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Random Assignment in Experiments

By Jim Frost 4 Comments

Random assignment uses chance to assign subjects to the control and treatment groups in an experiment. This process helps ensure that the groups are equivalent at the beginning of the study, which makes it safer to assume the treatments caused any differences between groups that the experimenters observe at the end of the study.

Huh? That might be a big surprise! At this point, you might be wondering about all of those studies that use statistics to assess the effects of different treatments. There’s a critical separation between significance and causality:

• Statistical procedures determine whether an effect is significant.
• Experimental designs determine how confidently you can assume that a treatment causes the effect.

In this post, learn how using random assignment in experiments can help you identify causal relationships.

Correlation, Causation, and Confounding Variables

Random assignment helps you separate 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. The idea is to determine whether the effect, which is the difference between a treatment group and the control group, is statistically significant. If the effect is significant, group assignment correlates with different outcomes.

However, as you have no doubt heard, correlation does not necessarily imply causation. In other words, the experimental groups can have different mean outcomes, but the treatment might not be causing those differences even though the differences are statistically significant.

The difficulty in definitively stating that a treatment caused the difference is due to potential confounding variables or confounders. Confounders are alternative explanations for differences between the experimental groups. Confounding variables correlate with both the experimental groups and the outcome variable. In this situation, confounding variables can be the actual cause for the outcome differences rather than the treatments themselves. As you’ll see, if an experiment does not account for confounding variables, they can bias the results and make them untrustworthy.

Related posts : Understanding Correlation in Statistics , Causation versus Correlation , and Hill’s Criteria for Causation .

Example of Confounding in an Experiment

• Control group: Does not consume vitamin supplements
• Treatment group: Regularly consumes vitamin supplements.

Imagine we measure a specific health outcome. After the experiment is complete, we perform a 2- sample t-test to determine whether the mean outcomes for these two groups are different. Assume the test results indicate that the mean health outcome in the treatment group is significantly better than the control group.

Why can’t we assume that the vitamins improved the health outcomes? After all, only the treatment group took the vitamins.

Related post : Confounding Variables in Regression Analysis

Alternative Explanations for Differences in Outcomes

The answer to that question depends on how we assigned the subjects to the experimental groups. If we let the subjects decide which group to join based on their existing vitamin habits, it opens the door to confounding variables. It’s reasonable to assume that people who take vitamins regularly also tend to have other healthy habits. These habits are confounders because they correlate with both vitamin consumption (experimental group) and the health outcome measure.

Random assignment prevents this self sorting of participants and reduces the likelihood that the groups start with systematic differences.

In fact, studies have found that supplement users are more physically active, have healthier diets, have lower blood pressure, and so on compared to those who don’t take supplements. If subjects who already take vitamins regularly join the treatment group voluntarily, they bring these healthy habits disproportionately to the treatment group. Consequently, these habits will be much more prevalent in the treatment group than the control group.

The healthy habits are the confounding variables—the potential alternative explanations for the difference in our study’s health outcome. It’s entirely possible that these systematic differences between groups at the start of the study might cause the difference in the health outcome at the end of the study—and not the vitamin consumption itself!

If our experiment doesn’t account for these confounding variables, we can’t trust the results. While we obtained statistically significant results with the 2-sample t-test for health outcomes, we don’t know for sure whether the vitamins, the systematic difference in habits, or some combination of the two caused the improvements.

Learn why many randomized clinical experiments use a placebo to control for the Placebo Effect .

Experiments Must Account for Confounding Variables

Your experimental design must account for confounding variables to avoid their problems. Scientific studies commonly use the following methods to handle confounders:

• Use control variables to keep them constant throughout an experiment.
• Statistically control for them in an observational study.
• Use random assignment to reduce the likelihood that systematic differences exist between experimental groups when the study begins.

Let’s take a look at how random assignment works in an experimental design.

Random Assignment Can Reduce the Impact of Confounding Variables

Note that random assignment is different than random sampling. Random sampling is a process for obtaining a sample that accurately represents a population .

Random assignment uses a chance process to assign subjects to experimental groups. Using random assignment requires that the experimenters can control the group assignment for all study subjects. For our study, we must be able to assign our participants to either the control group or the supplement group. Clearly, if we don’t have the ability to assign subjects to the groups, we can’t use random assignment!

Additionally, the process must have an equal probability of assigning a subject to any of the groups. For example, in our vitamin supplement study, we can use a coin toss to assign each subject to either the control group or supplement group. For more complex experimental designs, we can use a random number generator or even draw names out of a hat.

Random Assignment Distributes Confounders Equally

The random assignment process distributes confounding properties amongst your experimental groups equally. In other words, randomness helps eliminate systematic differences between groups. For our study, flipping the coin tends to equalize the distribution of subjects with healthier habits between the control and treatment group. Consequently, these two groups should start roughly equal for all confounding variables, including healthy habits!

Random assignment is a simple, elegant solution to a complex problem. For any given study area, there can be a long list of confounding variables that you could worry about. However, using random assignment, you don’t need to know what they are, how to detect them, or even measure them. Instead, use random assignment to equalize them across your experimental groups so they’re not a problem.

Because random assignment helps ensure that the groups are comparable when the experiment begins, you can be more confident that the treatments caused the post-study differences. Random assignment helps increase the internal validity of your study.

Comparing the Vitamin Study With and Without Random Assignment

Let’s compare two scenarios involving our hypothetical vitamin study. We’ll assume that the study obtains statistically significant results in both cases.

Scenario 1: We don’t use random assignment and, unbeknownst to us, subjects with healthier habits disproportionately end up in the supplement treatment group. The experimental groups differ by both healthy habits and vitamin consumption. Consequently, we can’t determine whether it was the habits or vitamins that improved the outcomes.

Scenario 2: We use random assignment and, consequently, the treatment and control groups start with roughly equal levels of healthy habits. The intentional introduction of vitamin supplements in the treatment group is the primary difference between the groups. Consequently, we can more confidently assert that the supplements caused an improvement in health outcomes.

For both scenarios, the statistical results could be identical. However, the methodology behind the second scenario makes a stronger case for a causal relationship between vitamin supplement consumption and health outcomes.

How important is it to use the correct methodology? Well, if the relationship between vitamins and health outcomes is not causal, then consuming vitamins won’t cause your health outcomes to improve regardless of what the study indicates. Instead, it’s probably all the other healthy habits!

Learn more about Randomized Controlled Trials (RCTs) that are the gold standard for identifying causal relationships because they use random assignment.

Drawbacks of Random Assignment

Random assignment helps reduce the chances of systematic differences between the groups at the start of an experiment and, thereby, mitigates the threats of confounding variables and alternative explanations. However, the process does not always equalize all of the confounding variables. Its random nature tends to eliminate systematic differences, but it doesn’t always succeed.

Sometimes random assignment is impossible because the experimenters cannot control the treatment or independent variable. For example, if you want to determine how individuals with and without depression perform on a test, you cannot randomly assign subjects to these groups. The same difficulty occurs when you’re studying differences between genders.

In other cases, there might be ethical issues. For example, in a randomized experiment, the researchers would want to withhold treatment for the control group. However, if the treatments are vaccinations, it might be unethical to withhold the vaccinations.

Other times, random assignment might be possible, but it is very challenging. For example, with vitamin consumption, it’s generally thought that if vitamin supplements cause health improvements, it’s only after very long-term use. It’s hard to enforce random assignment with a strict regimen for usage in one group and non-usage in the other group over the long-run. Or imagine a study about smoking. The researchers would find it difficult to assign subjects to the smoking and non-smoking groups randomly!

Fortunately, if you can’t use random assignment to help reduce the problem of confounding variables, there are different methods available. The other primary approach is to perform an observational study and incorporate the confounders into the statistical model itself. For more information, read my post Observational Studies Explained .

Read About Real Experiments that Used Random Assignment

I’ve written several blog posts about studies that have used random assignment to make causal inferences. Read studies about the following:

• Flu Vaccinations
• COVID-19 Vaccinations

Sullivan L.  Random assignment versus random selection . SAGE Glossary of the Social and Behavioral Sciences, SAGE Publications, Inc.; 2009.

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Reader Interactions

November 13, 2019 at 4:59 am

Hi Jim, I have a question of randomly assigning participants to one of two conditions when it is an ongoing study and you are not sure of how many participants there will be. I am using this random assignment tool for factorial experiments. http://methodologymedia.psu.edu/most/rannumgenerator It asks you for the total number of participants but at this point, I am not sure how many there will be. Thanks for any advice you can give me, Floyd

May 28, 2019 at 11:34 am

Jim, can you comment on the validity of using the following approach when we can’t use random assignments. I’m in education, we have an ACT prep course that we offer. We can’t force students to take it and we can’t keep them from taking it either. But we want to know if it’s working. Let’s say that by senior year all students who are going to take the ACT have taken it. Let’s also say that I’m only including students who have taking it twice (so I can show growth between first and second time taking it). What I’ve done to address confounders is to go back to say 8th or 9th grade (prior to anyone taking the ACT or the ACT prep course) and run an analysis showing the two groups are not significantly different to start with. Is this valid? If the ACT prep students were higher achievers in 8th or 9th grade, I could not assume my prep course is effecting greater growth, but if they were not significantly different in 8th or 9th grade, I can assume the significant difference in ACT growth (from first to second testing) is due to the prep course. Yes or no?

May 26, 2019 at 5:37 pm

Nice post! I think the key to understanding scientific research is to understand randomization. And most people don’t get it.

May 27, 2019 at 9:48 pm

Thank you, Anoop!

I think randomness in an experiment is a funny thing. The issue of confounding factors is a serious problem. You might not even know what they are! But, use random assignment and, voila, the problem usually goes away! If you can’t use random assignment, suddenly you have a whole host of issues to worry about, which I’ll be writing about in more detail in my upcoming post about observational experiments!

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Statistics Made Easy

Random Selection vs. Random Assignment

Random selection and random assignment  are two techniques in statistics that are commonly used, but are commonly confused.

Random selection  refers to the process of randomly selecting individuals from a population to be involved in a study.

Random assignment  refers to the process of randomly  assigning  the individuals in a study to either a treatment group or a control group.

You can think of random selection as the process you use to “get” the individuals in a study and you can think of random assignment as what you “do” with those individuals once they’re selected to be part of the study.

The Importance of Random Selection and Random Assignment

When a study uses  random selection , it selects individuals from a population using some random process. For example, if some population has 1,000 individuals then we might use a computer to randomly select 100 of those individuals from a database. This means that each individual is equally likely to be selected to be part of the study, which increases the chances that we will obtain a representative sample – a sample that has similar characteristics to the overall population.

By using a representative sample in our study, we’re able to generalize the findings of our study to the population. In statistical terms, this is referred to as having  external validity – it’s valid to externalize our findings to the overall population.

When a study uses  random assignment , it randomly assigns individuals to either a treatment group or a control group. For example, if we have 100 individuals in a study then we might use a random number generator to randomly assign 50 individuals to a control group and 50 individuals to a treatment group.

By using random assignment, we increase the chances that the two groups will have roughly similar characteristics, which means that any difference we observe between the two groups can be attributed to the treatment. This means the study has  internal validity  – it’s valid to attribute any differences between the groups to the treatment itself as opposed to differences between the individuals in the groups.

Examples of Random Selection and Random Assignment

It’s possible for a study to use both random selection and random assignment, or just one of these techniques, or neither technique. A strong study is one that uses both techniques.

The following examples show how a study could use both, one, or neither of these techniques, along with the effects of doing so.

Example 1: Using both Random Selection and Random Assignment

Study:  Researchers want to know whether a new diet leads to more weight loss than a standard diet in a certain community of 10,000 people. They recruit 100 individuals to be in the study by using a computer to randomly select 100 names from a database. Once they have the 100 individuals, they once again use a computer to randomly assign 50 of the individuals to a control group (e.g. stick with their standard diet) and 50 individuals to a treatment group (e.g. follow the new diet). They record the total weight loss of each individual after one month.

Results:  The researchers used random selection to obtain their sample and random assignment when putting individuals in either a treatment or control group. By doing so, they’re able to generalize the findings from the study to the overall population  and  they’re able to attribute any differences in average weight loss between the two groups to the new diet.

Example 2: Using only Random Selection

Study:  Researchers want to know whether a new diet leads to more weight loss than a standard diet in a certain community of 10,000 people. They recruit 100 individuals to be in the study by using a computer to randomly select 100 names from a database. However, they decide to assign individuals to groups based solely on gender. Females are assigned to the control group and males are assigned to the treatment group. They record the total weight loss of each individual after one month.

Results:  The researchers used random selection to obtain their sample, but they did not use random assignment when putting individuals in either a treatment or control group. Instead, they used a specific factor – gender – to decide which group to assign individuals to. By doing this, they’re able to generalize the findings from the study to the overall population but they are  not  able to attribute any differences in average weight loss between the two groups to the new diet. The internal validity of the study has been compromised because the difference in weight loss could actually just be due to gender, rather than the new diet.

Example 3: Using only Random Assignment

Study:  Researchers want to know whether a new diet leads to more weight loss than a standard diet in a certain community of 10,000 people. They recruit 100 males athletes to be in the study. Then, they use a computer program to randomly assign 50 of the male athletes to a control group and 50 to the treatment group. They record the total weight loss of each individual after one month.

Results:  The researchers did not use random selection to obtain their sample since they specifically chose 100 male athletes. Because of this, their sample is not representative of the overall population so their external validity is compromised – they will not be able to generalize the findings from the study to the overall population. However, they did use random assignment, which means they can attribute any difference in weight loss to the new diet.

Example 4: Using Neither Technique

Study:  Researchers want to know whether a new diet leads to more weight loss than a standard diet in a certain community of 10,000 people. They recruit 50 males athletes and 50 female athletes to be in the study. Then, they assign all of the female athletes to the control group and all of the male athletes to the treatment group. They record the total weight loss of each individual after one month.

Results:  The researchers did not use random selection to obtain their sample since they specifically chose 100 athletes. Because of this, their sample is not representative of the overall population so their external validity is compromised – they will not be able to generalize the findings from the study to the overall population. Also, they split individuals into groups based on gender rather than using random assignment, which means their internal validity is also compromised – differences in weight loss might be due to gender rather than the diet.

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Difference between Random Selection and Random Assignment

Random selection and random assignment are commonly confused or used interchangeably, though the terms refer to entirely different processes.  Random selection refers to how sample members (study participants) are selected from the population for inclusion in the study.  Random assignment is an aspect of experimental design in which study participants are assigned to the treatment or control group using a random procedure.

Random selection requires the use of some form of random sampling (such as stratified random sampling , in which the population is sorted into groups from which sample members are chosen randomly).  Random sampling is a probability sampling method, meaning that it relies on the laws of probability to select a sample that can be used to make inference to the population; this is the basis of statistical tests of significance .

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Random assignment takes place following the selection of participants for the study.  In a true experiment, all study participants are randomly assigned either to receive the treatment (also known as the stimulus or intervention) or to act as a control in the study (meaning they do not receive the treatment).  Although random assignment is a simple procedure (it can be accomplished by the flip of a coin), it can be challenging to implement outside of controlled laboratory conditions.

A study can use both, only one, or neither.  Here are some examples to illustrate each situation:

A researcher gets a list of all students enrolled at a particular school (the population).  Using a random number generator, the researcher selects 100 students from the school to participate in the study (the random sample).  All students’ names are placed in a hat and 50 are chosen to receive the intervention (the treatment group), while the remaining 50 students serve as the control group.  This design uses both random selection and random assignment.

A study using only random assignment could ask the principle of the school to select the students she believes are most likely to enjoy participating in the study, and the researcher could then randomly assign this sample of students to the treatment and control groups.  In such a design the researcher could draw conclusions about the effect of the intervention but couldn’t make any inference about whether the effect would likely to be found in the population.

A study using only random selection could randomly select students from the overall population of the school, but then assign students in one grade to the intervention and students in another grade to the control group.  While any data collected from this sample could be used to make inference to the population of the school, the lack of random assignment to be in the treatment or control group would make it impossible to conclude whether the intervention had any effect.

Random selection is thus essential to external validity, or the extent to which the researcher can use the results of the study to generalize to the larger population.  Random assignment is central to internal validity, which allows the researcher to make causal claims about the effect of the treatment.  Nonrandom assignment often leads to non-equivalent groups, meaning that any effect of the treatment might be a result of the groups being different at the outset rather than different at the end as a result of the treatment.  The consequences of random selection and random assignment are clearly very different, and a strong research design will employ both whenever possible to ensure both internal and external validity .

Random Assignment in Psychology: Definition & Examples

Julia Simkus

Editor at Simply Psychology

BA (Hons) Psychology, Princeton University

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

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Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

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

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

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

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

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

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

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

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

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

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

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

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

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

Importance 

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

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

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

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

Random Selection vs. Random Assignment 

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

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

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

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

Random Assignment vs Random Sampling

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

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

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

When to Use Random Assignment

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

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

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

How to Use Random Assignment

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

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

When is Random Assignment not used?

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

Drawbacks of Random Assignment

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

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

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

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

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

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

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

What is the difference between random sampling and random assignment?

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

Does random assignment increase internal validity?

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

Does random assignment reduce sampling error?

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

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

When is random assignment not possible?

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

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

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

Does random assignment eliminate confounding variables?

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

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

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

Further Reading

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

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Statistics and probability

Course: statistics and probability   >   unit 6.

• Introduction to experiment design
• Matched pairs experiment design
• The language of experiments
• Principles of experiment design
• Experiment designs

Random sampling vs. random assignment (scope of inference)

• (Choice A)   Just the residents involved in Hilary's study. A Just the residents involved in Hilary's study.
• (Choice B)   All residents in Hilary's town. B All residents in Hilary's town.
• (Choice C)   All residents in Hilary's country. C All residents in Hilary's country.
• (Choice A)   Yes A Yes
• (Choice B)   No B No
• (Choice A)   Just the residents in Hilary's study. A Just the residents in Hilary's study.

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Random Selection vs. Random Assignment

Random selection and random assignment  are two techniques in statistics that are commonly used, but are commonly confused.

Random selection  refers to the process of randomly selecting individuals from a population to be involved in a study.

Random assignment  refers to the process of randomly  assigning  the individuals in a study to either a treatment group or a control group.

You can think of random selection as the process you use to “get” the individuals in a study and you can think of random assignment as what you “do” with those individuals once they’re selected to be part of the study.

The Importance of Random Selection and Random Assignment

When a study uses  random selection , it selects individuals from a population using some random process. For example, if some population has 1,000 individuals then we might use a computer to randomly select 100 of those individuals from a database. This means that each individual is equally likely to be selected to be part of the study, which increases the chances that we will obtain a representative sample – a sample that has similar characteristics to the overall population.

By using a representative sample in our study, we’re able to generalize the findings of our study to the population. In statistical terms, this is referred to as having  external validity – it’s valid to externalize our findings to the overall population.

When a study uses  random assignment , it randomly assigns individuals to either a treatment group or a control group. For example, if we have 100 individuals in a study then we might use a random number generator to randomly assign 50 individuals to a control group and 50 individuals to a treatment group.

By using random assignment, we increase the chances that the two groups will have roughly similar characteristics, which means that any difference we observe between the two groups can be attributed to the treatment. This means the study has  internal validity  – it’s valid to attribute any differences between the groups to the treatment itself as opposed to differences between the individuals in the groups.

Examples of Random Selection and Random Assignment

It’s possible for a study to use both random selection and random assignment, or just one of these techniques, or neither technique. A strong study is one that uses both techniques.

The following examples show how a study could use both, one, or neither of these techniques, along with the effects of doing so.

Example 1: Using both Random Selection and Random Assignment

Study:  Researchers want to know whether a new diet leads to more weight loss than a standard diet in a certain community of 10,000 people. They recruit 100 individuals to be in the study by using a computer to randomly select 100 names from a database. Once they have the 100 individuals, they once again use a computer to randomly assign 50 of the individuals to a control group (e.g. stick with their standard diet) and 50 individuals to a treatment group (e.g. follow the new diet). They record the total weight loss of each individual after one month.

Results:  The researchers used random selection to obtain their sample and random assignment when putting individuals in either a treatment or control group. By doing so, they’re able to generalize the findings from the study to the overall population  and  they’re able to attribute any differences in average weight loss between the two groups to the new diet.

Example 2: Using only Random Selection

Study:  Researchers want to know whether a new diet leads to more weight loss than a standard diet in a certain community of 10,000 people. They recruit 100 individuals to be in the study by using a computer to randomly select 100 names from a database. However, they decide to assign individuals to groups based solely on gender. Females are assigned to the control group and males are assigned to the treatment group. They record the total weight loss of each individual after one month.

Results:  The researchers used random selection to obtain their sample, but they did not use random assignment when putting individuals in either a treatment or control group. Instead, they used a specific factor – gender – to decide which group to assign individuals to. By doing this, they’re able to generalize the findings from the study to the overall population but they are  not  able to attribute any differences in average weight loss between the two groups to the new diet. The internal validity of the study has been compromised because the difference in weight loss could actually just be due to gender, rather than the new diet.

Example 3: Using only Random Assignment

Study:  Researchers want to know whether a new diet leads to more weight loss than a standard diet in a certain community of 10,000 people. They recruit 100 males athletes to be in the study. Then, they use a computer program to randomly assign 50 of the male athletes to a control group and 50 to the treatment group. They record the total weight loss of each individual after one month.

Results:  The researchers did not use random selection to obtain their sample since they specifically chose 100 male athletes. Because of this, their sample is not representative of the overall population so their external validity is compromised – they will not be able to generalize the findings from the study to the overall population. However, they did use random assignment, which means they can attribute any difference in weight loss to the new diet.

Example 4: Using Neither Technique

Study:  Researchers want to know whether a new diet leads to more weight loss than a standard diet in a certain community of 10,000 people. They recruit 50 males athletes and 50 female athletes to be in the study. Then, they assign all of the female athletes to the control group and all of the male athletes to the treatment group. They record the total weight loss of each individual after one month.

Results:  The researchers did not use random selection to obtain their sample since they specifically chose 100 athletes. Because of this, their sample is not representative of the overall population so their external validity is compromised – they will not be able to generalize the findings from the study to the overall population. Also, they split individuals into groups based on gender rather than using random assignment, which means their internal validity is also compromised – differences in weight loss might be due to gender rather than the diet.

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MA121: Introduction to Statistics

Descriptive and Inferential Statistics

Read these sections and complete the questions at the end of each section. Here, we introduce descriptive statistics using examples and discuss the difference between descriptive and inferential statistics. We also talk about samples and populations, explain how you can identify biased samples, and define differential statistics.

Inferential Statistics

Random assignment.

In experimental research, populations are often hypothetical. For example, in an experiment comparing the effectiveness of a new anti-depressant drug with a placebo, there is no actual population of individuals taking the drug. In this case, a specified population of people with some degree of depression is defined and a random sample is taken from this population. The sample is then randomly divided into two groups; one group is assigned to the treatment condition (drug) and the other group is assigned to the control condition (placebo). This random division of the sample into two groups is called  random assignment .  Random assignment  is critical for the validity of an experiment. For example, consider the bias that could be introduced if the first 20 subjects to show up at the experiment were assigned to the experimental group and the second 20 subjects were assigned to the control group. It is possible that subjects who show up late tend to be more depressed than those who show up early, thus making the experimental group less depressed than the control group even before the treatment was administered.

In experimental research of this kind, failure to assign subjects randomly to groups is generally more serious than having a non-random sample. Failure to randomize (the former error) invalidates the experimental findings. A non-random sample (the latter error) simply restricts the generalizability of the results.

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Methodology

• Simple Random Sampling | Definition, Steps & Examples

Simple Random Sampling | Definition, Steps & Examples

Published on August 28, 2020 by Lauren Thomas . Revised on December 18, 2023.

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

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

Table of contents

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

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

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

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

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

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

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

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

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There are 4 key steps to select a simple random sample.

Step 1: Define the population

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

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

Step 2: Decide on the sample size

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

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

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

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

Step 3: Randomly select your sample

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

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

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

Step 4: Collect data from your sample

Finally, you should collect data from your sample.

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

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

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

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

Research bias

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

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

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

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

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

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

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

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

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

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The Definition of Random Assignment According to Psychology

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

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

Materio / Getty Images

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

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

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

Random Assignment In Research

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

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

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

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

Random Selection

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

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

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

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

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

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

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

Example of Random Assignment

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

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

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

A Word From Verywell

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

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

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

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

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

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

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

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34.4 - creating random assignments.

We now turn our focus from randomly sampling a subset of observations from a data set to that of generating a random assignment of treatments to experimental units in a randomized, controlled experiment. The good news is that the techniques used to sample without replacement can easily be extended to generate such random assignment plans.

It's probably a good time to remind you of the existence of the PLAN procedure. As I mentioned earlier, due to time constraints of the course and the complexity of the PLAN procedure, we will not use it to accomplish any of our random assignments. You should be aware, however, of its existence should you want to explore it on your own in the future.

Example 34.15 Section  

Suppose we are interested in conducting an experiment so that we can compare the effects of two drugs (A and B) and one placebo on headache pain. We have 30 subjects enrolled in our study but need to determine a plan for randomly assigning 10 of the subjects to treatment A, 10 of the subjects to treatment B, and 10 of the subjects to the placebo. The following program does just that for us. That is, it creates a random assignment for 30 subjects in a completely randomized design with one factor having 3 levels:

Okay, let's first launch and run    the SAS program, so you can review the resulting output to convince yourself that the code did indeed generate the desired treatment plan. You should see that 10 of the subjects were randomly assigned to treatment A, 10 to treatment B, and 10 to the placebo.

Now, let's walk ourselves through the program to make sure we understand how it works. The first DATA step merely uses a simple DO loop to create a temporary data set called exper1 that contains one observation for each of the experimental units (in our case, the experimental units are subjects). The only variable in the data set, unit , contains an arbitrary label 1, 2, ..., 30 assigned to each of the experimental units.

The remainder of the code generates a random assignment. To do so, the code from Example 34.5 is simply extended. That is:

• The second DATA step uses the ranuni function to generate a uniform random number between 0 and 1 for each observation in the exper1 data set. The result is stored in a temporary data set called random1 .
• The random1 data set is sorted in order of the random number.
• The third DATA step uses an IF-THEN-ELSE construct to assign the first ten units in sorted order to Group 1, the second ten to Group 2, and the last ten to Group 3.
• A FORMAT is defined to label the groups meaningfully.
• The final randomization list is printed.

Example 34.16 Section  

To create a random assignment for a completely randomized design with two factors , you can just modify the IF statement in the previous example. The following program generates a random assignment of treatments to 30 subjects, in which Factor A has 2 levels and Factor B has 3 levels (and hence 6 treatments). The code is similar to the code from the previous example except the IF statement now divides the 30 subjects into 6 treatment groups and (arbitrarily) assigns the levels of factors A and B to the groups:

First, my apologies for the formatting that makes the IF-THEN-ELSE statement a little difficult to read. I needed to format it as such so that I could easily capture the image of the program for you.

Again, it's probably best if you first launch and run    the SAS program, so you can review the resulting output to convince yourself that the code did indeed generate the desired treatment plan. You should see that five of the subjects were randomly assigned to the A=1, B=1 group, five to the A=1, B=2 group, five to the A=1, B=3 group, and so on.

Then, if you compare the code to the code from the previous example, the only substantial difference you should see is the difference between the two IF statements. As previously mentioned, the IF statement here divides the 30 subjects into 6 treatment groups and (arbitrarily) assigns the levels of factors A and B to the groups:

Example 34.17 Section  

Thus far, our random assignments have not involved dealing with a blocking factor. As you know, it is natural in some experiments to block some of the experimental units together in an attempt to reduce unnecessary variability in your measurements that might otherwise prevent you from making good treatment comparisons. Suppose, for example, that your workload would prevent you from making more than nine experimental measurements in a day. Then, it would be a good idea then to treat the day as a blocking factor. The following program creates a random assignment for 27 subjects in a randomized block design with one factor having three levels.

Again, my apologies about the formatting that makes the program a little more difficult than usual to read. I needed to format it as such so that I could easily capture the image of the program for you.

It's probably going to be best if you first launch and run    the SAS program, so you can first review the contents of the initial exper2 data set:

EXPER2: Definition of Experimental Units

and then the resulting output that contains the desired treatment plan... first in block-treatment order:

Random Assignments for RBD: Sorted in BLOCK-TRT order

and then in block-unit order:

Random Assignments for RBD: Sorted in BLOCK-UNIT order

As you can see, the exper2 data set is created to contain one observation for each of the experimental units (27 subjects here). The variable unit contains an arbitrary label (1, 2, ..., 30) assigned to each of the experimental units. The variable block , which identifies the block number (1, 2, and 3), divides the experimental units into three equal-sized blocks of nine.

Now, to create the random assignment:

• We use the ranuni function to generate a uniform random number between 0 and 1 for each observation.
• Then, within each block, we sort the data in order of the random number.
• Then, we create a counter variable to count the number of observations within each block: for the first observation within each block ("if first.block "), we set the counter ( k ) to 0; otherwise, we increase the counter by 1 for each observation within the block. (For this to work, we must retain k from iteration to iteration).
• Using an IF-THEN-ELSE construct, within each block , assign the first three units in sorted order ( k =0,1,2) to group 1, the second three ( k =3,4,5) to group 2, and the last three ( k =6,7,8) to group 3.

Depending on how the experiment will be conducted, you can print the random assignment in different orders:

• First, the randomization is printed in order of treatment within each block. This will accommodate experiments for which it is natural to perform the treatments in groups on the randomized experimental units.
• Then, the randomization is printed in order of units within the block. This will accommodate experiments for which it is natural to perform the treatments in random order on consecutive experimental units.

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

Random Assignment in Experiments | Introduction & Examples

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

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

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

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

Table of contents

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Random assignment in block designs

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

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

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

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

When comparing different groups

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

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

When it’s not ethically permissible

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

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

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

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

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

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

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

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

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

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

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

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Applied Causal Analysis (with R)

4.23 independence assumption & random assignment.

• = a statistical solution (Holland 1986 , 948f)
• Units randomly assigned to treatment/control have identical distributions of covariates/potential outcomes in both groups ( (infinite) long run! ) 25
• Random assignment induces independence between treatment status and potential outcomes
• Contrast a randomized experiment here in the class (e.g., N = 4) with a bigger sample (e.g., N = 1000).
• Compare average outcome among treatment units with average outcome among control units

Holland, Paul W. 1986. “Statistics and Causal Inference.” J. Am. Stat. Assoc. 81 (396): 945–60.

“When units are assigned at random either to cause t or to cause c, certain physical randomization processes are carried out so that the determination of which cause (t or c) u is exposed to is regarded as statistically independent of all other variables, including Y t and Y c . This means that if the physical randomization is carried out correctly, then it is plausible that S [= treatment D] is independent of Y, and Y, and all other variables over U. This is the independence assumption” (Holland 1986 , 948) . ↩

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AP Statistics : How to do random assignments in an experiment

Study concepts, example questions & explanations for ap statistics, all ap statistics resources, example questions, example question #1 : data collection.

A researcher wants to randomly assign participants to a treatment and control group. Which of the following approaches ensures that the treatment assignment is random?

Obtaining nationally representative samples for both

Assigning the treatment by gender

Assigning the treatment based on who needs it the most 

Flipping a coin

The only random procedure here is the coin flip. In expectation, the coin flip ensures that no background variables influence treatment assignment whereas the other examples either have nothing to do with random assignment (e.g. nationally representative sample) or completely contradict the purpose of random assignment (e.g. assigning the treatment based on who needs it the most). 

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Elements of Research

Random assignment is a procedure used in experiments to create multiple study groups that include participants with similar characteristics so that the groups are equivalent at the beginning of the study. The procedure involves assigning individuals to an experimental treatment or program at random, or by chance (like the flip of a coin). This means that each individual has an equal chance of being assigned to either group. Usually in studies that involve random assignment, participants will receive a new treatment or program, will receive nothing at all or will receive an existing treatment. When using random assignment, neither the researcher nor the participant can choose the group to which the participant is assigned. The benefit of using random assignment is that it “evens the playing field.” This means that the groups will differ only in the program or treatment to which they are assigned. If both groups are equivalent except for the program or treatment that they receive, then any change that is observed after comparing information collected about individuals at the beginning of the study and again at the end of the study can be attributed to the program or treatment. This way, the researcher has more confidence that any changes that might have occurred are due to the treatment under study and not to the characteristics of the group. A potential problem with random assignment is the temptation to ignore the random assignment procedures. For example, it may be tempting to assign an overweight participant to the treatment group that includes participation in a weight-loss program. Ignoring random assignment procedures in this study limits the ability to determine whether or not the weight loss program is effective because the groups will not be randomized. Research staff must follow random assignment protocol, if that is part of the study design, to maintain the integrity of the research. Failure to follow procedures used for random assignment prevents the study outcomes from being meaningful and applicable to the groups represented.                                                                                                                                               Help | Advanced Search Statistics > Machine Learning Title: generative assignment flows for representing and learning joint distributions of discrete data. Abstract: We introduce a novel generative model for the representation of joint probability distributions of a possibly large number of discrete random variables. The approach uses measure transport by randomized assignment flows on the statistical submanifold of factorizing distributions, which also enables to sample efficiently from the target distribution and to assess the likelihood of unseen data points. The embedding of the flow via the Segre map in the meta-simplex of all discrete joint distributions ensures that any target distribution can be represented in principle, whose complexity in practice only depends on the parametrization of the affinity function of the dynamical assignment flow system. Our model can be trained in a simulation-free manner without integration by conditional Riemannian flow matching, using the training data encoded as geodesics in closed-form with respect to the e-connection of information geometry. By projecting high-dimensional flow matching in the meta-simplex of joint distributions to the submanifold of factorizing distributions, our approach has strong motivation from first principles of modeling coupled discrete variables. Numerical experiments devoted to distributions of structured image labelings demonstrate the applicability to large-scale problems, which may include discrete distributions in other application areas. Performance measures show that our approach scales better with the increasing number of classes than recent related work. Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG) Cite as: [stat.ML]   (or [stat.ML] for this version)   Focus to learn more arXiv-issued DOI via DataCite Submission history Access paper:. HTML (experimental) Other Formats References & Citations Google Scholar Semantic Scholar BibTeX formatted citation Bibliographic and Citation Tools Code, data and media associated with this article, recommenders and search tools. Institution arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . 438 IMAGES Random Assignment in Experiments Random Selection vs. Random Assignment Introduction to Random Assignment -Voxco Random Assignment Random Sample v Random Assignment Chapter 8 Populations and Generalizability VIDEO Randomly Select Random Assignment Assignment Stats Sem2 2022/2023 DSC430 Assignment War and Random Numbers RANDOM ASSIGNMENT random sampling & assignment COMMENTS Random Assignment in Experiments 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 ... Random Assignment in Experiments Correlation, Causation, and Confounding Variables. Random assignment helps you separate 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. The idea is to determine whether the effect, which is the difference between a treatment group and ... Random sampling vs. random assignment (scope of inference) Random sampling vs. random assignment (scope of inference) Google Classroom. Microsoft Teams. Hilary wants to determine if any relationship exists between Vitamin D and blood pressure. She is considering using one of a few different designs for her study. Determine what type of conclusions can be drawn from each study design. Random Sampling vs. Random Assignment So, to summarize, random sampling refers to how you select individuals from the population to participate in your study. Random assignment refers to how you place those participants into groups (such as experimental vs. control). Knowing this distinction will help you clearly and accurately describe the methods you use to collect your data and ... Random Selection vs. Random Assignment Random selection and random assignment are two techniques in statistics that are commonly used, but are commonly confused. Random selection refers to the process of randomly selecting individuals from a population to be involved in a study. Random assignment refers to the process of randomly assigning the individuals in a study to either a ... 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. This ensures that each participant or subject has an equal chance of being placed in ... PDF Random sampling vs. assignment Random sampling allows us to obtain a sample representative of the population. Therefore, results of the study can be generalized to the population. Random assignment allows us to make sure that the only difference between the various treatment groups is what we are studying. For example, in the serif/sans serif example, random assignment helps ... Difference between Random Selection and Random Assignment Random selection is thus essential to external validity, or the extent to which the researcher can use the results of the study to generalize to the larger population. Random assignment is central to internal validity, which allows the researcher to make causal claims about the effect of the treatment. Nonrandom assignment often leads to non ... Random Assignment in Psychology: Definition & Examples 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 ... Random sampling vs. random assignment (scope of inference) Random sampling Not random sampling; Random assignment: Can determine causal relationship in population. This design is relatively rare in the real world. Can determine causal relationship in that sample only. This design is where most experiments would fit. No random assignment: Can detect relationships in population, but cannot determine ... Types of sampling methods Cluster sampling- she puts 50 into random groups of 5 so we get 10 groups then randomly selects 5 of them and interviews everyone in those groups --> 25 people are asked. 2. Stratified sampling- she puts 50 into categories: high achieving smart kids, decently achieving kids, mediumly achieving kids, lower poorer achieving kids and clueless ... Random Selection vs. Random Assignment Random selection and random assignment are two techniques in statistics that are commonly used, but are commonly confused.. Random selection refers to the process of randomly selecting individuals from a population to be involved in a study. Random assignment refers to the process of randomly assigning the individuals in a study to either a treatment group or a control group. Descriptive and Inferential Statistics: Random Assignment Random assignment is critical for the validity of an experiment. For example, consider the bias that could be introduced if the first 20 subjects to show up at the experiment were assigned to the experimental group and the second 20 subjects were assigned to the control group. It is possible that subjects who show up late tend to be more ... Simple Random Sampling Revised on December 18, 2023. A simple random sample is a randomly selected subset of a population. In this sampling method, each member of the population has an exactly equal chance of being selected. This method is the most straightforward of all the probability sampling methods, since it only involves a single random selection and requires ... The Definition of Random Assignment In Psychology The Definition of Random Assignment According to Psychology. 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 ... PDF Random Assignment Random Assignment In the context of the all causes model, we may state the random assignment assumption as follows: Assumption 1 (Random assignment; RA) Let (Y, W, U) be a random vector with joint distribution characterized by Equation (1). Random assignment assumes W ‹‹ U. (3) In words: the policy W is independent of all other determinants U. 34.4 34.4 - Creating Random Assignments. We now turn our focus from randomly sampling a subset of observations from a data set to that of generating a random assignment of treatments to experimental units in a randomized, controlled experiment. The good news is that the techniques used to sample without replacement can easily be extended to generate ... Random Assignment in Experiments 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 ... 4.23 Independence assumption & random assignment Random assignment = a statistical solution (Holland 1986, 948f) ... J. Am. Stat. Assoc. 81 (396): 945-60. "When units are assigned at random either to cause t or to cause c, certain physical randomization processes are carried out so that the determination of which cause ... Experimental Design: Variables, Groups, and Random Assignment In this video, Dr. Kushner outlines how to conduct a psychology experiment. The experimental method is a powerful tool for psychologists because it is the on... AP Statistics : How to do random assignments in an experiment Explanation: . The only random procedure here is the coin flip. In expectation, the coin flip ensures that no background variables influence treatment assignment whereas the other examples either have nothing to do with random assignment (e.g. nationally representative sample) or completely contradict the purpose of random assignment (e.g. assigning the treatment based on who needs it the most). Elements of Research : Random Assignment Random assignment is a procedure used in experiments to create multiple study groups that include participants with similar characteristics so that the groups are equivalent at the beginning of the study. The procedure involves assigning individuals to an experimental treatment or program at random, or by chance (like the flip of a coin). PDF AP® Statistics STATISTICS 2019 SCORING GUIDELINES . Question 2 (continued) • For responses that use random number generators (or a 20-sided die): o If the initial assignment of numbers to units does not give each unit the same probability of being assigned to each treatment (e.g., units are represented by different numbers of integers), Generative Assignment Flows for Representing and Learning Joint View PDF HTML (experimental) Abstract: We introduce a novel generative model for the representation of joint probability distributions of a possibly large number of discrete random variables. The approach uses measure transport by randomized assignment flows on the statistical submanifold of factorizing distributions, which also enables to sample efficiently from the target distribution and to ... assignment business plan essay writing homework research paper review writing