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• Random Assignment in Experiments | Introduction & Examples

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 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.

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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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15 Random Assignment Examples

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

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

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

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

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

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

Methods for Random Assignment of Participants

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

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

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

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

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

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

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

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

Random Assignment Examples

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Read Next: Types of Research Design

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

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

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

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

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

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AP®︎/College Statistics

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• Statistical significance of experiment

Random sampling vs. random assignment (scope of inference)

• Conclusions in observational studies versus experiments
• Finding errors in study conclusions
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• (Choice C)   All residents in Hilary's country. C All residents in Hilary's country.
• (Choice A)   Yes A Yes
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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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Random Assignment in Psychology: Definition & Examples

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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.

Statistical Thinking: A Simulation Approach to Modeling Uncertainty (UM STAT 216 edition)

3.6 causation and random assignment.

Medical researchers may be interested in showing that a drug helps improve people’s health (the cause of improvement is the drug), while educational researchers may be interested in showing a curricular innovation improves students’ learning (the curricular innovation causes improved learning).

To attribute a causal relationship, there are three criteria a researcher needs to establish:

• Association of the Cause and Effect: There needs to be a association between the cause and effect.
• Timing: The cause needs to happen BEFORE the effect.
• No Plausible Alternative Explanations: ALL other possible explanations for the effect need to be ruled out.

Please read more about each of these criteria at the Web Center for Social Research Methods .

The third criterion can be quite difficult to meet. To rule out ALL other possible explanations for the effect, we want to compare the world with the cause applied to the world without the cause. In practice, we do this by comparing two different groups: a “treatment” group that gets the cause applied to them, and a “control” group that does not. To rule out alternative explanations, the groups need to be “identical” with respect to every possible characteristic (aside from the treatment) that could explain differences. This way the only characteristic that will be different is that the treatment group gets the treatment and the control group doesn’t. If there are differences in the outcome, then it must be attributable to the treatment, because the other possible explanations are ruled out.

So, the key is to make the control and treatment groups “identical” when you are forming them. One thing that makes this task (slightly) easier is that they don’t have to be exactly identical, only probabilistically equivalent . This means, for example, that if you were matching groups on age that you don’t need the two groups to have identical age distributions; they would only need to have roughly the same AVERAGE age. Here roughly means “the average ages should be the same within what we expect because of sampling error.”

Now we just need to create the groups so that they have, on average, the same characteristics … for EVERY POSSIBLE CHARCTERISTIC that could explain differences in the outcome.

It turns out that creating probabilistically equivalent groups is a really difficult problem. One method that works pretty well for doing this is to randomly assign participants to the groups. This works best when you have large sample sizes, but even with small sample sizes random assignment has the advantage of at least removing the systematic bias between the two groups (any differences are due to chance and will probably even out between the groups). As Wikipedia’s page on random assignment points out,

Random assignment of participants helps to ensure that any differences between and within the groups are not systematic at the outset of the experiment. Thus, any differences between groups recorded at the end of the experiment can be more confidently attributed to the experimental procedures or treatment. … Random assignment does not guarantee that the groups are matched or equivalent. The groups may still differ on some preexisting attribute due to chance. The use of random assignment cannot eliminate this possibility, but it greatly reduces it.

We use the term internal validity to describe the degree to which cause-and-effect inferences are accurate and meaningful. Causal attribution is the goal for many researchers. Thus, by using random assignment we have a pretty high degree of evidence for internal validity; we have a much higher belief in causal inferences. Much like evidence used in a court of law, it is useful to think about validity evidence on a continuum. For example, a visualization of the internal validity evidence for a study that employed random assignment in the design might be:

The degree of internal validity evidence is high (in the upper-third). How high depends on other factors such as sample size.

To learn more about random assignment, you can read the following:

• The research report, Random Assignment Evaluation Studies: A Guide for Out-of-School Time Program Practitioners

3.6.1 Example: Does sleep deprivation cause an decrease in performance?

Let’s consider the criteria with respect to the sleep deprivation study we explored in class.

3.6.1.1 Association of cause and effect

First, we ask, Is there an association between the cause and the effect? In the sleep deprivation study, we would ask, “Is sleep deprivation associated with an decrease in performance?”

This is what a hypothesis test helps us answer! If the result is statistically significant , then we have an association between the cause and the effect. If the result is not statistically significant, then there is not sufficient evidence for an association between cause and effect.

In the case of the sleep deprivation experiment, the result was statistically significant, so we can say that sleep deprivation is associated with a decrease in performance.

3.6.1.2 Timing

Second, we ask, Did the cause come before the effect? In the sleep deprivation study, the answer is yes. The participants were sleep deprived before their performance was tested. It may seem like this is a silly question to ask, but as the link above describes, it is not always so clear to establish the timing. Thus, it is important to consider this question any time we are interested in establishing causality.

3.6.1.3 No plausible alternative explanations

Finally, we ask Are there any plausible alternative explanations for the observed effect? In the sleep deprivation study, we would ask, “Are there plausible alternative explanations for the observed difference between the groups, other than sleep deprivation?” Because this is a question about plausibility, human judgment comes into play. Researchers must make an argument about why there are no plausible alternatives. As described above, a strong study design can help to strengthen the argument.

At first, it may seem like there are a lot of plausible alternative explanations for the difference in performance. There are a lot of things that might affect someone’s performance on a visual task! Sleep deprivation is just one of them! For example, artists may be more adept at visual discrimination than other people. This is an example of a potential confounding variable. A confounding variable is a variable that might affect the results, other than the causal variable that we are interested in.

Here’s the thing though. We are not interested in figuring out why any particular person got the score that they did. Instead, we are interested in determining why one group was different from another group. In the sleep deprivation study, the participants were randomly assigned. This means that the there is no systematic difference between the groups, with respect to any confounding variables. Yes—artistic experience is a possible confounding variable, and it may be the reason why two people score differently. BUT: There is no systematic difference between the groups with respect to artistic experience, and so artistic experience is not a plausible explanation as to why the groups would be different. The same can be said for any possible confounding variable. Because the groups were randomly assigned, it is not plausible to say that the groups are different with respect to any confounding variable. Random assignment helps us rule out plausible alternatives.

3.6.1.4 Making a causal claim

Now, let’s see about make a causal claim for the sleep deprivation study:

• Association: There is a statistically significant result, so the cause is associated with the effect
• Timing: The participants were sleep deprived before their performance was measured, so the cause came before the effect
• Plausible alternative explanations: The participants were randomly assigned, so the groups are not systematically different on any confounding variable. The only systematic difference between the groups was sleep deprivation. Thus, there are no plausible alternative explanations for the difference between the groups, other than sleep deprivation

Thus, the internal validity evidence for this study is high, and we can make a causal claim. For the participants in this study, we can say that sleep deprivation caused a decrease in performance.

Key points: Causation and internal validity

To make a cause-and-effect inference, you need to consider three criteria:

• Association of the Cause and Effect: There needs to be a association between the cause and effect. This can be established by a hypothesis test.

Random assignment removes any systematic differences between the groups (other than the treatment), and thus helps to rule out plausible alternative explanations.

Internal validity describes the degree to which cause-and-effect inferences are accurate and meaningful.

Confounding variables are variables that might affect the results, other than the causal variable that we are interested in.

Probabilistic equivalence means that there is not a systematic difference between groups. The groups are the same on average.

How can we make "equivalent" experimental groups?

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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Random Assignment – A Simple Introduction with Examples

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

Inhaltsverzeichnis

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

Random Assignment – In a Nutshell

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

Definition: Random assignment

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

Importance of random assignment

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

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

Example: Different levels of independent variables

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

Three independent participant levels are applicable here:

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

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

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

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

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

Random assignment vs. random sampling

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

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

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

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

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

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

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

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

How to use random assignment

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

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

Random assignment in block experimental designs

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

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

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

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

When random assignment is not used

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

Comparing different groups

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

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

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

No ethical justifiability

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

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

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

What is the definition of random assignment?

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

When is random assignment applicable?

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

What is the importance of random assignment?

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

When should you NOT use random assignment

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

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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?

Assigning the treatment based on who needs it the most 

Obtaining nationally representative samples for both

Assigning the treatment by gender

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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3.4 - experimental and observational studies.

Now that Jaylen can weigh the different sampling strategies, he might want to consider the type of study he is conduction. As a note, for students interested in research designs, please consult STAT 503 for a much more in-depth discussion. However, for this example, we will simply distinguish between experimental and observational studies.

Now that we know how to collect data, the next step is to determine the type of study. The type of study will determine what type of relationship we can conclude.

There are predominantly two different types of studies: 

Let's say that there is an option to take quizzes throughout this class. In an  observational study , we may find that better students tend to take the quizzes and do better on exams. Consequently, we might conclude that there may be a relationship between quizzes and exam scores.

In an experimental study , we would randomly assign quizzes to specific students to look for improvements. In other words, we would look to see whether taking quizzes causes higher exam scores.

Causation Section  

It is very important to distinguish between observational and experimental studies since one has to be very skeptical about drawing cause and effect conclusions using observational studies. The use of random assignment of treatments (i.e. what distinguishes an experimental study from an observational study) allows one to employ cause and effect conclusions.

Ethics is an important aspect of experimental design to keep in mind. For example, the original relationship between smoking and lung cancer was based on an observational study and not an assignment of smoking behavior.

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13.3: Simple Random Samples and Statistics

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• Page ID 10840

• Paul Pfeiffer
• Rice University

Simple Random Samples and Statistics

We formulate the notion of a (simple) random sample , which is basic to much of classical statistics. Once formulated, we may apply probability theory to exhibit several basic ideas of statistical analysis.

We begin with the notion of a population distribution . A population may be most any collection of individuals or entities. Associated with each member is a quantity or a feature that can be assigned a number. The quantity varies throughout the population. The population distribution is the distribution of that quantity among the members of the population.

If each member could be observed, the population distribution could be determined completely. However, that is not always feasible. In order to obtain information about the population distribution, we select “at random” a subset of the population and observe how the quantity varies over the sample. Hopefully, the sample distribution will give a useful approximation to the population distribution.

The sampling process

We take a sample of size \(n\), which means we select n members of the population and observe the quantity associated with each. The selection is done in such a manner that on any trial each member is equally likely to be selected. Also, the sampling is done in such a way that the result of any one selection does not affect, and is not affected by, the others. It appears that we are describing a composite trial. We model the sampling process as follows:

Let \(X_i\), \(1 \le i \le n\) be the random variable for the i th component trial. Then the class \(\{X_i: 1 \le i \le n\}\) is iid, with each member having the population distribution.

This provides a model for sampling either from a very large population (often referred to as an infinite population) or sampling with replacement from a small population.

The goal is to determine as much as possible about the character of the population. Two important parameters are the mean and the variance. We want the population mean and the population variance. If the sample is representative of the population, then the sample mean and the sample variance should approximate the population quantities.

• The sampling process is the iid class \(\{X_i: 1 \le i \le n\}\).
• A random sample is an observation, or realization, \((t_1, t_2, \cdot\cdot\cdot, t_n)\) of the sampling process.

The sample average and the population mean

Consider the numerical average of the values in the sample \(\bar{x} = \dfrac{1}{n} \sum_{i = 1}^{n} t_i\). This is an observation of the sample average

\(A_n = \dfrac{1}{n} \sum_{i = 1}^{n} X_i = \dfrac{1}{n} S_n\)

The sample sum \(S_n\) and the sample average \(A_n\) are random variables. If another observation were made (another sample taken), the observed value of these quantities would probably be different. Now \(S_n\) and \(A_n\) are functions of the random variables \(\{X_i: 1 \le i \le n\}\) in the sampling process. As such, they have distributions related to the population distribution (the common distribution of the \(X_i\)). According to the central limit theorem, for any reasonable sized sample they should be approximately normally distributed. As the examples demonstrating the central limit theorem show, the sample size need not be large in many cases. Now if the population mean \(E[X]\) is \(\mu\) and the population variance \(\text{Var} [X]\) is \(\sigma^2\), then

\(E[S_n] = \sum_{i = 1}^{n} E[X_i] = nE[X] = n\mu\) and \(\text{Var}[S_n] = \sum_{i = 1}^{n} \text{Var} [X_i] = n \text{Var} [X] = n \sigma^2\)

\(E[A_n] = \dfrac{1}{n} E[S_n] = \mu\) and \(\text{Var}[A_n] = \dfrac{1}{n^2} \text{Var} [S_n] = \sigma^2/n\)

Herein lies the key to the usefulness of a large sample. The mean of the sample average \(A_n\) is the same as the population mean, but the variance of the sample average is \(1/n\) times the population variance. Thus, for large enough sample, the probability is high that the observed value of the sample average will be close to the population mean . The population standard deviation, as a measure of the variation is reduced by a factor \(1/\sqrt{n}\).

Example \(\PageIndex{1}\) Sample size

Suppose a population has mean \(\mu\) and variance \(\sigma^2\). A sample of size \(n\) is to be taken. There are complementary questions:

• If \(n\) is given, what is the probability the sample average lies within distance a from the population mean?
• What value of \(n\) is required to ensure a probability of at least p that the sample average lies within distance a from the population mean?

Suppose the sample variance is known or can be approximated reasonably. If the sample size \(n\) is reasonably large, depending on the population distribution (as seen in the previous demonstrations), then \(A_n\) is approximately \(N(\mu, \sigma^2/n)\).

1. Sample size given, probability to be determined.

\(p = P(|A_n - \mu| \le a) = P(|\dfrac{A_n - \mu}{\sigma/\sqrt{n}}| \le \dfrac{a \sqrt{n}}{\sigma} = 2\phi (a \sqrt{n}/\sigma) -1\)

2. Sample size to be determined, probability specified.

\(2 \phi (a \sqrt{n}/\sigma) - 1 \ge p\) iff \(\phi (a\sqrt{n} /\sigma) \ge \dfrac{p + 1}{2}\)

Find from a table or by use of the inverse normal function the value of \(x = a\sqrt{n}/\sigma\) required to make \(\phi (x)\) at least \((p + 1)/2\). Then

\(n \ge \sigma^2 (x/a)^2 = (\dfrac{\sigma}{a})^2 x^2\)

We may use the MATLAB function norminv to calculate values of \(x\) for various \(p\).

For \(p = 0.95\), \(\sigma = 2\), \(a = 0.2\), \(n \ge (2/0.2)^2 3.8415 = 384.15\). Use at least 385 or perhaps 400 because of uncertainty about the actual \(\sigma^2\)

The idea of a statistic

As a function of the random variables in the sampling process, the sample average is an example of a statistic.

Definition: statistic

A statistic is a function of the class \(\{X_i: 1 \le i \le n\}\) which uses explicitly no unknown parameters of the population.

Example \(\PageIndex{2}\) Statistics as functions of the sampling progress

The random variable

\(W = \dfrac{1}{n} \sum_{i = 1}^{n} (X_i - \mu)^2\), where \(\mu = E[X]\)

is not a statistic, since it uses the unknown parameter \(\mu\). However, the following is a statistic.

\(V_n^* = \dfrac{1}{n} \sum_{i = 1}^{n} (X_i - A_n)^2 = \dfrac{1}{n} \sum_{i = 1}^{n} X_i^2 - A_n^2\)

It would appear that \(V_n^*\) might be a reasonable estimate of the population variance. However, the following result shows that a slight modification is desirable.

Example \(\PageIndex{3}\) An estimator for the population variance

The statistic

\(V_n = \dfrac{1}{n - 1} \sum_{i = 1}^{n} (X_i - A_n)^2\)

is an estimator for the population variance.

VERIFICATION

Consider the statistic

Noting that \(E[X^2] = \sigma^2 + \mu^2\), we use the last expression to show

\(E[V_n^*] = \dfrac{1}{n} n (\sigma^2 + \mu^2) - (\dfrac{\sigma^2}{n} + \mu^2) = \dfrac{n - 1}{n} \sigma^2\)

The quantity has a bias in the average. If we consider

\(V_n = \dfrac{n}{n - 1} V_n^* = \dfrac{1}{n - 1} \sum_{i = 1}^{n} (X_i - A_n)^2\), then \(E[V_n] = \dfrac{n}{n - 1} \dfrac{n - 1}{n} \sigma^2 = \sigma^2\)

The quantity \(V_n\) with \(1/(n - 1)\) rather than \(1/n\) is often called the sample variance to distinguish it from the population variance. If the set of numbers

\((t_1, t_2, \cdot\cdot\cdot, t_N)\)

represent the complete set of values in a population of \(N\) members, the variance for the population would be given by

\(\sigma^2 = \dfrac{1}{N} \sum_{i = 1}^{N} t_i^2 - (\dfrac{1}{N} \sum_{i = 1}^{N} t_i)^2\)

Here we use \(1/N\) rather than \(1/(N -1)\).

Since the statistic \(V_n\) has mean value \(\sigma^2\), it seems a reasonable candidate for an estimator of the population variance. If we ask how good is it, we need to consider its variance. As a random variable, it has a variance. An evaluation similar to that for the mean, but more complicated in detail, shows that

\(\text{Var} [V_n] = \dfrac{1}{n} (\mu_4 - \dfrac{n - 3}{n - 1} \sigma^4)\) where \(\mu_4 = E[(X - \mu)^4]\)

For large \(n\), \(\text{Var} [V_n]\) is small, so that \(V_n\) is a good large-sample estimator for \(\sigma^2\).

Example \(\PageIndex{4}\) A sampling demonstration of the CLT

Consider a population random variable \(X\) ~ uniform [-1, 1]. Then \(E[X] = 0\) and \(\text{Var} [X] = 1/3\). We take 100 samples of size 100, and determine the sample sums. This gives a sample of size 100 of the sample sum random variable \(S_{100}\), which has mean zero and variance 100/3. For each observed value of the sample sum random variable, we plot the fraction of observed sums less than or equal to that value. This yields an experimental distribution function for \(S_{100}\), which is compared with the distribution function for a random variable \(Y\) ~ \(N(0, 100/3)\).

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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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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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Random Assignment in Psychology (Definition + 40 Examples)

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

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

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

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

History of Random Assignment

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

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

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

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

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

Early Studies Utilizing Random Assignment

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

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

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

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

Evolution of the Methodology

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

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

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

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

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

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

Principles of Random Assignment

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

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

Basic Principles of Random Assignment

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

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

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

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

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

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

Theoretical Foundation

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

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

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

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

Differentiating Random Assignment from Random Selection

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

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

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

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

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

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

Methodology of Random Assignment

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

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

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

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

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

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

Tools and Techniques Used

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

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

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

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

Ethical Considerations

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

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

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

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

Conclusion of Methodology

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

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

Benefits of Random Assignment in Psychological Research

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

Facilitating Causal Inferences

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

This ability to determine the cause is called causal inference .

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

Ensuring Internal Validity

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

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

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

Enhancing Generalizability

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

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

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

Limitations of Random Assignment

Potential for implementation issues.

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

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

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

Ethical Dilemmas

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

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

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

Generalizability Concerns

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

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

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

Practical and Real-World Limitations

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

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

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

Response to Critiques

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

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

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

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

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

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

Real-World Applications and Examples

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

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

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

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

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

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

Real-world Impact of Random Assignment

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

Health and Medicine

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

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

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

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

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

Workplace and Organizational Behavior

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

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

Environmental and Social Changes

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

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

Technology and Human Interaction

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

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

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

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

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

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

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

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

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

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

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• v.43(2); Mar-Apr 2008

Issues in Outcomes Research: An Overview of Randomization Techniques for Clinical Trials

Minsoo kang.

1 Middle Tennessee State University, Murfreesboro, TN

Brian G Ragan

2 University of Northern Iowa, Cedar Falls, IA

Jae-Hyeon Park

3 Korea National Sport University, Seoul, Korea

To review and describe randomization techniques used in clinical trials, including simple, block, stratified, and covariate adaptive techniques.

Background:

Clinical trials are required to establish treatment efficacy of many athletic training procedures. In the past, we have relied on evidence of questionable scientific merit to aid the determination of treatment choices. Interest in evidence-based practice is growing rapidly within the athletic training profession, placing greater emphasis on the importance of well-conducted clinical trials. One critical component of clinical trials that strengthens results is random assignment of participants to control and treatment groups. Although randomization appears to be a simple concept, issues of balancing sample sizes and controlling the influence of covariates a priori are important. Various techniques have been developed to account for these issues, including block, stratified randomization, and covariate adaptive techniques.

Advantages:

Athletic training researchers and scholarly clinicians can use the information presented in this article to better conduct and interpret the results of clinical trials. Implementing these techniques will increase the power and validity of findings of athletic medicine clinical trials, which will ultimately improve the quality of care provided.

Outcomes research is critical in the evidence-based health care environment because it addresses scientific questions concerning the efficacy of treatments. Clinical trials are considered the “gold standard” for outcomes in biomedical research. In athletic training, calls for more evidence-based medical research, specifically clinical trials, have been issued. 1 , 2

The strength of clinical trials is their superior ability to measure change over time from a treatment. Treatment differences identified from cross-sectional observational designs rather than experimental clinical trials have methodologic weaknesses, including confounding, cohort effects, and selection bias. 3 For example, using a nonrandomized trial to examine the effectiveness of prophylactic knee bracing to prevent medial collateral ligament injuries may suffer from confounders and jeopardize the results. One possible confounder is a history of knee injuries. Participants with a history of knee injuries may be more likely to wear braces than those with no such history. Participants with a history of injury are more likely to suffer additional knee injuries, unbalancing the groups and influencing the results of the study.

The primary goal of comparative clinical trials is to provide comparisons of treatments with maximum precision and validity. 4 One critical component of clinical trials is random assignment of participants into groups. Randomizing participants helps remove the effect of extraneous variables (eg, age, injury history) and minimizes bias associated with treatment assignment. Randomization is considered by most researchers to be the optimal approach for participant assignment in clinical trials because it strengthens the results and data interpretation. 4 – , 9

One potential problem with small clinical trials (n < 100) 7 is that conventional simple randomization methods, such as flipping a coin, may result in imbalanced sample size and baseline characteristics (ie, covariates) among treatment and control groups. 9 , 10 This imbalance of baseline characteristics can influence the comparison between treatment and control groups and introduce potential confounding factors. Many procedures have been proposed for random group assignment of participants in clinical trials. 11 Simple, block, stratified, and covariate adaptive randomizations are some examples. Each technique has advantages and disadvantages, which must be carefully considered before a method is selected. Our purpose is to introduce the concept and significance of randomization and to review several conventional and relatively new randomization techniques to aid in the design and implementation of valid clinical trials.

What Is Randomization?

Randomization is the process of assigning participants to treatment and control groups, assuming that each participant has an equal chance of being assigned to any group. 12 Randomization has evolved into a fundamental aspect of scientific research methodology. Demands have increased for more randomized clinical trials in many areas of biomedical research, such as athletic training. 2 , 13 In fact, in the last 2 decades, internationally recognized major medical journals, such as the Journal of the American Medical Association and the BMJ , have been increasingly interested in publishing studies reporting results from randomized controlled trials. 5

Since Fisher 14 first introduced the idea of randomization in a 1926 agricultural study, the academic community has deemed randomization an essential tool for unbiased comparisons of treatment groups. Five years after Fisher's introductory paper, the first randomized clinical trial involving tuberculosis was conducted. 15 A total of 24 participants were paired (ie, 12 comparable pairs), and by a flip of a coin, each participant within the pair was assigned to either the control or treatment group. By employing randomization, researchers offer each participant an equal chance of being assigned to groups, which makes the groups comparable on the dependent variable by eliminating potential bias. Indeed, randomization of treatments in clinical trials is the only means of avoiding systematic characteristic bias of participants assigned to different treatments. Although randomization may be accomplished with a simple coin toss, more appropriate and better methods are often needed, especially in small clinical trials. These other methods will be discussed in this review.

Why Randomize?

Researchers demand randomization for several reasons. First, participants in various groups should not differ in any systematic way. In a clinical trial, if treatment groups are systematically different, trial results will be biased. Suppose that participants are assigned to control and treatment groups in a study examining the efficacy of a walking intervention. If a greater proportion of older adults is assigned to the treatment group, then the outcome of the walking intervention may be influenced by this imbalance. The effects of the treatment would be indistinguishable from the influence of the imbalance of covariates, thereby requiring the researcher to control for the covariates in the analysis to obtain an unbiased result. 16

Second, proper randomization ensures no a priori knowledge of group assignment (ie, allocation concealment). That is, researchers, participants, and others should not know to which group the participant will be assigned. Knowledge of group assignment creates a layer of potential selection bias that may taint the data. Schulz and Grimes 17 stated that trials with inadequate or unclear randomization tended to overestimate treatment effects up to 40% compared with those that used proper randomization. The outcome of the trial can be negatively influenced by this inadequate randomization.

Statistical techniques such as analysis of covariance (ANCOVA), multivariate ANCOVA, or both, are often used to adjust for covariate imbalance in the analysis stage of the clinical trial. However, the interpretation of this postadjustment approach is often difficult because imbalance of covariates frequently leads to unanticipated interaction effects, such as unequal slopes among subgroups of covariates. 18 , 19 One of the critical assumptions in ANCOVA is that the slopes of regression lines are the same for each group of covariates (ie, homogeneity of regression slopes). The adjustment needed for each covariate group may vary, which is problematic because ANCOVA uses the average slope across the groups to adjust the outcome variable. Thus, the ideal way of balancing covariates among groups is to apply sound randomization in the design stage of a clinical trial (before the adjustment procedure) instead of after data collection. In such instances, random assignment is necessary and guarantees validity for statistical tests of significance that are used to compare treatments.

How To Randomize?

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

Simple Randomization

Randomization based on a single sequence of random assignments is known as simple randomization. 10 This technique maintains complete randomness of the assignment of a person to a particular group. The most common and basic method of simple randomization is flipping a coin. For example, with 2 treatment groups (control versus treatment), the side of the coin (ie, heads  =  control, tails  =  treatment) determines the assignment of each participant. Other methods include using a shuffled deck of cards (eg, even  =  control, odd  =  treatment) or throwing a die (eg, below and equal to 3  =  control, over 3  =  treatment). A random number table found in a statistics book or computer-generated random numbers can also be used for simple randomization of participants.

This randomization approach is simple and easy to implement in a clinical trial. In large trials (n > 200), simple randomization can be trusted to generate similar numbers of participants among groups. However, randomization results could be problematic in relatively small sample size clinical trials (n < 100), resulting in an unequal number of participants among groups. For example, using a coin toss with a small sample size (n  =  10) may result in an imbalance such that 7 participants are assigned to the control group and 3 to the treatment group ( Figure 1 ).

Block Randomization

The block randomization method is designed to randomize participants into groups that result in equal sample sizes. This method is used to ensure a balance in sample size across groups over time. Blocks are small and balanced with predetermined group assignments, which keeps the numbers of participants in each group similar at all times. According to Altman and Bland, 10 the block size is determined by the researcher and should be a multiple of the number of groups (ie, with 2 treatment groups, block size of either 4 or 6). Blocks are best used in smaller increments as researchers can more easily control balance. 7 After block size has been determined, all possible balanced combinations of assignment within the block (ie, equal number for all groups within the block) must be calculated. Blocks are then randomly chosen to determine the participants' assignment into the groups.

For a clinical trial with control and treatment groups involving 40 participants, a randomized block procedure would be as follows: (1) a block size of 4 is chosen, (2) possible balanced combinations with 2 C (control) and 2 T (treatment) subjects are calculated as 6 (TTCC, TCTC, TCCT, CTTC, CTCT, CCTT), and (3) blocks are randomly chosen to determine the assignment of all 40 participants (eg, one random sequence would be [TTCC / TCCT / CTTC / CTTC / TCCT / CCTT / TTCC / TCTC / CTCT / TCTC]). This procedure results in 20 participants in both the control and treatment groups ( Figure 2 ).

Although balance in sample size may be achieved with this method, groups may be generated that are rarely comparable in terms of certain covariates. 6 For example, one group may have more participants with secondary diseases (eg, diabetes, multiple sclerosis, cancer) that could confound the data and may negatively influence the results of the clinical trial. Pocock and Simon 11 stressed the importance of controlling for these covariates because of serious consequences to the interpretation of the results. Such an imbalance could introduce bias in the statistical analysis and reduce the power of the study. 4 , 6 , 8 Hence, sample size and covariates must be balanced in small clinical trials.

Stratified Randomization

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

The stratified randomization method controls for the possible influence of covariates that would jeopardize the conclusions of the clinical trial. For example, a clinical trial of different rehabilitation techniques after a surgical procedure will have a number of covariates. It is well known that the age of the patient affects the rate of healing. Thus, age could be a confounding variable and influence the outcome of the clinical trial. Stratified randomization can balance the control and treatment groups for age or other identified covariates.

For example, with 2 groups involving 40 participants, the stratified randomization method might be used to control the covariates of sex (2 levels: male, female) and body mass index (3 levels: underweight, normal, overweight) between study arms. With these 2 covariates, possible block combinations total 6 (eg, male, underweight). A simple randomization procedure, such as flipping a coin, is used to assign the participants within each block to one of the treatment groups ( Figure 3 ).

Although stratified randomization is a relatively simple and useful technique, especially for smaller clinical trials, it becomes complicated to implement if many covariates must be controlled. 20 For example, too many block combinations may lead to imbalances in overall treatment allocations because a large number of blocks can generate small participant numbers within the block. Therneau 21 purported that a balance in covariates begins to fail when the number of blocks approaches half the sample size. If another 4-level covariate was added to the example, the number of block combinations would increase from 6 to 24 (2 × 3 × 4), for an average of fewer than 2 (40 / 24  =  1.7) participants per block, reducing the usefulness of the procedure to balance the covariates and jeopardizing the validity of the clinical trial. In small studies, it may not be feasible to stratify more than 1 or 2 covariates because the number of blocks can quickly approach the number of participants. 10

Stratified randomization has another limitation: it works only when all participants have been identified before group assignment. This method is rarely applicable, however, because clinical trial participants are often enrolled one at a time on a continuous basis. When baseline characteristics of all participants are not available before assignment, using stratified randomization is difficult. 7

Covariate Adaptive Randomization

Covariate adaptive randomization has been recommended by many researchers as a valid alternative randomization method for clinical trials. 9 , 22 In covariate adaptive randomization, a new participant is sequentially assigned to a particular treatment group by taking into account the specific covariates and previous assignments of participants. 9 , 12 , 18 , 23 , 24 Covariate adaptive randomization uses the method of minimization by assessing the imbalance of sample size among several covariates. This covariate adaptive approach was first described by Taves. 23

The Taves covariate adaptive randomization method allows for the examination of previous participant group assignments to make a case-by-case decision on group assignment for each individual who enrolls in the study. Consider again the example of 2 groups involving 40 participants, with sex (2 levels: male, female) and body mass index (3 levels: underweight, normal, overweight) as covariates. Assume the first 9 participants have already been randomly assigned to groups by flipping a coin. The 9 participants' group assignments are broken down by covariate level in Figure 4 . Now the 10th participant, who is male and underweight, needs to be assigned to a group (ie, control versus treatment). Based on the characteristics of the 10th participant, the Taves method adds marginal totals of the corresponding covariate categories for each group and compares the totals. The participant is assigned to the group with the lower covariate total to minimize imbalance. In this example, the appropriate categories are male and underweight, which results in the total of 3 (2 for male category + 1 for underweight category) for the control group and a total of 5 (3 for male category + 2 for underweight category) for the treatment group. Because the sum of marginal totals is lower for the control group (3 < 5), the 10th participant is assigned to the control group ( Figure 5 ).

The Pocock and Simon method 11 of covariate adaptive randomization is similar to the method Taves 23 described. The difference in this approach is the temporary assignment of participants to both groups. This method uses the absolute difference between groups to determine group assignment. To minimize imbalance, the participant is assigned to the group determined by the lowest sum of the absolute differences among the covariates between the groups. For example, using the previous situation in assigning the 10th participant to a group, the Pocock and Simon method would (1) assign the 10th participant temporarily to the control group, resulting in marginal totals of 3 for male category and 2 for underweight category; (2) calculate the absolute difference between control and treatment group (males: 3 control – 3 treatment  =  0; underweight: 2 control – 2 treatment  =  0) and sum (0 + 0  =  0); (3) temporarily assign the 10th participant to the treatment group, resulting in marginal totals of 4 for male category and 3 for underweight category; (4) calculate the absolute difference between control and treatment group (males: 2 control – 4 treatment  =  2; underweight: 1 control – 3 treatment  =  2) and sum (2 + 2  =  4); and (5) assign the 10th participant to the control group because of the lowest sum of absolute differences (0 < 4).

Pocock and Simon 11 also suggested using a variance approach. Instead of calculating absolute difference among groups, this approach calculates the variance among treatment groups. Although the variance method performs similarly to the absolute difference method, both approaches suffer from the limitation of handling only categorical covariates. 25

Frane 18 introduced a covariate adaptive randomization for both continuous and categorical types. Frane used P values to identify imbalance among treatment groups: a smaller P value represents more imbalance among treatment groups.

The Frane method for assigning participants to either the control or treatment group would include (1) temporarily assigning the participant to both the control and treatment groups; (2) calculating P values for each of the covariates using a t test and analysis of variance (ANOVA) for continuous variables and goodness-of-fit χ 2 test for categorical variables; (3) determining the minimum P value for each control or treatment group, which indicates more imbalance among treatment groups; and (4) assigning the participant to the group with the larger minimum P value (ie, try to avoid more imbalance in groups).

Going back to the previous example of assigning the 10th participant (male and underweight) to a group, the Frane method would result in the assignment to the control group. The steps used to make this decision were calculating P values for each of the covariates using the χ 2 goodness-of-fit test represented in the Table . The t tests and ANOVAs were not used because the covariates in this example were categorical. Based on the Table , the lowest minimum P values were 1.0 for the control group and 0.317 for the treatment group. The 10th participant was assigned to the control group because of the higher minimum P value, which indicates better balance in the control group (1.0 > 0.317).

Probabilities From χ 2 Goodness-of-Fit Tests for the Example Shown in Figure 5 (Frane 18 Method)

Covariate adaptive randomization produces less imbalance than other conventional randomization methods and can be used successfully to balance important covariates among control and treatment groups. 6 Although the balance of covariates among groups using the stratified randomization method begins to fail when the number of blocks approaches half the sample size, covariate adaptive randomization can better handle the problem of increasing numbers of covariates (ie, increased block combinations). 9

One concern of these covariate adaptive randomization methods is that treatment assignments sometimes become highly predictable. Investigators using covariate adaptive randomization sometimes come to believe that group assignment for the next participant can be readily predicted, going against the basic concept of randomization. 12 , 26 , 27 This predictability stems from the ongoing assignment of participants to groups wherein the current allocation of participants may suggest future participant group assignment. In their review, Scott et al 9 argued that this predictability is also true of other methods, including stratified randomization, and it should not be overly penalized. Zielhuis et al 28 and Frane 18 suggested a practical approach to prevent predictability: a small number of participants should be randomly assigned into the groups before the covariate adaptive randomization technique being applied.

The complicated computation process of covariate adaptive randomization increases the administrative burden, thereby limiting its use in practice. A user-friendly computer program for covariate adaptive randomization is available (free of charge) upon request from the authors (M.K., B.G.R., or J.H.P.). 29

Conclusions

Our purpose was to introduce randomization, including its concept and significance, and to review several randomization techniques to guide athletic training researchers and practitioners to better design their randomized clinical trials. Many factors can affect the results of clinical research, but randomization is considered the gold standard in most clinical trials. It eliminates selection bias, ensures balance of sample size and baseline characteristics, and is an important step in guaranteeing the validity of statistical tests of significance used to compare treatment groups.

Before choosing a randomization method, several factors need to be considered, including the size of the clinical trial; the need for balance in sample size, covariates, or both; and participant enrollment. 16 Figure 6 depicts a flowchart designed to help select an appropriate randomization technique. For example, a power analysis for a clinical trial of different rehabilitation techniques after a surgical procedure indicated a sample size of 80. A well-known covariate for this study is age, which must be balanced among groups. Because of the nature of the study with postsurgical patients, participant recruitment and enrollment will be continuous. Using the flowchart, the appropriate randomization technique is covariate adaptive randomization technique.

Simple randomization works well for a large trial (eg, n > 200) but not for a small trial (n < 100). 7 To achieve balance in sample size, block randomization is desirable. To achieve balance in baseline characteristics, stratified randomization is widely used. Covariate adaptive randomization, however, can achieve better balance than other randomization methods and can be successfully used for clinical trials in an effective manner.

Acknowledgments

This study was partially supported by a Faculty Grant (FRCAC) from the College of Graduate Studies, at Middle Tennessee State University, Murfreesboro, TN.

Minsoo Kang, PhD; Brian G. Ragan, PhD, ATC; and Jae-Hyeon Park, PhD, contributed to conception and design; acquisition and analysis and interpretation of the data; and drafting, critical revision, and final approval of the article.