randomization is that it requires identification of all participants before they can be allocated. Its utility is also disputed by some researchers, especially in the context of trials with large sample sizes, wherein covariates are more likely to be balanced naturally even when using simpler randomization techniques. [6]

Adaptive randomization in clinical trials

Adaptive randomization describes schemes in which treatment allocation probabilities are adjusted as the trial progresses.In adaptive randomization,allocation probabilities can be altered in order to either minimize imbalances in prognostic variables (covariate-adaptive randomization, or “minimization”), or to increase the allocation of patients to the treatment arm(s) showing better patient outcomes (“response-adaptive randomization”). [7] Adaptive randomization methods can thus address the issue of covariate imbalance, or can be employed to offer a unique ethical advantage in studies wherein preliminary or interim analyses indicate that one treatment arm is significantly more effective, maximizing potential therapeutic benefit for patients by increasing allocation to the most-effective treatment arm.

One of the main disadvantages associated with adaptive randomization methods is that they are time-consuming and complex; recalculation is necessary for each new patient or when any treatment arm is terminated.

Outcome-adaptive (response-adaptive) randomization

Outcome-adaptive randomization was first proposed in 1969 as “play-the-winner” treatment assignments. [8] This method involves adjusting the allocation probabilities based on the data and results being collected in the ongoing trial. The aim is to increase the ratio of patients being assigned to the more effective treatment arm, representing a significant ethical advantage especially for trials in which one or more treatments are clearly demonstrating promising therapeutic benefit. The maximization of therapeutic benefit for participants comes at the expense of statistical power, which is one of the major drawbacks of this randomization method.

Outcome-adaptive randomization can decrease power because, by increasing the allocation of participants to the more-effective treatment arm, which then in turn demonstrates better outcomes, an increasing bias toward that treatment arm is created. Thus, outcome-adaptive randomization is unsuitable for long-term phase III clinical trials requiring high statistical power, and some argue that the high design complexity is not warranted as the benefits offered are minimal (or can be achieved through other designs). [8]

Covariate-adaptive randomization (Minimization)

Minimization is a complex form of adaptive randomization which, similarly to stratified randomization, aims to maximize the balance amongst covariates between treatment groups. Rather than achieving this by initially stratifying participants into separate strata based on covariates and then randomizing, the first participants are allocated randomly and then each new allocation involves hypothetically allocating the new participant to all groups and calculating a resultant “imbalance score.” The participant will then be assigned in such a way that this covariate imbalance is minimized (hence the name minimization). [9]

A principal drawback of minimization is that it is labor-intensive due to frequent recalculation of imbalance scores as new patients enroll in the trial. However, there are web-based tools and computer programs that can be used to facilitate the recalculation and allocation processes. [10]

Randomization in clinical trials is important as it ensures fair allocation of patients to study groups and enables researchers to make accurate and valid comparisons. The choice of the specific randomization schedule will depend on the trial type/phase, sample size, research objectives, and the condition being treated. A balance should be sought between ease of implementation, prevention of bias, and maximization of power. To further minimize bias, considerations such as blinding and allocation concealment should be combined with randomization techniques.

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Random Assignment – A Simple Introduction with Examples

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Random-assignment-Definition

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

Inhaltsverzeichnis

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

Random Assignment – In a Nutshell

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

Definition: Random assignment

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

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Importance of random assignment

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

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

Example: Different levels of independent variables

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

Three independent participant levels are applicable here:

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

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

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

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

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

Random assignment vs. random sampling

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

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

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

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

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

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

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

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

Random-assignment-vs-random-sampling

How to use random assignment

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

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

Random assignment in block experimental designs

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

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

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

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

When random assignment is not used

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

Comparing different groups

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

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

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

No ethical justifiability

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

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

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

What is the definition of random assignment?

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

When is random assignment applicable?

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

What is the importance of random assignment?

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

When should you NOT use random assignment

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

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Counteracting Methodological Errors in Behavioral Research pp 39–54 Cite as

Random Assignment

  • Gideon J. Mellenbergh 2  
  • First Online: 17 May 2019

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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.

  • Cluster randomization
  • Cross-over design
  • Independent and dependent variables
  • Random assignment and random selection
  • Randomized block design

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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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Design and Analysis of Experiments with randomizr (Stata)

Alexander coppock.

randomizr is a small package for Stata that simplifies the design and analysis of randomized experiments. In particular, it makes the random assignment procedure transparent, flexible, and most importantly reproduceable. By the time that many experiments are written up and made public, the process by which some units received treatments is lost or imprecisely described. The randomizr package makes it easy for even the most forgetful of researchers to generate error-free, reproduceable random assignments.

A hazy understanding of the random assignment procedure leads to two main problems at the analysis stage. First, units may have different probabilities of assignment to treatment. Analyzing the data as though they have the same probabilities of assignment leads to biased estimates of the treatment effect. Second, units are sometimes assigned to treatment as a cluster. For example, all the students in a single classroom may be assigned to the same intervention together. If the analysis ignores the clustering in the assignments, estimates of average causal effects and the uncertainty attending to them may be incorrect.

A Hypothetical Experiment

Throughout this vignette, we’ll pretend we’re conducting an experiment among the 592 individuals in R’s HairEyeColor dataset. As we’ll see, there are many ways to randomly assign subjects to treatments. We’ll step through five common designs, each associated with one of the five randomizr functions: simple_ra , complete_ra , block_ra , cluster_ra , and block_and_cluster_ra .

Typically, researchers know some basic information about their subjects before deploying treatment. For example, they usually know how many subjects there are in the experimental sample (N), and they usually know some basic demographic information about each subject.

Our new dataset has 592 subjects. We have three pretreatment covariates, Hair, Eye, and Sex, which describe the hair color, eye color, and gender of each subject. We also have potential outcomes. We call the untreated outcome Y0 and we call the treated outcome Y1.

Imagine that in the absence of any intervention, the outcome (Y0) is correlated with out pretreatment covariates. Imagine further that the effectiveness of the program varies according to these covariates, i.e., the difference between Y1 and Y0 is correlated with the pretreatment covariates.

If we were really running an experiment, we would only observe either Y0 or Y1 for each subject, but since we are simulating, we have both. Our inferential target is the average treatment effect (ATE), which is defined as the average difference between Y0 and Y1.

Simple Random Assignment

Simple random assignment assigns all subjects to treatment with an equal probability by flipping a (weighted) coin for each subject. The main trouble with simple random assignment is that the number of subjects assigned to treatment is itself a random number - depending on the random assignment, a different number of subjects might be assigned to each group.

The simple_ra function has no required arguments. If no other arguments are specified, simple_ra assumes a two-group design and a 0.50 probability of assignment.

To change the probability of assignment, specify the prob argument:

If you specify num_arms without changing prob_each, simple_ra will assume equal probabilities across all arms.

You can also just specify the probabilities of your multiple arms. The probabilities must sum to 1.

You can also name your treatment arms.

Complete Random Assignment

Complete random assignment is very similar to simple random assignment, except that the researcher can specify exactly how many units are assigned to each condition.

The syntax for complete_ra is very similar to that of simple_ra . The argument m is the number of units assigned to treatment in two-arm designs; it is analogous to simple_ra ’s prob. Similarly, the argument m_each is analogous to prob_each.

If you specify no arguments in complete_ra , it assigns exactly half of the subjects to treatment.

To change the number of units assigned, specify the m argument:

If you specify multiple arms, complete_ra will assign an equal (within rounding) number of units to treatment.

You can also specify exactly how many units should be assigned to each arm. The total of m_each must equal N.

Simple and Complete Random Assignment Compared

When should you use simple_ra versus complete_ra ? Basically, if the number of units is known beforehand, complete_ra is always preferred, for two reasons: 1. Researchers can plan exactly how many treatments will be deployed. 2. The standard errors associated with complete random assignment are generally smaller, increasing experimental power. See this guide on EGAP for more on experimental power.

Since you need to know N beforehand in order to use simple_ra , it may seem like a useless function. Sometimes, however, the random assignment isn’t directly in the researcher’s control. For example, when deploying a survey experiment on a platform like Qualtrics, simple random assignment is the only possibility due to the inflexibility of the built-in random assignment tools. When reconstructing the random assignment for analysis after the experiment has been conducted, simple_ra provides a convenient way to do so.

To demonstrate how complete_ra is superior to simple_ra , let’s conduct a small simulation with our HairEyeColor dataset.

The standard error of an estimate is defined as the standard deviation of the sampling distribution of the estimator. When standard errors are estimated (i.e., by using the summary() command on a model fit), they are estimated using some approximation. This simulation allows us to measure the standard error directly, since the vectors simple_ests and complete_ests describe the sampling distribution of each design.

In this simulation complete random assignment led to a 6% decrease in sampling variability. This decrease was obtained with a small design tweak that costs the researcher essentially nothing.

Block Random Assignment

Block random assignment (sometimes known as stratified random assignment) is a powerful tool when used well. In this design, subjects are sorted into blocks (strata) according to their pre-treatment covariates, and then complete random assignment is conducted within each block. For example, a researcher might block on gender, assigning exactly half of the men and exactly half of the women to treatment.

Why block? The first reason is to signal to future readers that treatment effect heterogeneity may be of interest: is the treatment effect different for men versus women? Of course, such heterogeneity could be explored if complete random assignment had been used, but blocking on a covariate defends a researcher (somewhat) against claims of data dredging. The second reason is to increase precision. If the blocking variables are predictive of the outcome (i.e., they are correlated with the outcome), then blocking may help to decrease sampling variability. It’s important, however, not to overstate these advantages. The gains from a blocked design can often be realized through covariate adjustment alone.

Blocking can also produce complications for estimation. Blocking can produce different probabilities of assignment for different subjects. This complication is typically addressed in one of two ways: “controlling for blocks” in a regression context, or inverse probability weights (IPW), in which units are weighted by the inverse of the probability that the unit is in the condition that it is in.

The only required argument to block_ra is block_var, which is a variable that describes which block a unit belongs to. block_var can be a string or numeric variable. If no other arguments are specified, block_ra assigns an approximately equal proportion of each block to treatment.

For multiple treatment arms, use the num_arms argument, with or without the conditions argument

block_ra provides a number of ways to adjust the number of subjects assigned to each conditions. The prob_each argument describes what proportion of each block should be assigned to treatment arm. Note of course, that block_ra still uses complete random assignment within each block; the appropriate number of units to assign to treatment within each block is automatically determined.

For finer control, use the block_m_each argument, which takes a matrix with as many rows as there are blocks, and as many columns as there are treatment conditions. Remember that the rows are in the same order as seen in tab block_var, a command that is good to run before constructing a block_m_each matrix. The matrix can either be defined using the matrix define command or be inputted directly into the block_m_each option.

Clustered Assignment

Clustered assignment is unfortunate. If you can avoid assigning subjects to treatments by cluster, you should. Sometimes, clustered assignment is unavoidable. Some common situations include:

  • Housemates in households: whole households are assigned to treatment or control
  • Students in classrooms: whole classrooms are assigned to treatment or control
  • Residents in towns or villages: whole communities are assigned to treatment or control

Clustered assignment decreases the effective sample size of an experiment. In the extreme case when outcomes are perfectly correlated with clusters, the experiment has an effective sample size equal to the number of clusters. When outcomes are perfectly uncorrelated with clusters, the effective sample size is equal to the number of subjects. Almost all cluster-assigned experiments fall somewhere in the middle of these two extremes.

The only required argument for the cluster_ra function is the clust_var argument, which indicates which cluster each subject belongs to. Let’s pretend that for some reason, we have to assign treatments according to the unique combinations of hair color, eye color, and gender.

This shows that each cluster is either assigned to treatment or control. No two units within the same cluster are assigned to different conditions.

As with all functions in randomizr, you can specify multiple treatment arms in a variety of ways:

…or using conditions.

… or using m_each, which describes how many clusters should be assigned to each condition. m_each must sum to the number of clusters.

Block and Clustered Assignment

The power of clustered experiments can sometimes be improved through blocking. In this scenario, whole clusters are members of a particular block – imagine villages nested within discrete regions, or classrooms nested within discrete schools.

As an example, let’s group our clusters into blocks by size

IMAGES

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COMMENTS

  1. Random Assignment in Experiments

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

  2. The Definition of Random Assignment In Psychology

    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.

  3. Random Assignment in Psychology: Definition & Examples

    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.

  4. Random Assignment in Psychology (Definition + 40 Examples)

    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.

  5. Random Assignment in Experiments

    Random assignment helps you separation causation from correlation and rule out confounding variables. As a critical component of the scientific method, experiments typically set up contrasts between a control group and one or more treatment groups.

  6. Random assignment

    Random assignment or random placement is an experimental technique for assigning human participants or animal subjects to different groups in an experiment (e.g., a treatment group versus a control group) using randomization, such as by a chance procedure (e.g., flipping a coin) or a random number generator. [1]

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    Statistical Power for Random Assignment Evaluations of Education Programs Peter Z. Schochet Mathematica Policy Research, Inc. This article examines theoretical and empirical issues related to the statistical power of impact estimates for experimental evaluations of education programs.

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    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 ...

  9. Statistical Power for Random Assignment Evaluations of Education

    Abstract. This article examines theoretical and empirical issues related to the statistical power of impact estimates for experimental evaluations of education programs. The author considers designs where random assignment is conducted at the school, classroom, or student level, and employs a unified analytic framework using statistical methods ...

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  11. PDF The Politics of Random Assignment: Implementing Studies and ...

    Random assignment, because of its unique methodological strengths, can help avoid this kind of conflict — what Aaron called "self-canceling research." But random assignment studies must be used judiciously and interpreted carefully to assure that they meet ethical norms and that their findings are correctly understood. It is also important

  12. Issues in Outcomes Research: An Overview of Randomization Techniques

    Randomizing participants helps remove the effect of extraneous variables (eg, age, injury history) and minimizes bias associated with treatment assignment.

  13. PDF Statistical Power for Random Assignment Evaluations of Education Programs

    Statistical Power for Random Assignment Evaluations of Education Programs June 22, 2005 Peter Z. Schochet Submitted to: Institute of Education Sciences U.S. Department of Education 80 F Street, NW Washington, DC 20208 Project Officer: Elizabeth Warner Submitted by: Mathematica Policy Research, Inc. P.O. Box 2393 Princeton, NJ 08543-2393

  14. How often does random assignment fail? Estimates and recommendations

    Abstract. A fundamental goal of the scientific process is to make causal inferences. Random assignment to experimental conditions has been taken to be a gold-standard technique for establishing causality. Despite this, it is unclear how often random assignment fails to eliminate non-trivial differences between experimental conditions.

  15. [PDF] Statistical Power for Random Assignment Evaluations of Education

    This article examines theoretical and empirical issues related to the statistical power of impact estimates for experimental evaluations of education programs. The author considers designs where random assignment is conducted at the school, classroom, or student level, and employs a unified analytic framework using statistical methods from the ...

  16. Statistical primer: sample size and power calculations—why, when and

    Calculations. A simple example of a sample size calculation is that of comparing two means for a continuous outcome. Assume that the null hypothesis is H0:μ1 = μ2 with an alternative hypothesis H1:μ1 ≠ μ2, where μ1 is the true population mean in the control population, and μ2 the mean in the treated population.

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    'Randomly' assign Planner tasks to members of a team 02-05-2020 11:58 PM Hi guys, For my team I want to build a flow that does the following: A person (not a member of the team) emails a channel. This email is made into a task in a Planner board in this channel (this I have been able to create)

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  19. Random Assignment ~ A Simple Introduction with Examples

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    # run one simulation with # an assignment function # and an effect size calculating function randomly_assign_and_find_effect_size <- function(# data to use for randomization inference # historical for power analyses # experiment outcomes for p values and confidence intervals dataset, # function that adds a random treatment assignment to the ...

  21. Random Assignment

    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.

  22. Design and Analysis of Experiments with randomizr (Stata)

    Complete random assignment is very similar to simple random assignment, except that the researcher can specify exactly how many units are assigned to each condition. ... Block and Clustered Assignment. The power of clustered experiments can sometimes be improved through blocking. In this scenario, whole clusters are members of a particular ...