complete random assignment

Design and Analysis of Experiments with randomizr

Alexander coppock.

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

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

A hypothetical experiment

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

We first need to transform the dataset, which has each row describe a type of subject, to a new dataset in which each row describes an individual subject.

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

Our new dataset has 592 subjects. We have three pretreatment covariates, Hair , Eye , and Sex , which describe the hair color, eye color, and gender of each subject.

We now need to create simulated potential outcomes . We’ll call the untreated outcome Y0 and we’ll call the treated outcome Y1 . Imagine that in the absence of any intervention, the outcome ( Y0 ) is correlated with out pretreatment covariates. Imagine further that the effectiveness of the program varies according to these covariates, i.e., the difference between Y1 and Y0 is correlated with the pretreatment covariates.

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

We are now ready to allocate treatment assignments to subjects. Let’s start by contrasting simple and complete random assignment.

Simple random assignment

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

The simple_ra() function has one required argument N , the total number of subjects. If no other arguments are specified, simple_ra() assumes a two-group design and a 0.50 probability of assignment.

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

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

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

You can also name your treatment arms.

Complete random assignment

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

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

If you only specify N , complete_ra() assigns exactly half of the subjects to treatment.

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

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

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

Simple and Complete random assignment compared

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

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

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

In this simulation complete random assignment led to a -0.59% decrease in sampling variability. This decrease was obtained with a small design tweak that costs the researcher essentially nothing.

Block random assignment

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

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

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

The only required argument to block_ra() is blocks , which is a vector of length N that describes which block a unit belongs to. blocks can be a factor, character, or numeric variable. If no other arguments are specified, block_ra() assigns an approximately equal proportion of each block to treatment.

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

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

For finer control, use the block_m_each argument, which takes a matrix with as many rows as there are blocks, and as many columns as there are treatment conditions. Remember that the rows are in the same order as sort(unique(blocks)) , a command that is good to run before constructing a block_m_each matrix.

In the example above, the different blocks have different probabilities of assignment to treatment. In this case, people with Black hair have a 30/108 = 27.8% chance of being treated, those with Brown hair have 100/286 = 35.0% change, etc. Left unaddressed, this discrepancy could bias treatment effects. We can see this directly with the declare_ra() function.

There are two common ways to address this problem: LSDV (Least-Squares Dummy Variable, also known as “control for blocks”) or IPW (Inverse-probability weights).

The following code snippet shows how to use either the LSDV approach or the IPW approach. A note for scrupulous readers: the estimands of these two approaches are subtly different from one another. The LSDV approach estimates the average block-level treatment effect. The IPW approach estimates the average individual-level treatment effect. They can be different. Since the average block-level treatment effect is not what most people have in mind when thinking about causal effects, analysts using this approach should present both. The obtain_condition_probabilities() function used to calculate the probabilities of assignment is explained below.

How to create blocks? In the HairEyeColor dataset, we could make blocks for each unique combination of hair color, eye color, and sex.

An alternative is to use the blockTools package, which constructs matched pairs, trios, quartets, etc. from pretreatment covariates.

A note for blockTools users: that package also has an assignment function. My preference is to extract the blocking variable, then conduct the assignment with block_ra() , so that fewer steps are required to reconstruct the random assignment or generate new random assignments for a randomization inference procedure.

Clustered assignment

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

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

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

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

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

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

… or using conditions

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

Blocked and clustered assignment

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

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

Calculating probabilities of assignment

All five random assignment functions in randomizr assign units to treatment with known (if sometimes complicated) probabilities. The declare_ra() and obtain_condition_probabilities() functions calculate these probabilities according to the parameters of your experimental design.

Let’s take a look at the block random assignment we used before.

In order to calculate the probabilities of assignment, we call the declare_ra() function with the same exact arguments as we used for the block_ra() call. The declaration object contains a matrix of probabilities of assignment:

The prob_mat objects has N rows and as many columns as there are treatment conditions, in this case 2.

In order to use inverse-probability weights, we need to know the probability of each unit being in the condition that it is in . For each unit, we need to pick the appropriate probability. This bookkeeping is handled automatically by the obtain_condition_probabilities() function.

Best practices

Random assignment procedure = random assignment function.

Random assignment procedures are often described as a series of steps that are manually carried out be the researcher. In order to make this procedure reproducible, these steps need to be translated into a function that returns a different random assignment each time it is called.

For example, consider the following procedure for randomly allocating school vouchers.

Every eligible student’s names is put on a list
Each name is assigned a random number
Balls with the numbers associated with all students are put in an urn.
Then the urn is “shuffled”
Students names are drawn one by one from the urn until all slots are given out.
If one sibling in a family wins, all other siblings automatically win too.

If we write such a procedure into a function, it might look like this:

This assignment procedure is complicated by the sibling rule, which has two effects: first, students are cluster-assigned by family, and second, the probability of assignment varies student to student. Obviously, families who have two children in the lottery have a higher probability of winning the lottery because they effectively have two “tickets.” There may be better ways of running this assignment procedure (for example, with cluster_ra() ), but the purpose of this example is to show how complicated real-world procedures can be written up in a simple function. With this function, the random assignment procedure can be reproduced exactly, the complicated probabilities of assignment can be calculated, and the analysis is greatly simplified.

Check probabilities of assignment directly

For many designs, the probability of assignment to treatment can be calculated analytically. For example, in a completely randomized design with 200 units, 60 of which are assigned to treatment, the probability is exactly 0.30 for all units. However, in more complicated designs (such as the schools example described above), analytic probabilities are difficult to calculate. In such a situation, an easy way to obtain the probabilities of assignment is through simulation.

Call your random assignment function an approximately infinite number of times (about 10,000 for most purposes).
Count how often each unit is assigned to each treatment arm.

This plot shows that the students who have a sibling in the lottery have a higher probability of assignment. The more simulations, the more precise the estimate of the probability of assignment.

Save your random assignment

Whenever you conduct a random assignment for use in an experiment, save it! At a minimum, the random assignment should be saved with an id variable in a csv.

Random Assignment in Psychology: Definition & Examples

Julia Simkus

Editor at Simply Psychology

BA (Hons) Psychology, Princeton University

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

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Saul McLeod, PhD

Editor-in-Chief for Simply Psychology

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

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

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

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

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

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

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

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

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

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

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

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

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

Importance

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

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

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

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

Random Selection vs. Random Assignment

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

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

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

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

Random Assignment vs Random Sampling

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

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

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

When to Use Random Assignment

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

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

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

How to Use Random Assignment

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

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

When is Random Assignment not used?

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

Drawbacks of Random Assignment

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

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

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

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

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

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

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

What is the difference between random sampling and random assignment?

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

Does random assignment increase internal validity?

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

Does random assignment reduce sampling error?

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

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

When is random assignment not possible?

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

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

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

Does random assignment eliminate confounding variables?

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

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

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

Design and Analysis of Experiments with randomizr (Stata)

Alexander coppock.

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

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

A Hypothetical Experiment

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

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

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

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

Simple Random Assignment

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

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

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

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

You can also name your treatment arms.

Complete Random Assignment

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

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

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

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

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

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

Simple and Complete Random Assignment Compared

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

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

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

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

Block Random Assignment

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

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

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

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

Clustered Assignment

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

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

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

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

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

…or using conditions.

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

Block and Clustered Assignment

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

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Completely Randomized Design: The One-Factor Approach

Completely Randomized Design (CRD) is a research methodology in which experimental units are randomly assigned to treatments without any systematic bias. CRD gained prominence in the early 20th century, largely attributed to the pioneering work of statistician Ronald A. Fisher . His method addressed the inherent variability in experimental units by randomly assigning treatments, thus countering potential biases. Today, CRD serves as an indispensable tool in various domains, including agriculture, medicine, industrial engineering, and quality control analysis.

CRD is particularly favored in situations with limited control over external variables. By leveraging its inherent randomness, CRD neutralizes potentially confounding factors. As a result, each experimental unit has an equal likelihood of receiving any specific treatment, ensuring a level playing field. Such random allocation is pivotal in eliminating systematic bias and bolstering the validity of experimental conclusions.

While CRD may sometimes necessitate larger sample sizes , the improved accuracy and consistency it introduces to results often justify this requirement.

Understanding CRD

At its core, CRD is centered on harnessing randomness to achieve objective experimental outcomes. This approach effectively addresses unanticipated extraneous variables —those not included in the study design but that can still influence the response variable. In the context of CRD, these extraneous variables are expected to be uniformly distributed across treatments, thereby mitigating their potential influence.

A key aspect of CRD is the single-factor experiment. This means that the experiment revolves around changing or manipulating one primary independent variable (or factor) to ascertain its effect on the dependent variable . Consider these examples across different fields:

Medical: An experiment might be designed where the independent variable is the dosage of a new drug, and the dependent variable is the speed of patient recovery. Researchers would vary the drug dosage and observe its effect on recovery rates.
Agriculture: An agricultural study could alter the amount of water irrigation (independent variable) given to crops and measure the resulting crop yield (dependent variable) to determine the optimal irrigation level.
Psychology: A psychologist might introduce different intensities of a visual cue (independent variable) to participants and then measure their reaction times (dependent variable) to understand the cue's influence.
Environmental Science: Scientists might introduce different concentrations of a pollutant (independent variable) to a freshwater pond and measure the health and survival rate of aquatic life (dependent variable) in response.
Education: In an educational setting, researchers could change the duration of digital learning (independent variable) students receive daily and then observe its effect on test scores (dependent variable) at the end of the term.
Engineering: In material science, an experiment might adjust the temperature (independent variable) during the curing process of a polymer and then measure its resultant tensile strength (dependent variable).

For each of these scenarios, only one key factor or independent variable is intentionally varied, while any changes or outcomes in another variable (the dependent variable) are observed and recorded. This distinct focus on a single variable, while keeping all others constant or controlled, underscores the essence of the single-factor experiment in CRD.

Advantages of CRD

Understanding the strengths of Completely Randomized Design is pivotal for effectively applying this research tool and interpreting results accurately. Below is an exploration of the benefits of employing CRD in research studies.

Simplicity: One of the most appealing features of CRD is its straightforwardness. Focusing on a single primary factor, CRD is easier to understand and implement compared to more complex research designs.
Flexibility: CRD enhances versatility by allowing the inclusion of various experimental units and treatments through random assignment, enabling researchers to explore a range of variables.
Robustness: Despite its simplicity, CRD stands as a robust research tool. The consistent use of randomization minimizes biases and uniformly distributes the effects of uncontrolled variables across all groups, contributing to the reliability of the results.
Generalizability: Proper application of CRD enables the extension of research findings to a broader population. The minimization of selection bias , thanks to random assignment, increases the probability that the sample closely represents the larger population.

Disadvantages of CRD

While CRD is marked by simplicity, flexibility, robustness, and enhanced generalizability, it is essential to carefully consider its limitations. A thoughtful analysis of these aspects will guide researchers in making informed decisions about the applicability of CRD to their specific research context.

Ignoring Nuisance Variables: CRD operates primarily under the assumption that all treatments are equivalent aside from the independent variable. If strong nuisance factors vary systematically across treatments, this assumption becomes a limitation, making CRD less suitable for studies where nuisance variables significantly impact the results.
Need for Large Sample Size: The pooling of all experimental units into one extensive set necessitates a larger sample size, potentially leading to increased time, cost, and resource investment.
Inefficiency in Some Cases: CRD might demonstrate statistical inefficiency with significant within-treatment group variability . In such cases, other designs that account for this variability may offer enhanced efficiency.

Differentiating CRD from other research design methods

CRD stands out in the realm of research designs due to its foundational simplicity. While its essence lies in the random assignment of experimental units to treatments without any systematic bias, other designs introduce varying layers of complexity tailored to specific experimental needs.

For instance, consider the Randomized Block Design (RBD) . Unlike the straightforward approach of CRD, RBD divides experimental units into homogenous blocks, based on known sources of variability, before assigning treatments. This method is especially useful when there's an identifiable source of variability that researchers wish to control for. Similarly, the Latin Square Design , while also involving random assignment, operates on a grid system to simultaneously control for two lurking variables , adding another dimension of complexity not found in CRD.

Factorial Design investigates the effects and interactions of multiple independent variables. This design can reveal interactions that might be overlooked in simpler designs. Then there's the Crossover Design , often used in medical trials. Unlike CRD, where each unit experiences only one treatment, in Crossover Design, participants receive multiple treatments over different periods, allowing each participant to serve as their own control.

The choice of research design, whether it be CRD, RBD, Latin Square, or any of the other methods available, is fundamentally guided by the nature of the research question , the characteristics of the experimental units, and the specific objectives the study aims to achieve. However, it's the inherent simplicity and flexibility of CRD that often makes it the go-to choice, especially in scenarios with many units or treatments, where intricate stratification or blocking isn't necessary.

Let us further explore the advantages and disadvantages of each method.

While CRD's simplicity and flexibility make it a popular choice for many research scenarios, the optimal design depends on the specific needs, objectives, and contexts of the study. Researchers must carefully consider these factors to select the most suitable research design method.

The role of CRD in mitigating extraneous variables

Within the framework of experimental research, extraneous variables persistently challenge the validity of findings, potentially compromising the established relationship between independent and dependent variables . CRD is a methodological safeguard that systematically addresses these extraneous variables. Below, we describe specific types of extraneous variables and how CRD counteracts their potential influence:

Definition: Variables that induce variance in the dependent variable, yet are not of primary academic interest. While they don't muddle the relationship between the primary variables, their presence can augment within-group variability, reducing statistical power.
CRD's Countermeasure: Through the mechanism of random assignment, CRD ensures an equitably distributed influence of nuisance variables across all experimental conditions. This distribution, theoretically, leads to mutual nullification of their effects when assessing the efficacy of treatments.
Definition: Variables not explicitly incorporated within the study design but can influence its outcomes. Their impact often manifests post-hoc, rendering them alternative explanations for observed phenomena.
CRD's Countermeasure: Random assignment intrinsic to CRD assures a uniform distribution of these lurking variables across experimental conditions. This diminishes the probability of them systematically influencing one group, thus safeguarding the experiment's conclusions.
Definition: Variables that not only influence the dependent variable but also correlate with the independent variable. Their simultaneous influence can mislead interpretations of causality.
CRD's Countermeasure: The tenet of random assignment inherent in CRD ensures an equitable distribution of potential confounders among groups. This bolsters confidence in attributing observed effects predominantly to the experimental treatments.
Definition: Deliberately held constant to ensure that they do not introduce variability into the experiment. They are intentionally kept constant to preserve experimental integrity.
CRD's Countermeasure: While CRD focuses on randomization, the nature of the design inherently assumes that controlled variables remain constant across all experimental units. By maintaining these constants, CRD ensures that the focus remains solely on the treatment effects, further validating the experiment's findings.

The foundational principle underpinning the Completely Randomized Design—randomization—serves as a bulwark against the influences of extraneous variables. By uniformly distributing these variables across experimental conditions, CRD enhances the validity and reliability of experimental outcomes. However, researchers should exercise caution and continuously evaluate potential extraneous influences, even in randomized designs.

Selecting the independent variable

The selection of the independent variable is crucial for research design . This pivotal step not only shapes the direction and quality of the research but also underpins the understanding of causal relationships within the studied system, influencing the dependent variable or response. When choosing this essential component of experimental design , several critical considerations emerge:

Relevance: Paramount to the success of the experiment is the variable's direct relevance to the research query. For instance, in a botanical study of phototropism, the light's intensity or duration would naturally serve as the independent variable.
Measurability: The chosen variable should be quantifiable or categorizable, enabling distinctions between its varying levels or types.
Controllability: The research environment must allow for steadfast control over the variable, ensuring extraneous influences are kept at bay.
Ethical Considerations: In disciplines like social sciences or medical research, it's vital to consider the ethical implications . The chosen variable should withstand ethical scrutiny, safeguarding the well-being and rights of participants.

Identifying the independent variable necessitates a methodical and structured approach where each step aligns with the overarching research objective:

Review Literature: Thoroughly review existing literature to provide invaluable insights into past research and highlight unexplored areas.
Define the Scope: Clearly delineating research boundaries is crucial. For example, when studying dietary impacts on metabolic health, the variable could span from diet types (like keto, vegan, Mediterranean) to specific nutrients.
Determine Levels of the Variable: This involves understanding the various levels or categories the independent variable might have. In educational research, one might look beyond simply "innovative vs. conventional methods" to a broader range of teaching techniques.
Consider Potential Outcomes: Anticipating possible outcomes based on variations in the independent variable is beneficial. If potential outcomes seem too vast, the variable might need further refinement.

In academic discourse, while CRD is praised for its rigor and clarity, the effectiveness of the design relies heavily on the meticulous selection of the independent variable. Making this choice with thorough consideration ensures the research offers valuable insights with both academic and wider societal implications.

Applications of CRD

CRD has found wide and varied applications in several areas of research. Its versatility and fundamental simplicity make it an attractive option for scientists and researchers across a multitude of disciplines.

CRD in agricultural research

Agricultural research was among the earliest fields to adopt the use of Completely Randomized Design. The broad application of CRD within agriculture not only encompasses crop improvement but also the systematic analysis of various fertilizers, pesticides, and cropping techniques. Agricultural scientists leverage the CRD framework to scrutinize the effects on yield enhancement and bolstered disease resistance. The fundamental randomization in CRD effectively mitigates the influence of nuisance variables such as soil variations and microclimate differences, ensuring more reliable and valid experimental outcomes.

Additionally, CRD in agricultural research paves the way for robust testing of new agricultural products and methods. The unbiased allocation of treatments serves as a solid foundation for accurately determining the efficacy and potential downsides of innovative fertilizers, genetically modified seeds, and novel pest control methods, contributing to informed decision-making and policy formulation in agricultural development.

However, the limitations of CRD within the agricultural context warrant acknowledgment. While it offers an efficient and straightforward approach for experimental design, CRD may not always capture spatial variability within large agricultural fields adequately. Such unaccounted variations can potentially skew results, underscoring the necessity for employing more intricate experimental designs, such as the Randomized Complete Block Design (RCBD), where necessary. This adaptation enhances the reliability and generalizability of the research findings, ensuring their applicability to real-world agricultural challenges.

CRD in medical research

The fields of medical and health research substantially benefit from the application of Completely Randomized Design, especially in executing randomized control trials. Within this context, participants, whether patients or others, are randomly assigned to either the treatment or control groups. This structured random allocation minimizes the impact of extraneous variables, ensuring that the groups are comparable. It fortifies the assertion that any discernible differences in outcomes are genuinely attributable to the treatment being analyzed, enhancing the robustness and reliability of the research findings.

CRD's randomized nature in medical research allows for a more objective assessment of varied medical treatments and interventions. By mitigating the influence of extraneous variables, researchers can more accurately gauge the effectiveness and potential side effects of novel medical approaches, including pharmaceuticals and surgical techniques. This precision is crucial for the continual advancement of medical science, offering a solid empirical foundation for the refinement of treatments that improve health outcomes and patient quality of life.

However, like other fields, the application of CRD in medical research has its limitations. Despite its effectiveness in controlling various factors, CRD may not always consider the complexity of human health conditions where multiple variables often interact in intricate ways. Hence, while CRD remains a valuable tool for medical research, it is crucial to apply it judiciously and alongside other research designs to ensure comprehensive and reliable insights into medical treatments and interventions.

CRD in industrial engineering

In industrial engineering, Completely Randomized Design plays a significant role in process and product testing, offering a reliable structure for the evaluation and improvement of industrial systems. Engineers often employ CRD in single-factor experiments to analyze the effects of a particular factor on a certain outcome, enhancing the precision and objectivity of the assessment.

For example, to discern the impact of varying temperatures on the strength of a metal alloy, engineers might utilize CRD. In this scenario, the different temperatures represent the single factor, and the alloy samples are randomly allocated to be tested at each designated temperature. This random assignment minimizes the influence of extraneous variables, ensuring that the observed effects on alloy strength are primarily attributable to the temperature variations.

CRD's implementation in industrial engineering also assists in the optimization of manufacturing processes. Through random assignment and structured testing, engineers can effectively evaluate process parameters, such as production speed, material quality, and machine settings. By accurately assessing the influence of these factors on production efficiency and product quality, engineers can implement informed adjustments and enhancements, promoting optimal operational performance and superior product standards. This systematic approach, anchored by CRD, facilitates consistent and robust industrial advancements, bolstering overall productivity and innovation in industrial engineering.

Despite these advantages, it's crucial to acknowledge the limitations of CRD in industrial engineering contexts. The design is efficient for single-factor experiments but may falter with experiments involving multiple factors and interactions, common in industrial settings. This limitation underscores the importance of combining CRD with other experimental designs. Doing so navigates the complex landscape of industrial engineering research, ensuring insights are comprehensive, accurate, and actionable for continuous innovation in industrial operations.

CRD in quality control analysis

Completely Randomized Design is also beneficial in quality control analysis, where ensuring the consistency of products is paramount.

For instance, a manufacturer keen on minimizing product defects may deploy CRD to empirically assess the effectiveness of various inspection techniques. By randomly assigning different inspection methods to identical or similar production batches, the manufacturer can gather data regarding the most effective techniques for identifying and mitigating defects, bolstering overall product quality and consumer satisfaction.

Furthermore, the utility of CRD in quality control extends to the analysis of materials, machinery settings, or operational processes that are pivotal to final product quality. This design enables organizations to rigorously test and compare assorted conditions or settings, ensuring the selection of parameters that optimize both quality and efficiency. This approach to quality analysis not only bolsters the reliability and performance of products but also significantly augments the optimization of organizational resources, curtailing wastage and improving profitability.

However, similar to other CRD applications, it is crucial to understand its limitations. While CRD can significantly aid in the analysis and optimization of various aspects of quality control, its effectiveness may be constrained when dealing with multi-factorial scenarios with complex interactions. In such situations, other experimental designs, possibly in tandem with CRD, might offer more robust and comprehensive insights, ensuring that quality control measures are not only effective but also adaptable to evolving industrial and market demands.

Future applications and emerging fields for CRD

The breadth of applications for Completely Randomized Design continues to expand. Emerging fields such as data science, business analytics, and environmental studies are increasingly recognizing the value of CRD in conducting reliable and uncomplicated experiments. In the realm of data science, CRD can be invaluable in assessing the performance of different algorithms, models, or data processing techniques. It enables researchers to randomize the variables, minimizing biases and providing a clearer understanding of the real-world applicability and effectiveness of various data-centric solutions.

In the domain of business analytics, CRD is paving the way for robust analysis of business strategies and initiatives. Businesses can employ CRD to randomly assign strategies or processes across various departments or teams, allowing for a comprehensive assessment of their impact. The insights from such assessments empower organizations to make data-driven decisions, optimizing their operations, and enhancing overall productivity and profitability. This approach is particularly crucial in the business environment of today, characterized by rapid changes, intense competition, and escalating customer expectations, where informed and timely decision-making is a key determinant of success.

Moreover, in environmental studies, CRD is increasingly being used to evaluate the impact of various factors on environmental health and sustainability. For example, researchers might use CRD to study the effects of different pollutants, conservation strategies, or land use patterns on ecosystem health. The randomized design ensures that the conclusions drawn are robust and reliable, providing a solid foundation for the development of policies and initiatives. As environmental concerns continue to mount, the role of reliable experimental designs like CRD in facilitating meaningful research and informed policy-making cannot be overstated.

Planning and conducting a CRD experiment

A CRD experiment involves meticulous planning and execution, outlined in the following structured steps. Each phase, from the preparatory steps to data collection and analysis, plays a pivotal role in bolstering the integrity and success of the experiment, ensuring that the findings stand as a valuable contribution to scientific knowledge and understanding.

Selecting Participants in a Random Manner: The heart of a CRD experiment is randomness. Regardless of whether the subjects are human participants, animals, plants, or objects, their selection must be truly random. This level of randomness ensures that every participant has an equal likelihood of being assigned to any treatment group, which plays a crucial role in eliminating selection bias.
Understanding and Selecting the Independent Variable: This is the variable of interest – the one that researchers aim to manipulate to observe its effects. Identifying and understanding this factor is pivotal. Its selection depends on the experiment's primary research question or hypothesis , and its clear definition is essential to ensuring the experiment's clarity and success.
The Process of Random Assignment in Experiments: Following the identification of subjects and the independent variable, researchers must randomly allocate subjects to various treatment groups. This process, known as random assignment, typically involves using random number generators or other statistical tools , ensuring that the principle of randomness is upheld.
Implementing the Single-factor Experiment: After random assignment, researchers can launch the main experiment. At this stage, they introduce the independent variable to the designated treatment groups, ensuring that all other conditions remain consistent across groups. The goal is to make certain that any observed effect or change is attributed only to the manipulation of the independent variable.
Data Cleaning and Preparation: The first step post-collection is to prepare and clean the data . This process involves rectifying errors, handling missing or inconsistent data, and eradicating duplicates. Employing tools like statistical software or languages such as Python and R can be immensely helpful. Handling outliers and maintaining consistency throughout the dataset is essential for accurate subsequent analysis.
Statistical Analysis Methods: The next step involves analyzing the data using appropriate statistical methodologies, dependent on the nature of the data and research questions . Analysis can range from basic descriptive statistics to complex inferential statistics or even advanced statistical modeling.
Interpreting the Results: Analysis culminates in the interpretation of results, wherein researchers draw conclusions based on the statistical outcomes. This stage is crucial in CRD, as it determines if observed effects can be attributed to the independent variable's manipulation or if they occurred purely by chance. Apart from statistical significance, the practical implications and relevance of the results also play a vital role in determining the experiment's success and potential real-world applications.

Navigating common challenges in CRD

While the Completely Randomized Design offers numerous advantages, researchers often encounter specific challenges when implementing it in real-world experiments. Recognizing these challenges early and being prepared with strategies to address them can significantly improve the integrity and success of the CRD experiment. Let's delve into some of the most common challenges and explore potential solutions:

Lack of Homogeneity: One foundational assumption of CRD is the homogeneity of experimental units . However, in reality, there may be inherent variability among units. To mitigate this, researchers can use stratified sampling or consider employing a randomized block design.
Improper Randomization: The essence of CRD is randomization. However, it's not uncommon for some researchers to inadvertently introduce biases during the assignment. Utilizing computerized random number generators or statistical software can help ensure true randomization.
Limited Number of Experimental Units: Sometimes, the available experimental units might be fewer than required for a robust experiment. In such cases, using a larger number of replications can help, albeit at the cost of increased resources.
Extraneous Variables: These external factors can influence the outcome of an experiment. They make it hard to attribute observed effects solely to the independent variable. Careful experimental design, pre-experimental testing, and post-experimental analysis can help identify and control these extraneous variables.
Overlooking Practical Significance: Even if a CRD experiment yields statistically significant results, these might not always be practically significant. Researchers need to assess the real-world implications of their findings, considering factors like cost, feasibility, and the magnitude of observed effects.
Data-related Challenges: From missing data to outliers, data-related issues may skew results. Regular data cleaning, rigorous validation, and employing robust statistical methods can help address these challenges.

While CRD is a powerful tool in experimental research, its successful implementation hinges on the researcher's ability to anticipate, recognize, and navigate challenges that might arise. By being proactive and employing strategies to mitigate potential pitfalls, researchers can maximize the reliability and validity of their CRD experiments, ensuring meaningful and impactful results.

In summary, the Completely Randomized Design holds a pivotal place in the field of research owing to its simplicity and straightforward approach. Its essence lies in the unbiased random assignment of experimental units to various treatments, ensuring the reliability and validity of the results. Although it may not control for other variables and often requires larger sample sizes, its ease of implementation frequently outweighs these drawbacks, solidifying it as a preferred choice for researchers across many fields.

Looking ahead, the future of CRD remains bright. As research continues to evolve, we anticipate the integration of CRD with more sophisticated design techniques and advanced analytical tools. This synergy will likely enhance the efficiency and applicability of CRD in varied research contexts, perpetuating its legacy as a fundamental research design method. While other designs might offer more control and complexity, the fundamental simplicity of CRD will continue to hold significant value in the rapidly evolving research landscape.

Moving forward, it is imperative to champion continuous learning and exploration in the field of CRD. Engaging in educational opportunities, staying abreast of the latest research and advancements, and actively participating in pertinent discussions and forums can markedly enrich understanding and expertise in CRD. Embracing this ongoing learning journey will not only bolster individual research skills but also make a significant contribution to the broader scientific community, fueling innovation and discovery in numerous fields of study.

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The Definition of Random Assignment According to Psychology

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

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

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

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

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

Random Assignment In Research

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

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

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

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

Random Selection

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

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

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

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

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

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

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

Example of Random Assignment

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

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

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

A Word From Verywell

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

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

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

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

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

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

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

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Chapter 6: Experimental Research

Experimental Design

Learning Objectives

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

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

Between-Subjects Experiments

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

Random Assignment

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

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

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

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

Treatment and Control Conditions

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

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

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

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

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

The Powerful Placebo

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

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

Within-Subjects Experiments

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

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

Carryover Effects and Counterbalancing

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

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

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

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

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

When 9 is “larger” than 221

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

Simultaneous Within-Subjects Designs

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

Between-Subjects or Within-Subjects?

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

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

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

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

Key Takeaways

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

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

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

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

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

A condition in a study where participants receive treatment.

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

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

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

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

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

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

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

Each participant is tested under all conditions.

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

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

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

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

Testing different participants in different orders.

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

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randomizr Easy-to-Use Tools for Common Forms of Random Assignment and Sampling

Design and Analysis of Experiments with randomizr
block_and_cluster_ra: Blocked and Clustered Random Assignment
block_and_cluster_ra_probabilities: probabilities of assignment: Blocked and Clustered Random...
block_ra: Block Random Assignment
block_ra_probabilities: probabilities of assignment: Block Random Assignment
cluster_ra: Cluster Random Assignment
cluster_ra_probabilities: probabilities of assignment: Cluster Random Assignment
cluster_rs: Cluster Random Sampling
cluster_rs_probabilities: Inclusion Probabilities: Cluster Sampling
complete_ra: Complete Random Assignment
complete_ra_probabilities: probabilities of assignment: Complete Random Assignment
complete_rs: Complete Random Sampling
complete_rs_probabilities: Inclusion Probabilities: Complete Random Sampling
conduct_ra: Conduct a random assignment
custom_ra: Custom Random Assignment
custom_ra_probabilities: probabilities of assignment: Custom Random Assignment
declare_ra: Declare a random assignment procedure.
declare_rs: Declare a random sampling procedure.
draw_rs: Draw a random sample
obtain_condition_probabilities: Obtain the probabilities of units being in the conditions...
obtain_inclusion_probabilities: Obtain inclusion probabilities
obtain_num_permutations: Obtain the Number of Possible Permutations from a Random...
obtain_permutation_matrix: Obtain Permutation Matrix from a Random Assignment...
obtain_permutation_probabilities: Obtain the probabilities of permutations
randomizr: randomizr
simple_ra: Simple Random Assignment
simple_ra_probabilities: probabilities of assignment: Simple Random Assignment
simple_rs: Simple Random Sampling
simple_rs_probabilities: Inclusion Probabilities: Simple Random Sampling
strata_and_cluster_rs: Stratified and Clustered Random Sampling
strata_and_cluster_rs_probabilities: Inclusion Probabilities: Stratified and Clustered Random...
strata_rs: Stratified Random Sampling
strata_rs_probabilities: Inclusion Probabilities: Stratified Random Sampling
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complete_ra : Complete Random Assignment In randomizr: Easy-to-Use Tools for Common Forms of Random Assignment and Sampling

View source: R/complete_ra.R

Complete Random Assignment

Description.

complete_ra implements a random assignment procedure in which fixed numbers of units are assigned to treatment conditions. The canonical example of complete random assignment is a procedure in which exactly m of N units are assigned to treatment and N-m units are assigned to control. Users can set the exact number of units to assign to each condition with m or m_each. Alternatively, users can specify probabilities of assignment with prob or prob_each and complete_ra will infer the correct number of units to assign to each condition. In a two-arm design, complete_ra will either assign floor(N*prob) or ceiling(N*prob) units to treatment, choosing between these two values to ensure that the overall probability of assignment is exactly prob. In a multi-arm design, complete_ra will first assign floor(N*prob_each) units to their respective conditions, then will assign the remaining units using simple random assignment, choosing these second-stage probabilities so that the overall probabilities of assignment are exactly prob_each. In most cases, users should specify N and not more than one of m, m_each, prob, prob_each, or num_arms. If only N is specified, a two-arm trial in which N/2 units are assigned to treatment is assumed. If N is odd, either floor(N/2) units or ceiling(N/2) units will be assigned to treatment.

A vector of length N that indicates the treatment condition of each unit. Is numeric in a two-arm trial and a factor variable (ordered by conditions) in a multi-arm trial.

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5.2 Experimental Design

Learning objectives.

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

Between-Subjects Experiments

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

Random Assignment

One problem with coin flipping and other strict procedures for random assignment is that they are likely to result in unequal sample sizes in the different conditions. Unequal sample sizes are generally not a serious problem, and you should never throw away data you have already collected to achieve equal sample sizes. However, for a fixed number of participants, it is statistically most efficient to divide them into equal-sized groups. It is standard practice, therefore, to use a kind of modified random assignment that keeps the number of participants in each group as similar as possible. One approach is block randomization . In block randomization, all the conditions occur once in the sequence before any of them is repeated. Then they all occur again before any of them is repeated again. Within each of these “blocks,” the conditions occur in a random order. Again, the sequence of conditions is usually generated before any participants are tested, and each new participant is assigned to the next condition in the sequence. Table 5.2 shows such a sequence for assigning nine participants to three conditions. The Research Randomizer website ( http://www.randomizer.org ) will generate block randomization sequences for any number of participants and conditions. Again, when the procedure is computerized, the computer program often handles the block randomization.

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

Matched Groups

An alternative to simple random assignment of participants to conditions is the use of a matched-groups design . Using this design, participants in the various conditions are matched on the dependent variable or on some extraneous variable(s) prior the manipulation of the independent variable. This guarantees that these variables will not be confounded across the experimental conditions. For instance, if we want to determine whether expressive writing affects people’s health then we could start by measuring various health-related variables in our prospective research participants. We could then use that information to rank-order participants according to how healthy or unhealthy they are. Next, the two healthiest participants would be randomly assigned to complete different conditions (one would be randomly assigned to the traumatic experiences writing condition and the other to the neutral writing condition). The next two healthiest participants would then be randomly assigned to complete different conditions, and so on until the two least healthy participants. This method would ensure that participants in the traumatic experiences writing condition are matched to participants in the neutral writing condition with respect to health at the beginning of the study. If at the end of the experiment, a difference in health was detected across the two conditions, then we would know that it is due to the writing manipulation and not to pre-existing differences in health.

Within-Subjects Experiments

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

One disadvantage of within-subjects experiments is that they make it easier for participants to guess the hypothesis. For example, a participant who is asked to judge the guilt of an attractive defendant and then is asked to judge the guilt of an unattractive defendant is likely to guess that the hypothesis is that defendant attractiveness affects judgments of guilt. This knowledge could lead the participant to judge the unattractive defendant more harshly because he thinks this is what he is expected to do. Or it could make participants judge the two defendants similarly in an effort to be “fair.”

Carryover Effects and Counterbalancing

The primary disadvantage of within-subjects designs is that they can result in order effects. An order effect occurs when participants’ responses in the various conditions are affected by the order of conditions to which they were exposed. One type of order effect is a carryover effect. A carryover effect is an effect of being tested in one condition on participants’ behavior in later conditions. One type of carryover effect is a practice effect , where participants perform a task better in later conditions because they have had a chance to practice it. Another type is a fatigue effect , where participants perform a task worse in later conditions because they become tired or bored. Being tested in one condition can also change how participants perceive stimuli or interpret their task in later conditions. This type of effect is called a context effect (or contrast effect) . For example, an average-looking defendant might be judged more harshly when participants have just judged an attractive defendant than when they have just judged an unattractive defendant. Within-subjects experiments also make it easier for participants to guess the hypothesis. For example, a participant who is asked to judge the guilt of an attractive defendant and then is asked to judge the guilt of an unattractive defendant is likely to guess that the hypothesis is that defendant attractiveness affects judgments of guilt.

There is a solution to the problem of order effects, however, that can be used in many situations. It is counterbalancing , which means testing different participants in different orders. The best method of counterbalancing is complete counterbalancing in which an equal number of participants complete each possible order of conditions. For example, half of the participants would be tested in the attractive defendant condition followed by the unattractive defendant condition, and others half would be tested in the unattractive condition followed by the attractive condition. With three conditions, there would be six different orders (ABC, ACB, BAC, BCA, CAB, and CBA), so some participants would be tested in each of the six orders. With four conditions, there would be 24 different orders; with five conditions there would be 120 possible orders. With counterbalancing, participants are assigned to orders randomly, using the techniques we have already discussed. Thus, random assignment plays an important role in within-subjects designs just as in between-subjects designs. Here, instead of randomly assigning to conditions, they are randomly assigned to different orders of conditions. In fact, it can safely be said that if a study does not involve random assignment in one form or another, it is not an experiment.

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

You can see in the diagram above that the square has been constructed to ensure that each condition appears at each ordinal position (A appears first once, second once, third once, and fourth once) and each condition preceded and follows each other condition one time. A Latin square for an experiment with 6 conditions would by 6 x 6 in dimension, one for an experiment with 8 conditions would be 8 x 8 in dimension, and so on. So while complete counterbalancing of 6 conditions would require 720 orders, a Latin square would only require 6 orders.

Finally, when the number of conditions is large experiments can use random counterbalancing in which the order of the conditions is randomly determined for each participant. Using this technique every possible order of conditions is determined and then one of these orders is randomly selected for each participant. This is not as powerful a technique as complete counterbalancing or partial counterbalancing using a Latin squares design. Use of random counterbalancing will result in more random error, but if order effects are likely to be small and the number of conditions is large, this is an option available to researchers.

When 9 Is “Larger” Than 221

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

Simultaneous Within-Subjects Designs

Between-Subjects or Within-Subjects?

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

Key Takeaways

Experiments can be conducted using either between-subjects or within-subjects designs. Deciding which to use in a particular situation requires careful consideration of the pros and cons of each approach.
Random assignment to conditions in between-subjects experiments or counterbalancing of orders of conditions in within-subjects experiments is a fundamental element of experimental research. The purpose of these techniques is to control extraneous variables so that they do not become confounding variables.
You want to test the relative effectiveness of two training programs for running a marathon.
Using photographs of people as stimuli, you want to see if smiling people are perceived as more intelligent than people who are not smiling.
In a field experiment, you want to see if the way a panhandler is dressed (neatly vs. sloppily) affects whether or not passersby give him any money.
You want to see if concrete nouns (e.g., dog ) are recalled better than abstract nouns (e.g., truth).
Birnbaum, M.H. (1999). How to show that 9>221: Collect judgments in a between-subjects design. Psychological Methods, 4 (3), 243-249. ↵

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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.

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.

Prevent plagiarism, run a free check.

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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15 Random Assignment Examples

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random assignment examples and definition, explained below

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):

a representation of a treatment condition showing 12 red people in the cohort

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:

a representation of a treatment condition showing 4 red people in the cohort

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.

How to Create a Responsibility Assignment Matrix (RAM) in 2025

8 mins read

by Zuri Baker

Updated On Nov 07, 2024

In the world of project management, creating a Responsibility Assignment Matrix (RAM) is essential for establishing clarity in team roles and responsibilities.

A Responsibility Assignment Matrix (RAM) is a project management tool used to identify key team members and organizations involved in a project, and clearly define each one's role.

The structured approach improves efficiency by mapping out clear expectations, enhancing communication, and minimizing project delays .

For instance, low role clarity is linked to a 3x higher rate of prolonged sickness absence in white-collar workers, emphasizing the need for tools like the RAM to mitigate such risks.

This guide will help you understand the importance of RAM in project management and the key components to improve your accountability and team collaboration.

Understanding the RACI Matrix: A Specialized Type of RAM

A RACI Matrix is a type of RAM, basically a table or a spreadsheet that highlights project stakeholders and their roles, denoted by Responsible, Accountable, Consulted, and Informed.

Here is what each term represents:

Understanding the RACI Matrix: A Specialized Type of RAM

Responsible : The "Responsible" designation is assigned to employees or professionals who are accountable for ensuring the completion of the work or deliverables. Typically, this is someone on the project team, often developers or creators. Every task must have at least one responsible person, though there may be several.

Accountable : The accountable role oversees and ensures that tasks are understood and completed on time. The role is essential for delegation and review and is typically held by a manager or leader. Each task should have only one accountable individual.

“In the application of RACI, Accountable is the most important step, as it ensures that there is absolute clarity on who is ensuring that the tasks are delivered on time and correctly. Making a single person accountable for a task means that there is clear ownership of a task, and as a CEO, I can clearly point out who is delivering and who is not.”

CEO & Executive Leadership EML, Kevin Murphy. .

Consulted: Consulted individuals offer feedback on tasks, providing insights based on their stakes in the project’s outcomes. Teams should seek their input before beginning tasks, during progress, and upon completion to incorporate feedback.

Informed: Those designated as “Informed” need regular updates on the project’s progress, as it may impact their work, but they aren’t involved in the task’s decision-making or detailed processes. Informed parties are typically from outside the project team and often include heads of related departments or senior leadership.

Why and When Do You Need a Responsibility Assignment Matrix?

The RACI matrix framework is beneficial for nearly any project, although its utility may vary across different teams.

Take for example, while drafting this article, I assume the role of the responsible party, as I am executing the writing. My editor holds accountability for the assignment and review of the content, likely consulting and informing others, such as a managing editor or an SEO manager.

In simpler projects, where tasks and stakeholders are limited, a formal RACI chart may not be essential. However, for complex, long-term initiatives involving numerous tasks and stakeholders, especially when tasks overlap, having a RACI matrix is crucial.

It is easy to overlook critical needs and requirements. Therefore, project managers typically implement a RACI chart to capture essential details and foster clear communication throughout the project duration.

Step-by-Step Guide to Creating a Responsibility Assignment Matrix

Step 1: identify project tasks and deliverables.

Begin by listing all project tasks and deliverables to ensure comprehensive coverage of what needs to be accomplished. The process involves breaking down the project into smaller, manageable components, making it easier to assign roles and responsibilities later. A clear understanding of the tasks lays the groundwork for effective collaboration and accountability.

Step 2: Define Team Roles and Stakeholders

Next, outline the roles of each team member and identify all relevant stakeholders involved in the project. You clarify who will be responsible for specific tasks and who will be consulted or informed during the project lifecycle. By defining the roles, you create a structured environment that promotes transparency and encourages engagement.

Step 3: Assign Responsibilities Using the RACI Framework

Utilize the RACI framework to assign specific responsibilities to each role defined in the previous step. In this matrix, designate individuals as Responsible, Accountable, Consulted, or Informed for each task and deliverable. The approach enhances accountability , ensuring that everyone understands their contributions to the project's success.

Step 4: Review and Refine Your RAM with Team Input

After completing the initial draft of the Responsibility Assignment Matrix, gather input from your team to refine and improve it. Collaborating with team members helps identify any oversights, clarify ambiguities, and ensure that the matrix accurately reflects the project’s needs. The process fosters a sense of ownership among team members and enhances commitment.

Step 5: Finalize and Distribute the RAM to All Stakeholders

Once your RAM has been reviewed and refined, finalize the document and distribute it to all relevant stakeholders. Sharing the completed matrix ensures everyone is on the same page regarding their roles and responsibilities, enhancing communication and collaboration. The step maintains clarity throughout the project and supports the effective execution of tasks.

According to a research report by Ardhendu Mandal, University of North Bengal, duplicated effort or work duplication is one of the major reasons for software project failures.

Common Mistakes to Avoid When Creating a RACI Matrix

Planning : Creating a RACI matrix should not be your initial step in project planning. Before developing the matrix, ensure you have assembled a full project team and established a comprehensive understanding of the project scope and key tasks. Without this foundation, the matrix may become disorganized and challenging to maintain.
Avoiding an Overly Large Team : The complexity of the RACI matrix increases with larger teams, potentially leading to confusion rather than clarity. A matrix with numerous roles or stakeholders may hinder responsibility tracking and dilute accountability. For larger teams, consider dividing the project into smaller, more manageable segments, or explore other frameworks.
Communicating Clearly with the Project Team : The purpose of a RACI matrix is to formalize, not introduce, responsibilities. Ensure that all team members understand their roles and the project’s goals before the matrix is created. Conducting a kickoff meeting to discuss tasks and responsibilities helps align everyone and prevent confusion during project execution.
Preventing Team Overload : Assigning too many roles to a single team member can lead to burnout and decreased efficiency. If one person is responsible and accountable for multiple tasks, they may become overextended and unable to perform effectively. Regularly review the RACI matrix to confirm that workload distribution remains balanced and that no single team member is overburdened.
Avoiding Decision-Making Delays : If accountability for decision-making is not assigned, delays may occur as teams wait for approvals. Such bottlenecks can slow project progress and lead to frustration. You identify who holds the decision-making authority to ensure a smoother workflow and prevent key tasks from stalling due to indecision.

“I strongly agree with the point about no duplication of roles, especially for decision making. Having one and only one decision maker for each decision point brings clarity and accountability. This is not to say that other stakeholder's should not have a voice. They should absolutely voice their viewpoint & concerns. However, everyone needs to know who is the ultimate decision maker for the decision in question.”

Product Director & Mentor, Mehdi Piraee .

The Most Common Misconceptions About RAMs

It's time-consuming:.

A common misconception is that using the RACI matrix is too time-consuming because it involves multiple parties, causing even small tasks to take longer. However, while initial setup may require time, the matrix ultimately streamlines communication and decision-making, saving time throughout the project's lifecycle.

It's Too Complex:

While some may perceive the RACI matrix as complicated, it is a straightforward tool designed to clarify roles and responsibilities within a project. Outlining who is responsible, accountable, consulted, and informed, simplifies communication among team members.

It's Unnecessary:

Contrary to the belief that the RACI matrix is superfluous, it serves as an invaluable tool for tracking project progress and fostering accountability. By clearly defining roles, it helps ensure that everyone understands their contributions, minimizing confusion and enhancing productivity.

It Restricts Team Flexibility:

Some argue that the RACI matrix limits team flexibility; however, it establishes a framework that supports decision-making while encouraging adaptability. By clarifying responsibilities, team members can quickly respond to changing circumstances without losing sight of their roles.

It's Only Useful for Large Projects:

Some project managers think the RACI matrix is only applicable to large-scale projects; however, it can be beneficial for projects of any size. Whether managing a small initiative or a large endeavor, the tool helps to define roles and ensure accountability.

5 Main Benefits of Using a RACI Matrix

1. Clarifies Roles and Responsibilities: Clearly defines who is responsible, accountable, consulted, and informed for each task, minimizing ambiguity.

2. Enhances Collaboration : Facilitates teamwork, especially in complex projects with overlapping tasks, by ensuring everyone knows their role.

3. Prevents Oversights: Reduces the risk of missed steps or unassigned tasks, particularly useful in projects involving numerous stakeholders and milestones.

4. Streamlines Communication: Maintains efficient communication by keeping only relevant people informed, thus avoiding excessive meetings and miscommunication.

5. Improves Efficiency in Complex Projects: Vital for extensive projects like website redesigns, where multiple departments (design, marketing, development) need to work together seamlessly.

What are the Best Practices for Implementing a Responsibility Assignment Matrix?

Here are some best practices for implementing a Responsibility Assignment Matrix (RAM), also referred to as a RACI matrix or RACI chart: You can also have a look at the below example of RAM.

Define Project Scope : Clearly outline the project's scope and objectives to ensure all team members understand expectations. Clarity helps prevent scope creep and highlights key tasks.
Identify Tasks and Responsibilities : Compile a comprehensive list of tasks needed to complete the project and assign specific roles and responsibilities to individuals and teams.
Assign Resources : Allocate necessary resources, including personnel, equipment, and materials, to each task to ensure effective execution.
Communicate : Maintain open lines of communication regarding the RAM to keep everyone updated and facilitate swift resolution of any issues.
Monitor Progress : Regularly track project progress and adjust resources as needed to stay on target.
Update the RAM : Continuously update the RAM throughout the project to keep all stakeholders informed of any changes.
Use the RAM to Identify Risks : Leverage the RAM to identify potential risks and issues early on so they can be addressed proactively.
Conduct a Stakeholder Analysis : Perform a stakeholder analysis early in the project to gain insights into the project's dynamics and identify necessary improvements.

Responsibility Assignment Matrix Usage Example

Background : In the realm of incident management, the primary objective is to swiftly restore business operations and mitigate any negative impact on services. Ensuring service quality and availability is paramount, and one effective metric for evaluating system reliability is the Mean Time to Recovery (MTTR). The study focuses on the roles and responsibilities inherent in incident management within IT service organizations, particularly when addressing unexpected system-wide outages.

Key activities, such as troubleshooting and coordination among team members, are essential for efficient service restoration. The capacity to effectively manage and direct diverse personnel and systems is crucial for maintaining situational awareness and adapting to ongoing changes.

Challenges : Organizations face numerous challenges in incident management, particularly during unplanned outages that disrupt services. Resource limitations often result in a reactive rather than proactive approach to incident resolution, complicating recovery efforts. Additionally, the need for situational awareness is often underestimated, leading to ineffective communication and collaboration among stakeholders.

The complexity of managing multiple tasks and teams can result in unclear responsibilities, which further hinders timely resolution. Many companies struggle with defining roles within the incident response framework, leading to confusion and delays in addressing critical issues.

Solutions : To address these challenges, implementing a Responsibility Assignment Matrix (RACI) provides a structured approach to defining roles within the incident management process. By mapping stakeholder responsibilities to the RACI framework, organizations can clarify who is responsible, accountable, consulted, and informed for each task. This structured approach enhances communication and collaboration, allowing teams to coordinate their efforts more effectively.

Integrating RACI matrices with the Business Process Model and Notation (BPMN) facilitates a clearer understanding of the incident management workflow.

Results : The implementation of the RACI matrix in incident management has demonstrated significant improvements in the handling of critical outages. Organizations have reported reduced MTTR as clarity in roles leads to faster identification and resolution of issues. By establishing well-defined responsibilities, teams experience increased accountability and ownership of tasks, which enhances overall performance. The integration of RACI with BPMN has resulted in more streamlined workflows, allowing for better tracking and management of incident response activities.

RACI Alternatives

RAPID : A structured decision-making framework guiding you through who Recommends, Agrees, Performs, Inputs, and ultimately Decides on critical decisions.
Gantt Chart : A visual tool that gives you a complete overview of tasks, showing who is responsible, what each task involves, and when it should be completed.
Work Breakdown Structure : This tool breaks down the full scope of your project, detailing all tasks in a clear, hierarchical format to ensure thorough coverage.
Project Dashboard : A dynamic, real-time resource keeping you updated with the latest information on project progress, roles, and responsibilities.

Free Responsibility Assignment Matrix Templates

Explore the collection of free Responsibility Assignment Matrix templates. These ready-to-use templates simplify the process of defining roles and responsibilities for your projects, helping to improve team collaboration and ensure tasks are managed efficiently. Download and customize them to fit your project needs and get started right away!

Template 1:

This template will enable you to assign tasks to stakeholders and employees, depending on the designation categories, Responsible, Accountable, Consulted, and Informed. The template is downloadable, customizable and free.

Click here to download the template

Template 2:

This streamlined RACI matrix template enables project managers, sponsors, team members, and stakeholders to easily track roles and responsibilities. Simply enter your project title, phases, and tasks, then assign team members accordingly.

Use the RACI designations to specify who is Responsible, Accountable, Consulted, and Informed for each task. Customizable and user-friendly, this template ensures effective management and completion of project deliverables.

Popularly Known Tools for Responsibility Assignment Matrix

You can assign roles like Responsible or Accountable directly within project boards.
You can also integrate RACI for clear accountability and to avoid task overlap.
Facilitates team collaboration with visible RACI assignments in one view.
To access Asana, visit Asana: https://asana.com
Allows you to link RACI roles to specific project tickets for task accountability.
Enables detailed progress tracking through reporting features.
Aligns with RACI by clarifying each stage's decision and approval process.
To access this tool visit Jira: https://jira.com
Use labels and categories to represent RACI roles visually.
Card-based layout aids small teams in managing responsibilities easily.
Provides clarity on task ownership at each project stage.
Visit Trello: https://trello.com to access this tool.

With these project resource allocation tools and templates, project managers can easily track each resource's daily rate, total cost, and overall resource cost for your project.

Empower your Team with the Skills to Effectively Implement RACI with Edstellar

Empowering your teams with the right skills is essential for effective project management and organizational success. Edstellar specializes in providing tailored training solutions that help organizations master key frameworks like RACI, ensuring clear roles, improved communication, and stronger accountability. By partnering with us, you’re not just implementing a framework you’re fostering a culture of collaboration, alignment, and productivity.

Let’s work together to build a stronger, more capable workforce for the future.

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COMMENTS

Random Assignment in Experiments
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.
Design and Analysis of Experiments with randomizr
Complete random assignment. Complete random assignment is very similar to simple random assignment, except that the researcher can specify exactly how many units are assigned to each condition.. The syntax for complete_ra() is very similar to that of simple_ra().The argument m is the number of units assigned to treatment in two-arm designs; it is analogous to simple_ra()'s prob.
Random Assignment in Psychology: Definition & Examples
Olivia Guy-Evans, MSc. 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 ...
Random Assignment in Experiments
By Jim Frost 4 Comments. Random assignment uses chance to assign subjects to the control and treatment groups in an experiment. This process helps ensure that the groups are equivalent at the beginning of the study, which makes it safer to assume the treatments caused any differences between groups that the experimenters observe at the end of ...
Complete Random Assignment
complete_ra implements a random assignment procedure in which fixed numbers of units are assigned to treatment conditions. The canonical example of complete random assignment is a procedure in which exactly m of N units are assigned to treatment and N-m units are assigned to control. Users can set the exact number of units to assign to each condition with m or m_each. Alternatively, users can ...
PDF randomizr: : CHEAT SHEET
Complete random assignment allocates a fixed number of units to each condition. Block random assignment conducts complete random assignment separately for groups of units. The *_each arguments in randomizr functions specify design parameters for each arm separately. Cluster random assignment allocates whole groups of units to conditions together.
7.2: Completely Randomized Design
Figure 7.2.1 7.2. 1: Greenhouse floor plan, showing arrangement of the 24 plants. We need to be able to randomly assign each of the treatment levels to 6 potted plants. To do this, assign physical position numbers on the bench for placing the pots. Figure 7.2.2 7.2. 2: Greenhouse floor plan, with the plant locations numbered in a grid pattern.
Design and Analysis of Experiments with randomizr (Stata)
Block Random Assignment. Block random assignment (sometimes known as stratified random assignment) is a powerful tool when used well. In this design, subjects are sorted into blocks (strata) according to their pre-treatment covariates, and then complete random assignment is conducted within each block.
34.4
To create a random assignment for a completely randomized design with two factors, you can just modify the IF statement in the previous example. The following program generates a random assignment of treatments to 30 subjects, in which Factor A has 2 levels and Factor B has 3 levels (and hence 6 treatments). The code is similar to the code from ...
How to Randomly Assign Subjects to Experimental Groups
Random assignment is a process used in experimental research to allocate subjects into different groups—such as treatment and control groups—using a random method. The goal is to distribute participants in a way that each individual has the same probability of being placed in any group. By doing so, researchers ensure that differences ...
PDF Completely Randomized Designs
Completely random assignment of treatments to units Completely random assignment means that every possible grouping of units into g groups with the given sample sizes is equally likely. This is the basic experimental design; everything else is a modi cation.1 The CRD is Easiest to do.
Completely Randomized Design: The One-Factor Approach
Completely Randomized Design (CRD) is a research methodology in which experimental units are randomly assigned to treatments without any systematic bias. CRD gained prominence in the early 20th century, largely attributed to the pioneering work of statistician Ronald A. Fisher. His method addressed the inherent variability in experimental units by randomly assigning treatments, thus countering ...
The Definition of Random Assignment In Psychology
Materio / Getty Images. Random assignment refers to the use of chance procedures in psychology experiments to ensure that each participant has the same opportunity to be assigned to any given group in a study to eliminate any potential bias in the experiment at the outset. Participants are randomly assigned to different groups, such as the ...
Experimental Design
Random assignment is a method for assigning participants in a sample to the different conditions, and it is an important element of all experimental research in psychology and other fields too. In its strictest sense, random assignment should meet two criteria. One is that each participant has an equal chance of being assigned to each condition ...
complete_ra: Complete Random Assignment in randomizr: Easy-to-Use Tools
The canonical example of complete random assignment is a procedure in which exactly m of N units are assigned to treatment and N-m units are assigned to control. Users can set the exact number of units to assign to each condition with m or m_each. Alternatively, users can specify probabilities of assignment with prob or prob_each and complete ...
Guide to Experimental Design
A completely randomized design vs a randomized block design. A between-subjects design vs a within-subjects design. Randomization. An experiment can be completely randomized or randomized within blocks (aka strata): In a completely randomized design, every subject is assigned to a treatment group at random.
5.2 Experimental Design
Random assignment is a method for assigning participants in a sample to the different conditions, and it is an important element of all experimental research in psychology and other fields too. In its strictest sense, random assignment should meet two criteria. One is that each participant has an equal chance of being assigned to each condition ...
Random Assignment in Psychology (Intro for Students)
If there are two conditions in an experiment, then the simplest way to implement random assignment is to flip a coin for each participant. Heads means being assigned to the treatment and tails means being assigned to the control (or vice versa). 3. Rolling a die. Rolling a single die is another way to randomly assign participants.
Random Assignment in Experiments
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 ...
15 Random Assignment Examples
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 ...
Random Forest
Random Forest creates different training sets for each tree by randomly picking data points from the original training set, with some numbers appearing multiple times. The unused data points become test sets for checking each tree's performance. ... Start at root node with complete bootstrap sample. When building each decision tree, Random ...
Responsibility Assignment Matrix: A Complete Guide [2025]
A Responsibility Assignment Matrix (RAM) is a project management tool used to identify key team members and organizations involved in a project, and clearly define each one's role. ... Compile a comprehensive list of tasks needed to complete the project and assign specific roles and responsibilities to individuals and teams. Assign Resources ...

Design and Analysis of Experiments with randomizr

A hypothetical experiment

Simple random assignment

Complete random assignment

Simple and Complete random assignment compared

Block random assignment

Clustered assignment

Blocked and clustered assignment

Calculating probabilities of assignment

Best practices

Check probabilities of assignment directly

Save your random assignment

Random Assignment in Psychology: Definition & Examples

Importance

Random Selection vs. Random Assignment

Random Assignment vs Random Sampling

When to Use Random Assignment

How to Use Random Assignment

When is Random Assignment not used?

Drawbacks of Random Assignment

What is the difference between random sampling and random assignment?

Does random assignment increase internal validity?

Does random assignment reduce sampling error?

When is random assignment not possible?

Does random assignment eliminate confounding variables?

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

Further Reading

Design and Analysis of Experiments with randomizr (Stata)

A Hypothetical Experiment

Simple Random Assignment

Complete Random Assignment

Simple and Complete Random Assignment Compared

Block Random Assignment

Clustered Assignment

Block and Clustered Assignment

Completely Randomized Design: The One-Factor Approach

Understanding CRD

Advantages of CRD

Disadvantages of CRD

Differentiating CRD from other research design methods

The role of CRD in mitigating extraneous variables

Selecting the independent variable

Applications of CRD

CRD in agricultural research

CRD in medical research

CRD in industrial engineering

CRD in quality control analysis

Future applications and emerging fields for CRD

Planning and conducting a CRD experiment

Navigating common challenges in CRD

The Definition of Random Assignment According to Psychology

Random Assignment In Research

Random Selection

Example of Random Assignment

A Word From Verywell

Experimental Design

Between-Subjects Experiments

Random Assignment

Treatment and Control Conditions

Within-Subjects Experiments

Carryover Effects and Counterbalancing

Simultaneous Within-Subjects Designs

Between-Subjects or Within-Subjects?

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randomizr Easy-to-Use Tools for Common Forms of Random Assignment and Sampling

complete_ra : Complete Random Assignment In randomizr: Easy-to-Use Tools for Common Forms of Random Assignment and Sampling

Complete Random Assignment

Related to complete_ra in randomizr ...

5.2 Experimental Design

Between-Subjects Experiments

Random Assignment

Matched Groups

Within-Subjects Experiments

Carryover Effects and Counterbalancing

When 9 Is “Larger” Than 221

Simultaneous Within-Subjects Designs

Between-Subjects or Within-Subjects?

Key Takeaways

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