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• Random Assignment in Experiments | Introduction & Examples

Random Assignment in Experiments | Introduction & Examples

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

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

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

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

Table of contents

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Random assignment in block designs

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

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

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

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

When comparing different groups

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

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

When it’s not ethically permissible

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

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

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

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

Research bias

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Importance 

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

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

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

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

Random Selection vs. Random Assignment 

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

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

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

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

Random Assignment vs Random Sampling

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

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

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

When to Use Random Assignment

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

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

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

How to Use Random Assignment

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

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

When is Random Assignment not used?

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

Drawbacks of Random Assignment

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

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

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

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

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

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

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

What is the difference between random sampling and random assignment?

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

Does random assignment increase internal validity?

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

Does random assignment reduce sampling error?

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

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

When is random assignment not possible?

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

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

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

Does random assignment eliminate confounding variables?

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

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

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

Further Reading

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

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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."

Random Assignment in Psychology (Intro for Students)

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

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

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

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

Why Researchers Use Random Assignment

Researchers use random assignment to control for confounds in research.

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

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

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

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

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

Fact File: Experiments 101

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

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

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

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

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

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

Methods of Random Assignment

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

1. Random number generator

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

2. Flipping a coin

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

3. Rolling a die

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

4. Condition names in a hat

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

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

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

Read About More Methods and Examples of Random Assignment Here

Potential Confounding Effects

Random assignment is all about minimizing confounding effects.

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

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

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

Limitations of the Random Assignment Procedure

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

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

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

Applications of Random Assignment

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

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

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

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

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

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

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

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

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

Boruch, R. F. (1998). Randomized controlled experiments for evaluation and planning. Handbook of applied social research methods , 161-191.

Box, G. E., Hunter, W. G., & Hunter, J. S. (2005). Design of experiments: Statistics for Experimenters: Design, Innovation and Discovery.

Dehue, T. (1997). Deception, efficiency, and random groups: Psychology and the gradual origination of the random group design. Isis , 88 (4), 653-673.

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

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

Goldberg, M. H. (2019). How often does random assignment fail? Estimates and recommendations. Journal of Environmental Psychology , 66 , 101351.

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

Lindquist, E. F. (1953). Design and analysis of experiments in psychology and education . Boston: Houghton Mifflin Company.

Marks, H. M. (1997). The progress of experiment: Science and therapeutic reform in the United States, 1900-1990 . Cambridge University Press.

Myers, J. L. (1972). Fundamentals of experimental design (2nd ed.). Allyn & Bacon.

Ong-Dean, C., Huie Hofstetter, C., & Strick, B. R. (2011). Challenges and dilemmas in implementing random assignment in educational research. American Journal of Evaluation , 32 (1), 29-49.

Orr, L. L. (1999). Social experiments: Evaluating public programs with experimental methods . Sage.

Shadish, W. R., Cook, T. D., & Campbell, D. T. (2002). Quasi-experiments: interrupted time-series designs. Experimental and quasi-experimental designs for generalized causal inference , 171-205.

Stigler, S. M. (1992). A historical view of statistical concepts in psychology and educational research. American Journal of Education , 101 (1), 60-70.

Dave Cornell (PhD)

Dr. Cornell has worked in education for more than 20 years. His work has involved designing teacher certification for Trinity College in London and in-service training for state governments in the United States. He has trained kindergarten teachers in 8 countries and helped businessmen and women open baby centers and kindergartens in 3 countries.

• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 25 Positive Punishment Examples
• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 25 Dissociation Examples (Psychology)
• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 15 Zone of Proximal Development Examples
• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ Perception Checking: 15 Examples and Definition

Chris Drew (PhD)

This article was peer-reviewed and edited by Chris Drew (PhD). The review process on Helpful Professor involves having a PhD level expert fact check, edit, and contribute to articles. Reviewers ensure all content reflects expert academic consensus and is backed up with reference to academic studies. Dr. Drew has published over 20 academic articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education and holds a PhD in Education from ACU.

• Chris Drew (PhD) #molongui-disabled-link 25 Positive Punishment Examples
• Chris Drew (PhD) #molongui-disabled-link 25 Dissociation Examples (Psychology)
• Chris Drew (PhD) #molongui-disabled-link 15 Zone of Proximal Development Examples
• Chris Drew (PhD) #molongui-disabled-link Perception Checking: 15 Examples and Definition

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Random Assignment in Psychology (Definition + 40 Examples)

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

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

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

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

History of Random Assignment

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

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

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

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

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

Early Studies Utilizing Random Assignment

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

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

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

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

Evolution of the Methodology

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

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

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

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

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

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

Principles of Random Assignment

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

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

Basic Principles of Random Assignment

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

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

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

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

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

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

Theoretical Foundation

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

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

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

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

Differentiating Random Assignment from Random Selection

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

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

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

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

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

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

Methodology of Random Assignment

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

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

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

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

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

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

Tools and Techniques Used

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

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

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

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

Ethical Considerations

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

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

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

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

Conclusion of Methodology

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

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

Benefits of Random Assignment in Psychological Research

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

Facilitating Causal Inferences

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

This ability to determine the cause is called causal inference .

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

Ensuring Internal Validity

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

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

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

Enhancing Generalizability

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

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

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

Limitations of Random Assignment

Potential for implementation issues.

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

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

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

Ethical Dilemmas

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

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

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

Generalizability Concerns

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

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

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

Practical and Real-World Limitations

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

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

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

Response to Critiques

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

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

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

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

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

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

Real-World Applications and Examples

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

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

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

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

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

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

Real-world Impact of Random Assignment

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

Health and Medicine

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

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

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

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

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

Workplace and Organizational Behavior

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

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

Environmental and Social Changes

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

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

Technology and Human Interaction

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

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

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

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

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

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

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

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

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

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

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6.2 Experimental Design

Learning objectives.

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

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

Between-Subjects Experiments

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

Random Assignment

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

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

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

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

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

Treatment and Control Conditions

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

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

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

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

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

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

The Powerful Placebo

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

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

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

Army Medicine – Surgery – CC BY 2.0.

Within-Subjects Experiments

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

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

Carryover Effects and Counterbalancing

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

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

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

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

When 9 Is “Larger” Than 221

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

Simultaneous Within-Subjects Designs

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

Between-Subjects or Within-Subjects?

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

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

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

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

Key Takeaways

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

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

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

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

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

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

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

Research Methods in Psychology Copyright © 2016 by University of Minnesota is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Causation and Experiments

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CO-3: Describe the strengths and limitations of designed experiments and observational studies.

Learning Objectives

LO 3.2: Explain how the study design impacts the types of conclusions that can be drawn.

LO 3.3: Identify and define key features of experimental design (randomized, blind etc.).

Video: Causation and Experiments (8:57)

Recall that in an experiment, it is the researchers who assign values of the explanatory variable to the participants. The key to ensuring that individuals differ only with respect to explanatory values — which is also the key to establishing causation — lies in the way this assignment is carried out. Let’s return to the smoking cessation study as a context to explore the essential ingredients of experimental design.

In our discussion of the distinction between observational studies and experiments, we described the following experiment: collect a representative sample of 1,000 individuals from the population of smokers who are just now trying to quit. We divide the sample into 4 groups of 250 and instruct each group to use a different method to quit. One year later, we contact the same 1,000 individuals and determine whose attempts succeeded while using our designated method.

This was an experiment, because the researchers themselves determined the values of the explanatory variable of interest for the individuals studied, rather than letting them choose.

We will begin by using the context of this smoking cessation example to illustrate the specialized vocabulary of experiments. First of all, the explanatory variable, or factor , in this case is the method used to quit. The different imposed values of the explanatory variable, or treatments (common abbreviation: ttt), consist of the four possible quitting methods. The groups receiving different treatments are called treatment groups . The group that tries to quit without drugs or therapy could be called the control group — those individuals on whom no specific treatment was imposed. Ideally, the subjects (human participants in an experiment) in each treatment group differ from those in the other treatment groups only with respect to the treatment (quitting method). As mentioned in our discussion of why lurking variables prevent us from establishing causation in observational studies, eliminating all other differences among treatment groups will be the key to asserting causation via an experiment. How can this be accomplished?

Randomized Controlled Experiments

Your intuition may already tell you, correctly, that random assignment to treatments is the best way to prevent treatment groups of individuals from differing from each other in ways other than the treatment assigned. Either computer software or tables can be utilized to accomplish the random assignment. The resulting design is called a randomized controlled experiment, because researchers control values of the explanatory variable with a randomization procedure. Under random assignment, the groups should not differ significantly with respect to any potential lurking variable. Then, if we see a relationship between the explanatory and response variables, we have evidence that it is a causal one.

• Note that in a randomized controlled experiment, a randomization procedure may be used in two phases. First, a sample of subjects is collected. Ideally it would be a random sample so that it would be perfectly representative of the entire population.
• Often researchers have no choice but to recruit volunteers. Using volunteers may help to offset one of the drawbacks to experimentation which will be discussed later, namely the problem of noncompliance.
• Second, we assign individuals randomly to the treatment groups to ensure that the only difference between them will be due to the treatment and we can get evidence of causation. At this stage, randomization is vital.

Let’s discuss some other issues related to experimentation.

Inclusion of a Control Group

A common misconception is that an experiment must include a control group of individuals receiving no treatment. There may be situations where a complete lack of treatment is not an option, or where including a control group is ethically questionable, or where researchers explore the effects of a treatment without making a comparison. Here are a few examples:

If doctors want to conduct an experiment to determine whether Prograf or Cyclosporin is more effective as an immunosuppressant, they could randomly assign transplant patients to take one or the other of the drugs. It would, of course, be unethical to include a control group of patients not receiving any immunosuppressants.

Recently, experiments have been conducted in which the treatment is a highly invasive brain surgery. The only way to have a legitimate control group in this case is to randomly assign half of the subjects to undergo the entire surgery except for the actual treatment component (inserting stem cells into the brain). This, of course, is also ethically problematic (but, believe it or not, is being done).

There may even be an experiment designed with only a single treatment. For example, makers of a new hair product may ask a sample of individuals to treat their hair with that product over a period of several weeks, then assess how manageable their hair has become. Such a design is clearly flawed because of the absence of a comparison group, but it is still an experiment because use of the product has been imposed by its manufacturers, rather than chosen naturally by the individuals. A flawed experiment is nevertheless an experiment.

• In the context of observational studies, we control for a confounding variable by separating it out.
• Referring to an experiment as a controlled experiment stresses that the values of the experiment’s explanatory variables (factors) have been assigned by researchers, as opposed to having occurred naturally.
• In the context of experiments, the control group consists of subjects who do not receive a treatment, but who are otherwise handled identically to those who do receive the treatment.

Learn By Doing: Random Assignment to Treatment Groups (Software)

Blind and Double-Blind Experiments

Suppose the experiment about methods for quitting smoking were carried out with randomized assignments of subjects to the four treatments, and researchers determined that the percentage succeeding with the combination drug/therapy method was highest, and the percentage succeeding with no drugs or therapy was lowest. In other words, suppose there is clear evidence of an association between method used and success rate. Could it be concluded that the drug/therapy method causes success more than trying to quit without using drugs or therapy? Perhaps.

Although randomized controlled experiments do give us a better chance of pinning down the effects of the explanatory variable of interest, they are not completely problem-free. For example, suppose that the manufacturers of the smoking cessation drug had just launched a very high-profile advertising campaign with the goal of convincing people that their drug is extremely effective as a method of quitting.

Even with a randomized assignment to treatments, there would be an important difference among subjects in the four groups: those in the drug and combination drug/therapy groups would perceive their treatment as being a promising one, and may be more likely to succeed just because of added confidence in the success of their assigned method. Therefore, the ideal circumstance is for the subjects to be unaware of which treatment is being administered to them: in other words, subjects in an experiment should be (if possible) blind to which treatment they received.

How could researchers arrange for subjects to be blind when the treatment involved is a drug? They could administer a placebo pill to the control group, so that there are no psychological differences between those who receive the drug and those who do not. The word “placebo” is derived from a Latin word that means “to please.” It is so named because of the natural tendency of human subjects to improve just because of the “pleasing” idea of being treated, regardless of the benefits of the treatment itself. When patients improve because they are told they are receiving treatment, even though they are not actually receiving treatment, this is known as the placebo effect.

Next, how could researchers arrange for subjects to be blind when the treatment involved is a type of therapy? This is more problematic. Clearly, subjects must be aware of whether they are undergoing some type of therapy or not. There is no practical way to administer a “placebo” therapy to some subjects. Thus, the relative success of the drug/therapy treatment may be due to subjects’ enhanced confidence in the success of the method they happened to be assigned. We may feel fairly certain that the method itself causes success in quitting, but we cannot be absolutely sure.

When the response of interest is fairly straightforward, such as giving up cigarettes or not, then recording its values is a simple process in which researchers need not use their own judgment in making an assessment. There are many experiments where the response of interest is less definite, such as whether or not a cancer patient has improved, or whether or not a psychiatric patient is less depressed. In such cases, it is important for researchers who evaluate the response to be blind to which treatment the subject received, in order to prevent the experimenter effect from influencing their assessments. If neither the subjects nor the researchers know who was assigned what treatment, then the experiment is called double-blind.

The most reliable way to determine whether the explanatory variable is actually causing changes in the response variable is to carry out a randomized controlled double-blind experiment . Depending on the variables of interest, such a design may not be entirely feasible, but the closer researchers get to achieving this ideal design, the more convincing their claims of causation (or lack thereof) are.

Did I Get This?: Experiments

Pitfalls in Experimentation

Some of the inherent difficulties that may be encountered in experimentation are the Hawthorne effect, lack of realism, noncompliance, and treatments that are unethical, impossible, or impractical to impose.

We already introduced a hypothetical experiment to determine if people tend to snack more while they watch TV:

• Recruit participants for the study.
• While they are presumably waiting to be interviewed, half of the individuals sit in a waiting room with snacks available and a TV on. The other half sit in a waiting room with snacks available and no TV, just magazines.
• Researchers determine whether people consume more snacks in the TV setting.

Suppose that, in fact, the subjects who sat in the waiting room with the TV consumed more snacks than those who sat in the room without the TV. Could we conclude that in their everyday lives, and in their own homes, people eat more snacks when the TV is on? Not necessarily, because people’s behavior in this very controlled setting may be quite different from their ordinary behavior.

If they suspect their snacking behavior is being observed, they may alter their behavior, either consciously or subconsciously. This phenomenon, whereby people in an experiment behave differently from how they would normally behave, is called the Hawthorne effect . Even if they don’t suspect they are being observed in the waiting room, the relationship between TV and snacking in the waiting room might not be representative of what it is in real life.

One of the greatest advantages of an experiment — that researchers take control of the explanatory variable — can also be a disadvantage in that it may result in a rather unrealistic setting. Lack of realism (also called lack of ecological validity ) is a possible drawback to the use of an experiment rather than an observational study to explore a relationship. Depending on the explanatory variable of interest, it may be quite easy or it may be virtually impossible to take control of the variable’s values and still maintain a fairly natural setting.

In our hypothetical smoking cessation example, both the observational study and the experiment were carried out on a random sample of 1,000 smokers with intentions to quit. In the case of the observational study, it would be reasonably feasible to locate 1,000 such people in the population at large, identify their intended method, and contact them again a year later to establish whether they succeeded or not.

In the case of the experiment, it is not so easy to take control of the explanatory variable (cessation method) merely by telling all 1,000 subjects what method they must use. Noncompliance (failure to submit to the assigned treatment) could enter in on such a large scale as to render the results invalid.

In order to ensure that the subjects in each treatment group actually undergo the assigned treatment, researchers would need to pay for the treatment and make it easily available. The cost of doing that for a group of 1,000 people would go beyond the budget of most researchers.

Even if the drugs or therapy were paid for, it is very unlikely that most of the subjects contacted at random would be willing to use a method not of their own choosing, but dictated by the researchers. From a practical standpoint, such a study would most likely be carried out on a smaller group of volunteers, recruited via flyers or some other sort of advertisement.

The fact that they are volunteers might make them somewhat different from the larger population of smokers with intentions to quit, but it would reduce the more worrisome problem of non-compliance. Volunteers may have a better overall chance of success, but if researchers are primarily concerned with which method is most successful, then the relative success of the various methods should be roughly the same for the volunteer sample as it would be for the general population, as long as the methods are randomly assigned. Thus, the most vital stage for randomization in an experiment is during the assignment of treatments, rather than the selection of subjects.

There are other, more serious drawbacks to experimentation, as illustrated in the following hypothetical examples:

Suppose researchers want to determine if the drug Ecstasy causes memory loss. One possible design would be to take a group of volunteers and randomly assign some to take Ecstasy on a regular basis, while the others are given a placebo. Test them periodically to see if the Ecstasy group experiences more memory problems than the placebo group.

The obvious flaw in this experiment is that it is unethical (and actually also illegal) to administer a dangerous drug like Ecstasy, even if the subjects are volunteers. The only feasible design to seek answers to this particular research question would be an observational study.

Suppose researchers want to determine whether females wash their hair more frequently than males.

It is impossible to assign some subjects to be female and others male, and so an experiment is not an option here. Again, an observational study would be the only way to proceed.

Suppose researchers want to determine whether being in a lower income bracket may be responsible for obesity in women, at least to some extent, because they can’t afford more nutritious meals and don’t have the means to participate in fitness activities.

The socioeconomic status of the study subject is a variable that cannot be controlled by the researchers, so an experiment is impossible. (Even if the researchers could somehow raise the money to provide a random sample of women with substantial salaries, the effects of their eating habits during their lives before the study began would still be present, and would affect the study’s outcome.)

These examples should convince you that, depending on the variables of interest, researching their relationship via an experiment may be too unrealistic, unethical, or impractical. Observational studies are subject to flaws, but often they are the only recourse.

Let’s summarize what we’ve learned so far:

1. Observational studies:

• The explanatory variable’s values are allowed to occur naturally.
• Because of the possibility of lurking variables, it is difficult to establish causation.
• If possible, control for suspected lurking variables by studying groups of similar individuals separately.
• Some lurking variables are difficult to control for; others may not be identified.

2. Experiments

• The explanatory variable’s values are controlled by researchers (treatment is imposed).
• Randomized assignment to treatments automatically controls for all lurking variables.
• Making subjects blind avoids the placebo effect.
• Making researchers blind avoids conscious or subconscious influences on their subjective assessment of responses.
• A randomized controlled double-blind experiment is generally optimal for establishing causation.
• A lack of realism may prevent researchers from generalizing experimental results to real-life situations.
• Noncompliance may undermine an experiment. A volunteer sample might solve (at least partially) this problem.
• It is impossible, impractical, or unethical to impose some treatments.

More About Experiments

Video: More About Experiments (4:09)

Experiments With More Than One Explanatory Variable

It is not uncommon for experiments to feature two or more explanatory variables (called factors). In this course, we focus on exploratory data analysis and statistical inference in situations which involve only one explanatory variable. Nevertheless, we will now consider the design for experiments involving several explanatory variables, in order to familiarize students with their basic structure.

Suppose researchers are not only interested in the effect of diet on blood pressure, but also the effect of two new drugs. Subjects are assigned to either Control Diet (no restrictions), Diet #1, or Diet #2, (the variable diet has, then, 3 possible values) and are also assigned to receive either Placebo, Drug #1, or Drug #2 (the variable Drug, then, also has three values). This is an example where the experiment has two explanatory variables and a response variable. In order to set up such an experiment, there has to be one treatment group for every combination of categories of the two explanatory variables . Thus, in this case there are 3 * 3 = 9 combinations of the two variables to which the subjects are assigned. The treatment groups are illustrated and labeled in the following table:

Subjects would be randomly assigned to one of the nine treatment groups. If we find differences in the proportions of subjects who achieve the lower “moderate zone” blood pressure among the nine treatment groups, then we have evidence that the diets and/or drugs may be effective for reducing blood pressure.

• Recall that randomization may be employed at two stages of an experiment: in the selection of subjects, and in the assignment of treatments. The former may be helpful in allowing us to generalize what occurs among our subjects to what would occur in the general population, but the reality of most experimental settings is that a convenience or volunteer sample is used. Most likely the blood pressure study described above would use volunteer subjects. The important thing is to make sure these subjects are randomly assigned to one of the nine treatment combinations.
• In order to gain optimal information about individuals in all the various treatment groups, we would like to make assignments not just randomly, but also evenly. If there are 90 subjects in the blood pressure study described above, and 9 possible treatment groups, then each group should be filled randomly with 10 individuals. A simple random sample of 10 could be taken from the larger group of 90, and those individuals would be assigned to the first treatment group. Next, the second treatment group would be filled by a simple random sample of 10 taken from the remaining 80 subjects. This process would be repeated until all 9 groups are filled with 10 individuals each.

Did I Get This?: Experiments #2

Modifications to Randomization

In some cases, an experiment’s design may be enhanced by relaxing the requirement of total randomization and blocking the subjects first, dividing them into groups of individuals who are similar with respect to an outside variable that may be important in the relationship being studied. This can help ensure that the effect of treatments, as well as background variables, are most precisely measured. In blocking, we simply split the sampled subjects into blocks based upon the different values of the background variable, and then randomly allocate treatments within each block. Thus, blocking in the assignment of subjects is analogous to stratification in sampling.

For example, consider again our experiment examining the differences between three versions of software from the last Learn By Doing activity. If we suspected that gender might affect individuals’ software preferences, we might choose to allocate subjects to separate blocks, one for males and one for females. Within each block, subjects are randomly assigned to treatments and the treatment proceeds as usual. A diagram of blocking in this situation is below:

Suppose producers of gasoline want to compare which of two types of gas results in better mileage for automobiles. In case the size of the vehicle plays a role in the effectiveness of different types of gasoline, they could first block by vehicle size, then randomly assign some cars within each block to Gasoline A and others to Gasoline B:

In the extreme, researchers may examine a relationship for a sample of blocks of just two individuals who are similar in many important respects, or even the same individual whose responses are compared for two explanatory values.

For example, researchers could compare the effects of Gasoline A and Gasoline B when both are used on the same car, for a sample of many cars of various sizes and models.

Such a study design, called matched pairs, may enable us to pinpoint the effects of the explanatory variable by comparing responses for the same individual under two explanatory values, or for two individuals who are as similar as possible except that the first gets one treatment, and the second gets another (or serves as the control). Treatments should usually be assigned at random within each pair, or the order of treatments should be randomized for each individual. In our gasoline example, for each car the order of testing (Gasoline A first, or Gasoline B first) should be randomized.

Suppose researchers want to compare the relative merits of toothpastes with and without tartar control ingredients. In order to make the comparison between individuals who are as similar as possible with respect to background and diet, they could obtain a sample of identical twins. One of each pair would randomly be assigned to brush with the tartar control toothpaste, while the other would brush with regular toothpaste of the same brand. These would be provided in unmarked tubes, so that the subjects would be blind. To make the experiment double-blind, dentists who evaluate the results would not know who used which toothpaste.

“Before-and-after” studies are another common type of matched pairs design. For each individual, the response variable of interest is measured twice: first before the treatment, then again after the treatment. The categorical explanatory variable is which treatment was applied, or whether a treatment was applied, to that participant.

• We have explained data production as a two-stage process: first obtain the sample, then evaluate the variables of interest via an appropriate study design. Even though the steps are carried out in this order chronologically, it is generally best for researchers to decide on a study design before they actually obtain the sample. For the toothpaste example above, researchers would first decide to use the matched pairs design, then obtain a sample of identical twins, then carry out the experiment and assess the results.

Did I Get This?: More About Experiments

What Is Random Assignment in Psychology?

Categories Research Methods

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Random assignment means that every participant has the same chance of being chosen for the experimental or control group. It involves using procedures that rely on chance to assign participants to groups. Doing this means that every participant in a study has an equal opportunity to be assigned to any group.

For example, in a psychology experiment, participants might be assigned to either a control or experimental group. Some experiments might only have one experimental group, while others may have several treatment variations.

Using random assignment means that each participant has the same chance of being assigned to any of these groups.

Table of Contents

How to Use Random Assignment

So what type of procedures might psychologists utilize for random assignment? Strategies can include:

• Flipping a coin
• Assigning random numbers
• Rolling dice
• Drawing names out of a hat

How Does Random Assignment Work?

A psychology experiment aims to determine if changes in one variable lead to changes in another variable. Researchers will first begin by coming up with a hypothesis. Once researchers have an idea of what they think they might find in a population, they will come up with an experimental design and then recruit participants for their study.

Once they have a pool of participants representative of the population they are interested in looking at, they will randomly assign the participants to their groups.

• Control group : Some participants will end up in the control group, which serves as a baseline and does not receive the independent variables.
• Experimental group : Other participants will end up in the experimental groups that receive some form of the independent variables.

By using random assignment, the researchers make it more likely that the groups are equal at the start of the experiment. Since the groups are the same on other variables, it can be assumed that any changes that occur are the result of varying the independent variables.

After a treatment has been administered, the researchers will then collect data in order to determine if the independent variable had any impact on the dependent variable.

Random Assignment vs. Random Selection

It is important to remember that random assignment is not the same thing as random selection , also known as random sampling.

Random selection instead involves how people are chosen to be in a study. Using random selection, every member of a population stands an equal chance of being chosen for a study or experiment.

So random sampling affects how participants are chosen for a study, while random assignment affects how participants are then assigned to groups.

Examples of Random Assignment

Imagine that a psychology researcher is conducting an experiment to determine if getting adequate sleep the night before an exam results in better test scores.

Forming a Hypothesis

They hypothesize that participants who get 8 hours of sleep will do better on a math exam than participants who only get 4 hours of sleep.

Obtaining Participants

The researcher starts by obtaining a pool of participants. They find 100 participants from a local university. Half of the participants are female, and half are male.

Randomly Assign Participants to Groups

The researcher then assigns random numbers to each participant and uses a random number generator to randomly assign each number to either the 4-hour or 8-hour sleep groups.

Conduct the Experiment

Those in the 8-hour sleep group agree to sleep for 8 hours that night, while those in the 4-hour group agree to wake up after only 4 hours. The following day, all of the participants meet in a classroom.

Collect and Analyze Data

Everyone takes the same math test. The test scores are then compared to see if the amount of sleep the night before had any impact on test scores.

Why Is Random Assignment Important in Psychology Research?

Random assignment is important in psychology research because it helps improve a study’s internal validity. This means that the researchers are sure that the study demonstrates a cause-and-effect relationship between an independent and dependent variable.

Random assignment improves the internal validity by minimizing the risk that there are systematic differences in the participants who are in each group.

Key Points to Remember About Random Assignment

• Random assignment in psychology involves each participant having an equal chance of being chosen for any of the groups, including the control and experimental groups.
• It helps control for potential confounding variables, reducing the likelihood of pre-existing differences between groups.
• This method enhances the internal validity of experiments, allowing researchers to draw more reliable conclusions about cause-and-effect relationships.
• Random assignment is crucial for creating comparable groups and increasing the scientific rigor of psychological studies.

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

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

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

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

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

Research Methods, Data Collection and Ethics Copyright © 2020 by Valerie Sheppard is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Experimental Research

24 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.

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 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 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 they are 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 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

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 do so.

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. 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. 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 precedes 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.

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) [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

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. 

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 any effect of the independent variable upon the dependent variable. Within-subjects experiments also require fewer participants than between-subjects experiments to detect an effect of the same size.

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.

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.

• 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 tested in only one condition.

Means using a random process to decide which participants are tested in which conditions.

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

An experiment design in which the participants in the various conditions are matched on the dependent variable or on some extraneous variable(s) prior the manipulation of the independent variable.

An experiment in which each participant is tested under all conditions.

An effect that occurs when participants' responses in the various conditions are affected by the order of conditions to which they were exposed.

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

An effect where participants perform a task better in later conditions because they have had a chance to practice it.

An effect where participants perform a task worse in later conditions because they become tired or bored.

Unintended influences on respondents’ answers because they are not related to the content of the item but to the context in which the item appears.

Varying the order of the conditions in which participants are tested, to help solve the problem of order effects in within-subjects experiments.

A method in which an equal number of participants complete each possible order of conditions. 

A method in which the order of the conditions is randomly determined for each participant.

Research Methods in Psychology Copyright © 2019 by Rajiv S. Jhangiani, I-Chant A. Chiang, Carrie Cuttler, & Dana C. Leighton is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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RESEARCH RANDOMIZER

Random sampling and random assignment made easy.

Research Randomizer is a free resource for researchers and students in need of a quick way to generate random numbers or assign participants to experimental conditions. This site can be used for a variety of purposes, including psychology experiments, medical trials, and survey research.

GENERATE NUMBERS

In some cases, you may wish to generate more than one set of numbers at a time (e.g., when randomly assigning people to experimental conditions in a "blocked" research design). If you wish to generate multiple sets of random numbers, simply enter the number of sets you want, and Research Randomizer will display all sets in the results.

Specify how many numbers you want Research Randomizer to generate in each set. For example, a request for 5 numbers might yield the following set of random numbers: 2, 17, 23, 42, 50.

Specify the lowest and highest value of the numbers you want to generate. For example, a range of 1 up to 50 would only generate random numbers between 1 and 50 (e.g., 2, 17, 23, 42, 50). Enter the lowest number you want in the "From" field and the highest number you want in the "To" field.

Selecting "Yes" means that any particular number will appear only once in a given set (e.g., 2, 17, 23, 42, 50). Selecting "No" means that numbers may repeat within a given set (e.g., 2, 17, 17, 42, 50). Please note: Numbers will remain unique only within a single set, not across multiple sets. If you request multiple sets, any particular number in Set 1 may still show up again in Set 2.

Sorting your numbers can be helpful if you are performing random sampling, but it is not desirable if you are performing random assignment. To learn more about the difference between random sampling and random assignment, please see the Research Randomizer Quick Tutorial.

Place Markers let you know where in the sequence a particular random number falls (by marking it with a small number immediately to the left). Examples: With Place Markers Off, your results will look something like this: Set #1: 2, 17, 23, 42, 50 Set #2: 5, 3, 42, 18, 20 This is the default layout Research Randomizer uses. With Place Markers Within, your results will look something like this: Set #1: p1=2, p2=17, p3=23, p4=42, p5=50 Set #2: p1=5, p2=3, p3=42, p4=18, p5=20 This layout allows you to know instantly that the number 23 is the third number in Set #1, whereas the number 18 is the fourth number in Set #2. Notice that with this option, the Place Markers begin again at p1 in each set. With Place Markers Across, your results will look something like this: Set #1: p1=2, p2=17, p3=23, p4=42, p5=50 Set #2: p6=5, p7=3, p8=42, p9=18, p10=20 This layout allows you to know that 23 is the third number in the sequence, and 18 is the ninth number over both sets. As discussed in the Quick Tutorial, this option is especially helpful for doing random assignment by blocks.

Please note: By using this service, you agree to abide by the SPN User Policy and to hold Research Randomizer and its staff harmless in the event that you experience a problem with the program or its results. Although every effort has been made to develop a useful means of generating random numbers, Research Randomizer and its staff do not guarantee the quality or randomness of numbers generated. Any use to which these numbers are put remains the sole responsibility of the user who generated them.

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Random Assignment – A Simple Introduction with Examples

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

Inhaltsverzeichnis

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

Random Assignment – In a Nutshell

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

Definition: Random assignment

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

Importance of random assignment

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

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

Example: Different levels of independent variables

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

Three independent participant levels are applicable here:

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

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

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

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

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

Random assignment vs. random sampling

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

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

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

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

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

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

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

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

How to use random assignment

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

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

Random assignment in block experimental designs

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

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

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

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

When random assignment is not used

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

Comparing different groups

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

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

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

No ethical justifiability

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

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

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

What is the definition of random assignment?

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

When is random assignment applicable?

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

What is the importance of random assignment?

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

When should you NOT use random assignment

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

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

Random Assignment in Experiments | Introduction & Examples

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

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

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

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

Table of contents

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Random assignment in block designs

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

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

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

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

When comparing different groups

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

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

When it’s not ethically permissible

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

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

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

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

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

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

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

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

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

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

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

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14.1 What is experimental design and when should you use it?

Learning objectives.

Learners will be able to…

• Describe the purpose of experimental design research
• Describe nomethetic causality and the logic of experimental design
• Identify the characteristics of a basic experiment
• Discuss the relationship between dependent and independent variables in experiments
• Identify the three major types of experimental designs

Pre-awareness check (Knowledge)

What are your thoughts on the phrase ‘experiment’ in the realm of social sciences? In an experiment, what is the independent variable?

The basics of experiments

In social work research, experimental design is used to test the effects of treatments, interventions, programs, or other conditions to which individuals, groups, organizations, or communities may be exposed to. There are a lot of experiments social work researchers can use to explore topics such as treatments for depression, impacts of school-based mental health on student outcomes, or prevention of abuse of people with disabilities. The American Psychological Association defines an experiment   as:

a series of observations conducted under controlled conditions to study a relationship with the purpose of drawing causal inferences about that relationship. An experiment involves the manipulation of an independent variable , the measurement of a dependent variable , and the exposure of various participants to one or more of the conditions being studied. Random selection of participants and their random assignment to conditions also are necessary in experiments .

In experimental design, the independent variable is the intervention, treatment, or condition that is being investigated as a potential cause of change (i.e., the experimental condition ). The effect, or outcome, of the experimental condition is the dependent variable. Trying out a new restaurant, dating a new person – we often call these things “experiments.” However, a true social science experiment would include recruitment of a large enough sample, random assignment to control and experimental groups, exposing those in the experimental group to an experimental condition, and collecting observations at the end of the experiment.

Social scientists use this level of rigor and control to maximize the internal validity of their research. Internal validity is the confidence researchers have about whether the independent variable (e.g, treatment) truly produces a change in the dependent, or outcome, variable. The logic and features of experimental design are intended to help establish causality and to reduce threats to internal validity , which we will discuss in Section 14.5 .

Experiments attempt to establish a nomothetic causal relationship between two variables—the treatment and its intended outcome.  We discussed the four criteria for establishing nomothetic causality in Section 4.3 :

• plausibility,
• covariation,
• temporality, and
• nonspuriousness.

Experiments should establish plausibility , having a plausible reason why their intervention would cause changes in the dependent variable. Usually, a theory framework or previous empirical evidence will indicate the plausibility of a causal relationship.

Covariation can be established for causal explanations by showing that the “cause” and the “effect” change together.  In experiments, the cause is an intervention, treatment, or other experimental condition. Whether or not a research participant is exposed to the experimental condition is the independent variable. The effect in an experiment is the outcome being assessed and is the dependent variable in the study. When the independent and dependent variables covary, they can have a positive association (e.g., those exposed to the intervention have increased self-esteem) or a negative association (e.g., those exposed to the intervention have reduced anxiety).

Since researcher controls when the intervention is administered, they can be assured that changes in the independent variable (the treatment) happens before changes in the dependent variable (the outcome). In this way, experiments assure temporality .

Finally, one of the most important features of experiments is that they allow researchers to eliminate spurious variables to support the criterion of nonspuriousness . True experiments are usually conducted under strictly controlled conditions. The intervention is given in the same way to each person, with a minimal number of other variables that might cause their post-test scores to change.

The logic of experimental design

How do we know that one phenomenon causes another? The complexity of the social world in which we practice and conduct research means that causes of social problems are rarely cut and dry. Uncovering explanations for social problems is key to helping clients address them, and experimental research designs are one road to finding answers.

Just because two phenomena are related in some way doesn’t mean that one causes the other. Ice cream sales increase in the summer, and so does the rate of violent crime; does that mean that eating ice cream is going to make me violent? Obviously not, because ice cream is great. The reality of that association is far more complex—it could be that hot weather makes people more irritable and, at times, violent, while also making people want ice cream. More likely, though, there are other social factors not accounted for in the way we just described this association.

As we have discussed, experimental designs can help clear up at least some of this fog by allowing researchers to isolate the effect of interventions on dependent variables by controlling extraneous variables . In true experimental design (discussed in the next section) and quasi-experimental design, researchers accomplish this w ith a control group or comparison group and the experimental group . The experimental group is sometimes called the treatment group because people in the experimental group receive the treatment or are exposed to the experimental condition (but we will call it the experimental group in this chapter.) The control/comparison group does not receive the treatment or intervention. Instead they may receive what is known as “treatment as usual” or perhaps no treatment at all.

In a well-designed experiment, the control group should look almost identical to the experimental group in terms of demographics and other relevant factors. What if we want to know the effect of CBT on social anxiety, but we have learned in prior research that men tend to have a more difficult time overcoming social anxiety? We would want our control and experimental groups to have a similar portions of men, since ostensibly, both groups’ results would be affected by the men in the group. If your control group has 5 women, 6 men, and 4 non-binary people, then your experimental group should be made up of roughly the same gender balance to help control for the influence of gender on the outcome of your intervention. (In reality, the groups should be similar along other dimensions, as well, and your group will likely be much larger.) The researcher will use the same outcome measures for both groups and compare them, and assuming the experiment was designed correctly, get a pretty good answer about whether the intervention had an effect on social anxiety.

Random assignment [/pb_glossary], also called randomization, entails using a random process to decide which participants are put into the control or experimental group (which participants receive an intervention and which do not). By randomly assigning participants to a group, you can reduce the effect of extraneous variables on your research because there won’t be a systematic difference between the groups.

Do not confuse random assignment with random sampling . Random sampling is a method for selecting a sample from a population and 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 related fields. Random sampling helps a great deal with external validity, or generalizability , whereas random assignment increases internal validity .

Other Features of Experiments that Help Establish Causality

To control for spuriousness (as well as meeting the three other criteria for establishing causality), experiments try to control as many aspects of the research process as possible: using control groups, having large enough sample sizes, standardizing the treatment, etc. Researchers in large experiments often employ clinicians or other research staff to help them. Researchers train their staff members exhaustively, provide pre-scripted responses to common questions, and control the physical environment of the experiment so each person who participates receives the exact same treatment. Experimental researchers also document their procedures, so that others can review them and make changes in future research if they think it will improve on the ability to control for spurious variables.

An interesting example is Bruce Alexander’s (2010) Rat Park experiments. Much of the early research conducted on addictive drugs, like heroin and cocaine, was conducted on animals other than humans, usually mice or rats. The scientific consensus up until Alexander’s experiments was that cocaine and heroin were so addictive that rats, if offered the drugs, would consume them repeatedly until they perished. Researchers claimed this behavior explained how addiction worked in humans, but Alexander was not so sure. He knew rats were social animals and the experimental procedure from previous experiments did not allow them to socialize. Instead, rats were kept isolated in small cages with only food, water, and metal walls. To Alexander, social isolation was a spurious variable, causing changes in addictive behavior not due to the drug itself. Alexander created an experiment of his own, in which rats were allowed to run freely in an interesting environment, socialize and mate with other rats, and of course, drink from a solution that contained an addictive drug. In this environment, rats did not become hopelessly addicted to drugs. In fact, they had little interest in the substance. To Alexander, the results of his experiment demonstrated that social isolation was more of a causal factor for addiction than the drug itself.

One challenge with Alexander’s findings is that subsequent researchers have had mixed success replicating his findings (e.g., Petrie, 1996; Solinas, Thiriet, El Rawas, Lardeux, & Jaber, 2009). Replication involves conducting another researcher’s experiment in the same manner and seeing if it produces the same results. If the causal relationship is real, it should occur in all (or at least most) rigorous replications of the experiment.

Replicability

[INSERT A PARAGRAPH ABOUT REPLICATION/REPRODUCTION HERE. CAN USE/REFERENCE THIS   IF IT’S HELPFUL; include glossary definition as well as other general info]

To allow for easier replication, researchers should describe their experimental methods diligently. Researchers with the Open Science Collaboration (2015) [1] conducted the Reproducibility Project , which caused a significant controversy regarding the validity of psychological studies. The researchers with the project attempted to reproduce the results of 100 experiments published in major psychology journals since 2008. What they found was shocking. Although 97% of the original studies reported significant results, only 36% of the replicated studies had significant findings. The average effect size in the replication studies was half that of the original studies. The implications of the Reproducibility Project are potentially staggering, and encourage social scientists to carefully consider the validity of their reported findings and that the scientific community take steps to ensure researchers do not cherry-pick data or change their hypotheses simply to get published.

Generalizability

Let’s return to Alexander’s Rat Park study and consider the implications of his experiment for substance use professionals.  The conclusions he drew from his experiments on rats were meant to be generalized to the population. If this could be done, the experiment would have a high degree of external validity , which is the degree to which conclusions generalize to larger populations and different situations. Alexander argues his conclusions about addiction and social isolation help us understand why people living in deprived, isolated environments may become addicted to drugs more often than those in more enriching environments. Similarly, earlier rat researchers argued their results showed these drugs were instantly addictive to humans, often to the point of death.

Neither study’s results will match up perfectly with real life. There are clients in social work practice who may fit into Alexander’s social isolation model, but social isolation is complex. Clients can live in environments with other sociable humans, work jobs, and have romantic relationships; does this mean they are not socially isolated? On the other hand, clients may face structural racism, poverty, trauma, and other challenges that may contribute to their social environment. Alexander’s work helps understand clients’ experiences, but the explanation is incomplete. Human existence is more complicated than the experimental conditions in Rat Park.

Effectiveness versus Efficacy

Social workers are especially attentive to how social context shapes social life. This consideration points out a potential weakness of experiments. They can be rather artificial. When an experiment demonstrates causality under ideal, controlled circumstances, it establishes the efficacy of an intervention.

How often do real-world social interactions occur in the same way that they do in a controlled experiment? Experiments that are conducted in community settings by community practitioners are less easily controlled than those conducted in a lab or with researchers who adhere strictly to research protocols delivering the intervention. When an experiment demonstrates causality in a real-world setting that is not tightly controlled, it establishes the effectiveness of the intervention.

The distinction between efficacy and effectiveness demonstrates the tension between internal and external validity. Internal validity and external validity are conceptually linked. Internal validity refers to the degree to which the intervention causes its intended outcomes, and external validity refers to how well that relationship applies to different groups and circumstances than the experiment. However, the more researchers tightly control the environment to ensure internal validity, the more they may risk external validity for generalizing their results to different populations and circumstances. Correspondingly, researchers whose settings are just like the real world will be less able to ensure internal validity, as there are many factors that could pollute the research process. This is not to suggest that experimental research findings cannot have high levels of both internal and external validity, but that experimental researchers must always be aware of this potential weakness and clearly report limitations in their research reports.

Types of Experimental Designs

Experimental design is an umbrella term for a research method that is designed to test hypotheses related to causality under controlled conditions. Table 14.1 describes the three major types of experimental design (pre-experimental, quasi-experimental, and true experimental) and presents subtypes for each. As we will see in the coming sections, some types of experimental design are better at establishing causality than others. It’s also worth considering that true experiments, which most effectively establish causality , are often difficult and expensive to implement. Although the other experimental designs aren’t perfect, they still produce useful, valid evidence and may be more feasible to carry out.

Key Takeaways

• Experimental designs are useful for establishing causality, but some types of experimental design do this better than others.
• Experiments help researchers isolate the effect of the independent variable on the dependent variable by controlling for the effect of extraneous variables .
• Experiments use a control/comparison group and an experimental group to test the effects of interventions. These groups should be as similar to each other as possible in terms of demographics and other relevant factors.
• True experiments have control groups with randomly assigned participants; quasi-experimental types of experiments have comparison groups to which participants are not randomly assigned; pre-experimental designs do not have a comparison group.

TRACK 1 (IF YOU  ARE  CREATING A RESEARCH PROPOSAL FOR THIS CLASS):

• Think about the research project you’ve been designing so far. How might you use a basic experiment to answer your question? If your question isn’t explanatory, try to formulate a new explanatory question and consider the usefulness of an experiment.
• Why is establishing a simple relationship between two variables not indicative of one causing the other?

TRACK 2 (IF YOU  AREN’T  CREATING A RESEARCH PROPOSAL FOR THIS CLASS):

Imagine you are interested in studying child welfare practice. You are interested in learning more about community-based programs aimed to prevent child maltreatment and to prevent out-of-home placement for children.

• Think about the research project stated above. How might you use a basic experiment to look more into this research topic? Try to formulate an explanatory question and consider the usefulness of an experiment.
• Open Science Collaboration. (2015). Estimating the reproducibility of psychological science. Science, 349 (6251), aac4716. Doi: 10.1126/science.aac4716 ↵

an operation or procedure carried out under controlled conditions in order to discover an unknown effect or law, to test or establish a hypothesis, or to illustrate a known law.

treatment, intervention, or experience that is being tested in an experiment (the independent variable) that is received by the experimental group and not by the control group.

Ability to say that one variable "causes" something to happen to another variable. Very important to assess when thinking about studies that examine causation such as experimental or quasi-experimental designs.

circumstances or events that may affect the outcome of an experiment, resulting in changes in the research participants that are not a result of the intervention, treatment, or experimental condition being tested

causal explanations that can be universally applied to groups, such as scientific laws or universal truths

as a criteria for causal relationship, the relationship must make logical sense and seem possible

when the values of two variables change at the same time

as a criteria for causal relationship, the cause must come before the effect

an association between two variables that is NOT caused by a third variable

variables and characteristics that have an effect on your outcome, but aren't the primary variable whose influence you're interested in testing.

the group of participants in our study who do not receive the intervention we are researching in experiments with random assignment

the group of participants in our study who do not receive the intervention we are researching in experiments without random assignment

in experimental design, the group of participants in our study who do receive the intervention we are researching

The ability to apply research findings beyond the study sample to some broader population,

This is a synonymous term for generalizability - the ability to apply the findings of a study beyond the sample to a broader population.

performance of an intervention under ideal and controlled circumstances, such as in a lab or delivered by trained researcher-interventionists

The performance of an intervention under "real-world" conditions that are not closely controlled and ideal

the idea that one event, behavior, or belief will result in the occurrence of another, subsequent event, behavior, or belief

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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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• Published: 15 April 2024

Demuxafy : improvement in droplet assignment by integrating multiple single-cell demultiplexing and doublet detection methods

• Drew Neavin 1 ,
• Anne Senabouth 1 ,
• Himanshi Arora 1 , 2 ,
• Jimmy Tsz Hang Lee 3 ,
• Aida Ripoll-Cladellas 4 ,
• sc-eQTLGen Consortium ,
• Lude Franke 5 ,
• Shyam Prabhakar 6 , 7 , 8 ,
• Chun Jimmie Ye 9 , 10 , 11 , 12 ,
• Davis J. McCarthy 13 , 14 ,
• Marta Melé 4 ,
• Martin Hemberg 15 &
• Joseph E. Powell   ORCID: orcid.org/0000-0002-5070-4124 1 , 16  

Genome Biology volume  25 , Article number:  94 ( 2024 ) Cite this article

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Recent innovations in single-cell RNA-sequencing (scRNA-seq) provide the technology to investigate biological questions at cellular resolution. Pooling cells from multiple individuals has become a common strategy, and droplets can subsequently be assigned to a specific individual by leveraging their inherent genetic differences. An implicit challenge with scRNA-seq is the occurrence of doublets—droplets containing two or more cells. We develop Demuxafy, a framework to enhance donor assignment and doublet removal through the consensus intersection of multiple demultiplexing and doublet detecting methods. Demuxafy significantly improves droplet assignment by separating singlets from doublets and classifying the correct individual.

Droplet-based single-cell RNA sequencing (scRNA-seq) technologies have provided the tools to profile tens of thousands of single-cell transcriptomes simultaneously [ 1 ]. With these technological advances, combining cells from multiple samples in a single capture is common, increasing the sample size while simultaneously reducing batch effects, cost, and time. In addition, following cell capture and sequencing, the droplets can be demultiplexed—each droplet accurately assigned to each individual in the pool [ 2 , 3 , 4 , 5 , 6 , 7 ].

Many scRNA-seq experiments now capture upwards of 20,000 droplets, resulting in ~16% (3,200) doublets [ 8 ]. Current demultiplexing methods can also identify doublets—droplets containing two or more cells—from different individuals (heterogenic doublets). These doublets can significantly alter scientific conclusions if they are not effectively removed. Therefore, it is essential to remove doublets from droplet-based single-cell captures.

However, demultiplexing methods cannot identify droplets containing multiple cells from the same individual (homogenic doublets) and, therefore, cannot identify all doublets in a single capture. If left in the dataset, those doublets could appear as transitional cells between two distinct cell types or a completely new cell type. Accordingly, additional methods have been developed to identify heterotypic doublets (droplets that contain two cells from different cell types) by comparing the transcriptional profile of each droplet to doublets simulated from the dataset [ 9 , 10 , 11 , 12 , 13 , 14 , 15 ]. It is important to recognise that demultiplexing methods achieve two functions—segregation of cells from different donors and separation of singlets from doublets—while doublet detecting methods solely classify singlets versus doublets.

Therefore, demultiplexing and transcription-based doublet detecting methods provide complementary information to improve doublet detection, providing a cleaner dataset and more robust scientific results. There are currently five genetic-based demultiplexing [ 2 , 3 , 4 , 5 , 6 , 7 , 16 ] and seven transcription-based doublet-detecting methods implemented in various languages [ 9 , 10 , 11 , 12 , 13 , 14 , 15 ]. Under different scenarios, each method is subject to varying performance and, in some instances, biases in their ability to accurately assign cells or detect doublets from certain conditions. The best combination of methods is currently unclear but will undoubtedly depend on the dataset and research question.

Therefore, we set out to identify the best combination of genetic-based demultiplexing and transcription-based doublet-detecting methods to remove doublets and partition singlets from different donors correctly. In addition, we have developed a software platform ( Demuxafy ) that performs these intersectional methods and provides additional commands to simplify the execution and interpretation of results for each method (Fig. 1 a).

Study design and qualitative method classifications. a  Demuxafy is a platform to perform demultiplexing and doublet detecting with consistent documentation. Demuxafy also provides wrapper scripts to quickly summarize the results from each method and assign clusters to each individual with reference genotypes when a reference-free demultiplexing method is used. Finally, Demuxafy provides a script to easily combine the results from multiple different methods into a single data frame and it provides a final assignment for each droplet based on the combination of multiple methods. In addition, Demuxafy provides summaries of the number of droplets classified as singlets or doublets by each method and a summary of the number of droplets assigned to each individual by each of the demultiplexing methods. b  Two datasets are included in this analysis - a PBMC dataset and a fibroblast dataset. The PBMC dataset contains 74 pools that captured approximately 20,000 droplets each with 12-16 donor cells multiplexed per pool. The fibroblast dataset contains 11 pools of roughly 7,000 droplets per pool with sizes ranging from six to eight donors per pool. All pools were processed by all demultiplexing and doublet detecting methods and the droplet and donor classifications were compared between the methods and between the PBMCs and fibroblasts. Then the PBMC droplets that were classified as singlets by all methods were taken as ‘true singlets’ and used to generate new pools in silico. Those pools were then processed by each of the demultiplexing and doublet detecting methods and intersectional combinations of demultiplexing and doublet detecting methods were tested for different experimental designs

To compare the demultiplexing and doublet detecting methods, we utilised two large, multiplexed datasets—one that contained ~1.4 million peripheral blood mononuclear cells (PBMCs) from 1,034 donors [ 17 ] and one with ~94,000 fibroblasts from 81 donors [ 18 ]. We used the true singlets from the PBMC dataset to generate new in silico pools to assess the performance of each method and the multi-method intersectional combinations (Fig. 1 b).

Here, we compare 14 demultiplexing and doublet detecting methods with different methodological approaches, capabilities, and intersectional combinations. Seven of those are demultiplexing methods ( Demuxalot [ 6 ], Demuxlet [ 3 ], Dropulation [ 5 ], Freemuxlet [ 16 ], ScSplit [ 7 ], Souporcell [ 4 ], and Vireo [ 2 ]) which leverage the common genetic variation between individuals to identify cells that came from each individual and to identify heterogenic doublets. The seven remaining methods ( DoubletDecon [ 9 ], DoubletDetection [ 14 ], DoubletFinder [ 10 ], ScDblFinder [ 11 ], Scds [ 12 ], Scrublet [ 13 ], and Solo [ 15 ]) identify doublets based on their similarity to simulated doublets generated by adding the transcriptional profiles of two randomly selected droplets in the dataset. These methods assume that the proportion of real doublets in the dataset is low, so combining any two droplets will likely represent the combination of two singlets.

We identify critical differences in the performance of demultiplexing and doublet detecting methods to classify droplets correctly. In the case of the demultiplexing techniques, their performance depends on their ability to identify singlets from doublets and assign a singlet to the correct individual. For doublet detecting methods, the performance is based solely on their ability to differentiate a singlet from a doublet. We identify limitations in identifying specific doublet types and cell types by some methods. In addition, we compare the intersectional combinations of these methods for multiple experimental designs and demonstrate that intersectional approaches significantly outperform all individual techniques. Thus, the intersectional methods provide enhanced singlet classification and doublet removal—a critical but often under-valued step of droplet-based scRNA-seq processing. Our results demonstrate that intersectional combinations of demultiplexing and doublet detecting software provide significant advantages in droplet-based scRNA-seq preprocessing that can alter results and conclusions drawn from the data. Finally, to provide easy implementation of our intersectional approach, we provide Demuxafy ( https://demultiplexing-doublet-detecting-docs.readthedocs.io/en/latest/index.html ) a complete platform to perform demultiplexing and doublet detecting intersectional methods (Fig. 1 a).

Study design

To evaluate demultiplexing and doublet detecting methods, we developed an experimental design that applies the different techniques to empirical pools and pools generated in silico from the combination of true singlets—droplets identified as singlets by every method (Fig. 1 a). For the first phase of this study, we used two empirical multiplexed datasets—the peripheral blood mononuclear cell (PBMC) dataset containing ~1.4 million cells from 1034 donors and a fibroblast dataset of ~94,000 cells from 81 individuals (Additional file 1 : Table S1). We chose these two cell systems to assess the methods in heterogeneous (PBMC) and homogeneous (fibroblast) cell types.

Demultiplexing and doublet detecting methods perform similarly for heterogeneous and homogeneous cell types

We applied the demultiplexing methods ( Demuxalot , Demuxlet , Dropulation , Freemuxlet , ScSplit , Souporcell , and Vireo ) and doublet detecting methods ( DoubletDecon , DoubletDetection , DoubletFinder , ScDblFinder , Scds , Scrublet , and Solo ) to the two datasets and assessed the results from each method. We first compared the droplet assignments by identifying the number of singlets and doublets identified by a given method that were consistently annotated by all methods (Fig. 2 a–d). We also identified the percentage of droplets that were annotated consistently between pairs of methods (Additional file 2 : Fig S1). In the cases where two demultiplexing methods were compared to one another, both the droplet type (singlet or doublet) and the assignment of the droplet to an individual had to match to be considered in agreement. In all other comparisons (i.e. demultiplexing versus doublet detecting and doublet detecting versus doublet detecting), only the droplet type (singlet or doublet) was considered for agreement since doublet detecting methods cannot annotate donor assignment. We found that the two method types were more similar to other methods of the same type (i.e., demultiplexing versus demultiplexing and doublet detecting versus doublet detecting) than they were to methods from a different type (demultiplexing methods versus doublet detecting methods; Supplementary Fig 1). We found that the similarity of the demultiplexing and doublet detecting methods was consistent in the PBMC and fibroblast datasets (Pearson correlation R = 0.78, P -value < 2×10 −16 ; Fig S1a-c). In addition, demultiplexing methods were more similar than doublet detecting methods for both the PBMC and fibroblast datasets (Wilcoxon rank-sum test: P < 0.01; Fig. 2 a–b and Additional file 2 : Fig S1).

Demultiplexing and Doublet Detecting Method Performance Comparison. a  The proportion of droplets classified as singlets and doublets by each method in the PBMCs. b  The number of other methods that classified the singlets and doublets identified by each method in the PBMCs. c  The proportion of droplets classified as singlets and doublets by each method in the fibroblasts. d The number of other methods that classified the singlets and doublets identified by each method in the fibroblasts. e - f The performance of each method when the majority classification of each droplet is considered the correct annotation in the PBMCs ( e ) and fibroblasts ( f ). g - h  The number of droplets classified as singlets (box plots) and doublets (bar plots) by all methods in the PBMC ( g ) and fibroblast ( h ) pools. i - j  The number of donors that were not identified by each method in each pool for PBMCs ( i ) and fibroblasts ( j ). PBMC: peripheral blood mononuclear cell. MCC: Matthew’s correlationcoefficient

The number of unique molecular identifiers (UMIs) and genes decreased in droplets that were classified as singlets by a larger number of methods while the mitochondrial percentage increased in both PBMCs and fibroblasts (Additional file 2 : Fig S2).

We next interrogated the performance of each method using the Matthew’s correlation coefficient (MCC) to calculate the consistency between Demuxify and true droplet classification. We identified consistent trends in the MCC scores for each method between the PBMCs (Fig. 2 e) and fibroblasts (Fig. 2 f). These data indicate that the methods behave similarly, relative to one another, for heterogeneous and homogeneous datasets.

Next, we sought to identify the droplets concordantly classified by all demultiplexing and doublet detecting methods in the PBMC and fibroblast datasets. On average, 732 singlets were identified for each individual by all the methods in the PBMC dataset. Likewise, 494 droplets were identified as singlets for each individual by all the methods in the fibroblast pools. However, the concordance of doublets identified by all methods was very low for both datasets (Fig. 2 e–f). Notably, the consistency of classifying a droplet as a doublet by all methods was relatively low (Fig. 2 b,d,g, and h). This suggests that doublet identification is not consistent between all the methods. Therefore, further investigation is required to identify the reasons for these inconsistencies between methods. It also suggests that combining multiple methods for doublet classification may be necessary for more complete doublet removal. Further, some methods could not identify all the individuals in each pool (Fig. 2 i–j). The non-concordance between different methods demonstrates the need to effectively test each method on a dataset where the droplet types are known.

Computational resources vary for demultiplexing and doublet detecting methods

We recorded each method’s computational resources for the PBMC pools, with ~20,000 cells captured per pool (Additional file 1 : Table S1). Of the demultiplexing methods, ScSplit took the most time (multiple days) and required the most steps, but Demuxalot , Demuxlet , and Freemuxlet used the most memory. Solo took the longest time (median 13 h) and most memory to run for the doublet detecting methods but is the only method built to be run directly from the command line, making it easy to implement (Additional file 2 : Fig S3).

Generate pools with known singlets and doublets

However, there is no gold standard to identify which droplets are singlets or doublets. Therefore, in the second phase of our experimental design (Fig. 1 b), we used the PBMC droplets classified as singlets by all methods to generate new pools in silico. We chose to use the PBMC dataset since our first analyses indicated that method performance is similar for homogeneous (fibroblast) and heterogeneous (PBMC) cell types (Fig. 2 and Additional file 2 : Fig S1) and because we had many more individuals available to generate in silico pools from the PBMC dataset (Additional file 1 : Table S1).

We generated 70 pools—10 each of pools that included 2, 4, 8, 16, 32, 64, or 128 individuals (Additional file 1 : Table S2). We assume a maximum 20% doublet rate as it is unlikely researchers would use a technology that has a higher doublet rate (Fig. 3 a).

In silico Pool Doublet Annotation and Method Performance. a  The percent of singlets and doublets in the in -silico pools - separated by the number of multiplexed individuals per pool. b  The percentage and number of doublets that are heterogenic (detectable by demultiplexing methods), heterotypic (detectable by doublet detecting methods), both (detectable by either method category) and neither (not detectable with current methods) for each multiplexed pool size. c  Percent of droplets that each of the demultiplexing and doublet detecting methods classified correctly for singlets and doublet subtypes for different multiplexed pool sizes. d  Matthew’s Correlation Coefficient (MCC) for each of the methods for each of the multiplexed pool sizes. e  Balanced accuracy for each of the methods for each of the multiplexed pool sizes

We used azimuth to classify the PBMC cell types for each droplet used to generate the in silico pools [ 19 ] (Additional file 2 : Fig S4). As these pools have been generated in silico using empirical singlets that have been well annotated, we next identified the proportion of doublets in each pool that were heterogenic, heterotypic, both, and neither. This approach demonstrates that a significant percentage of doublets are only detectable by doublet detecting methods (homogenic and heterotypic) for pools with 16 or fewer donors multiplexed (Fig. 3 b).

While the total number of doublets that would be missed if only using demultiplexing methods appears small for fewer multiplexed individuals (Fig. 3 b), it is important to recognise that this is partly a function of the ~732 singlet cells per individual used to generate these pools. Hence, the in silico pools with fewer individuals also have fewer cells. Therefore, to obtain numbers of doublets that are directly comparable to one another, we calculated the number of each doublet type that would be expected to be captured with 20,000 cells when 2, 4, 8, 16, or 32 individuals were multiplexed (Additional file 2 : Fig S5). These results demonstrate that many doublets would be falsely classified as singlets since they are homogenic when just using demultiplexing methods for a pool of 20,000 cells captured with a 16% doublet rate (Additional file 2 : Fig S5). However, as more individuals are multiplexed, the number of droplets that would not be detectable by demultiplexing methods (homogenic) decreases. This suggests that typical workflows that use only one demultiplexing method to remove doublets from pools that capture 20,000 droplets with 16 or fewer multiplexed individuals fail to adequately remove between 173 (16 multiplexed individuals) and 1,325 (2 multiplexed individuals) doublets that are homogenic and heterotypic which could be detected by doublet detecting methods (Additional file 2 : Fig S5). Therefore, a technique that uses both demultiplexing and doublet detecting methods in parallel will complement more complete doublet removal methods. Consequently, we next set out to identify the demultiplexing and doublet detecting methods that perform the best on their own and in concert with other methods.

Doublet and singlet droplet classification effectiveness varies for demultiplexing and doublet detecting methods

Demultiplexing methods fail to classify homogenic doublets.

We next investigated the percentage of the droplets that were correctly classified by each demultiplexing and doublet detecting method. In addition to the seven demultiplexing methods, we also included Demuxalot with the additional steps to refine the genotypes that can then be used for demultiplexing— Demuxalot (refined). Demultiplexing methods correctly classify a large portion of the singlets and heterogenic doublets (Fig. 3 c). This pattern is highly consistent across different cell types, with the notable exceptions being decreased correct classifications for erythrocytes and platelets when greater than 16 individuals are multiplexed (Additional file 2 : Fig S6).

However, Demuxalot consistently demonstrates the highest correct heterogenic doublet classification. Further, the percentage of the heterogenic doublets classified correctly by Souporcell decreases when large numbers of donors are multiplexed. ScSplit is not as effective as the other demultiplexing methods at classifying heterogenic doublets, partly due to the unique doublet classification method, which assumes that the doublets will generate a single cluster separate from the donors (Table 1 ). Importantly, the demultiplexing methods identify almost none of the homogenic doublets for any multiplexed pool size—demonstrating the need to include doublet detecting methods to supplement the demultiplexing method doublet detection.

Doublet detecting method classification performances vary greatly

In addition to assessing each of the methods with default settings, we also evaluated ScDblFinder with ‘known doublets’ provided. This method can take already known doublets and use them when detecting doublets. For these cases, we used the droplets that were classified as doublets by all the demultiplexing methods as ‘known doublets’.

Most of the methods classified a similarly high percentage of singlets correctly, with the exceptions of DoubletDecon and DoubletFinder for all pool sizes (Fig. 3 c). However, unlike the demultiplexing methods, there are explicit cell-type-specific biases for many of the doublet detecting methods (Additional file 2 : Fig S7). These differences are most notable for cell types with fewer cells (i.e. ASDC and cDC2) and proliferating cells (i.e. CD4 Proliferating, CD8 Proliferating, and NK Proliferating). Further, all of the softwares demonstrate high correct percentages for some cell types including CD4 Naïve and CD8 Naïve (Additional file 2 : Fig S7).

As expected, all doublet detecting methods identified heterotypic doublets more effectively than homotypic doublets (Fig. 3 c). However, ScDblFinder and Scrublet classified the most doublets correctly across all doublet types for pools containing 16 individuals or fewer. Solo was more effective at identifying doublets than Scds for pools containing more than 16 individuals. It is also important to note that it was not feasible to run DoubletDecon for the largest pools containing 128 multiplexed individuals and an average of 115,802 droplets (range: 113,594–119,126 droplets). ScDblFinder performed similarly when executed with and without known doublets (Pearson correlation P = 2.5 × 10 -40 ). This suggests that providing known doublets to ScDblFinder does not offer an added benefit.

Performances vary between demultiplexing and doublet detecting method and across the number of multiplexed individuals

We assessed the overall performance of each method with two metrics: the balanced accuracy and the MCC. We chose to use balanced accuracy since, with unbalanced group sizes, it is a better measure of performance than accuracy itself. Further, the MCC has been demonstrated as a more reliable statistical measure of performance since it considers all possible categories—true singlets (true positives), false singlets (false positives), true doublets (true negatives), and false doublets (false negatives). Therefore, a high score on the MCC scale indicates high performance in each metric. However, we provide additional performance metrics for each method (Additional file 1 : Table S3). For demultiplexing methods, both the droplet type (singlet or doublet) and the individual assignment were required to be considered a ‘true singlet’. In contrast, only the droplet type (singlet or doublet) was needed for doublet detection methods.

The MCC and balanced accuracy metrics are similar (Spearman’s ⍴ = 0.87; P < 2.2 × 10 -308 ). Further, the performance of Souporcell decreases for pools with more than 32 individuals multiplexed for both metrics (Student’s t -test for MCC: P < 1.1 × 10 -9 and balanced accuracy: P < 8.1 × 10 -11 ). Scds , ScDblFinder , and Scrublet are among the top-performing doublet detecting methods Fig. 3 d–e).

Overall, between 0.4 and 78.8% of droplets were incorrectly classified by the demultiplexing or doublet detecting methods depending on the technique and the multiplexed pool size (Additional file 2 : Fig S8). Demuxalot (refined) and DoubletDetection demonstrated the lowest percentage of incorrect droplets with about 1% wrong in the smaller pools (two multiplexed individuals) and about 3% incorrect in pools with at least 16 multiplexed individuals. Since some transitional states and cell types are present in low percentages in total cell populations (i.e. ASDCs at 0.02%), incorrect classification of droplets could alter scientific interpretations of the data, and it is, therefore, ideal for decreasing the number of erroneous assignments as much as possible.

False singlets and doublets demonstrate different metrics than correctly classified droplets

We next asked whether specific cell metrics might contribute to false singlet and doublet classifications for different methods. Therefore, we compared the number of genes, number of UMIs, mitochondrial percentage and ribosomal percentage of the false singlets and doublets to equal numbers of correctly classified cells for each demultiplexing and doublet detecting method.

The number of UMIs (Additional file 2 : Fig S9 and Additional file 1 : Table S4) and genes (Additional file 2 : Fig S10 and Additional file 1 : Table S5) demonstrated very similar distributions for all comparisons and all methods (Spearman ⍴ = 0.99, P < 2.2 × 10 -308 ). The number of UMIs and genes were consistently higher in false singlets and lower in false doublets for most demultiplexing methods except some smaller pool sizes (Additional file 2 : Fig S9a and Additional file 2 : Fig S10a; Additional file 1 : Table S4 and Additional file 1 : Table S5). The number of UMIs and genes was consistently higher in droplets falsely classified as singlets by the doublet detecting methods than the correctly identified droplets (Additional file 2 : Fig S9b and Additional file 2 : Fig S10b; Additional file 1 : Table S4 and Additional file 1 : Table S5). However, there was less consistency in the number of UMIs and genes detected in false singlets than correctly classified droplets between the different doublet detecting methods (Additional file 2 : Fig S9b and Additional file 2 : Fig S10b; Additional file 1 : Table S4 and Additional file 1 : Table S5).

The ribosomal percentage of the droplets falsely classified as singlets or doublets is similar to the correctly classified droplets for most methods—although they are statistically different for larger pool sizes (Additional file 2 : Fig S11a and Additional file 1 : Table S6). However, the false doublets classified by some demultiplexing methods ( Demuxalot , Demuxalot (refined), Demuxlet , ScSplit , Souporcell , and Vireo ) demonstrated higher ribosomal percentages. Some doublet detecting methods ( ScDblFinder , ScDblFinder with known doublets and Solo) demonstrated higher ribosomal percentages for the false doublets while other demonstrated lower ribosomal percentages ( DoubletDecon , DoubletDetection , and DoubletFinder ; Additional file 2 : Fig S11b and Additional file 1 : Table S6).

Like the ribosomal percentage, the mitochondrial percentage in false singlets is also relatively similar to correctly classified droplets for both demultiplexing (Additional file 2 : Fig S12a and Additional file 1 : Table S7) and doublet detecting methods (Additional file 2 : Fig S12b). The mitochondrial percentage for false doublets is statistically lower than the correctly classified droplets for a few larger pools for Freemuxlet , ScSplit , and Souporcell . The doublet detecting method Solo also demonstrates a small but significant decrease in mitochondrial percentage in the false doublets compared to the correctly annotated droplets. However, other doublet detecting methods including DoubletFinder and the larger pools of most other methods demonstrated a significant increase in mitochondrial percent in the false doublets compared to the correctly annotated droplets (Additional file 2 : Fig S12b).

Overall, these results demonstrate a strong relationship between the number of genes and UMIs and limited influence of ribosomal or mitochondrial percentage in a droplet and false classification, suggesting that the number of genes and UMIs can significantly bias singlet and doublet classification by demultiplexing and doublet detecting methods.

Ambient RNA, number of reads per cell, and uneven pooling impact method performance

To further quantify the variables that impact the performance of each method, we simulated four conditions that could occur with single-cell RNA-seq experiments: (1) decreased number of reads (reduced 50%), (2) increased ambient RNA (10%, 20% and 50%), (3) increased mitochondrial RNA (5%, 10% and 25%) and 4) uneven donor pooling from single donor spiking (0.5 or 0.75 proportion of pool from one donor). We chose these scenarios because they are common technical effects that can occur.

We observed a consistent decrease in the demultiplexing method performance when the number of reads were decreased by 50% but the degree of the effect varied for each method and was larger in pools containing more multiplexed donors (Additional file 2 : Fig S13a and Additional file 1 : Table S8). Decreasing the number of reads did not have a detectable impact on the performance of the doublet detecting methods.

Simulating additional ambient RNA (10%, 20%, or 50%) decreased the performance of all the demultiplexing methods (Additional file 2 : Fig S13b and Additional file 1 : Table S9) but some were unimpacted in pools that had 16 or fewer individuals multiplexed ( Souporcell and Vireo ). The performance of some of the doublet detecting methods were impacted by the ambient RNA but the performance of most methods did not decrease. Scrublet and ScDblFinder were the doublet detecting methods most impacted by ambient RNA but only in pools with at least 32 multiplexed donors (Additional file 2 : Fig S13b and Additional file 1 : Table S9).

Increased mitochondrial percent did not impact the performance of demultiplexing or doublet detecting methods (Additional file 2 : Fig S13c and Additional file 1 : Table S10).

We also tested whether experimental designs that pooling uneven proportions of donors would alter performance. We tested scenarios where either half the pool was composed of a single donor (0.5 spiked donor proportion) or where three quarters of the pool was composed of a single donor. This experimental design significantly reduced the demultiplexing method performance (Additional file 2 : Fig S13d and Additional file 1 : Table S11) with the smallest influence on Freemuxlet . The performance of most of the doublet detecting methods were unimpacted except for DoubletDetection that demonstrated significant decreases in performance in pools where at least 16 donors were multiplexed. Intriguingly, the performance of Solo increased with the spiked donor pools when the pools consisted of 16 donors or less.

Our results demonstrate significant differences in overall performance between different demultiplexing and doublet detecting methods. We further noticed some differences in the use of the methods. Therefore, we have accumulated these results and each method’s unique characteristics and benefits in a heatmap for visual interpretation (Fig. 4 ).

Assessment of each of the demultiplexing and doublet detecting methods. Assessments of a variety of metrics for each of the demultiplexing (top) and doublet detecting (bottom) methods

Framework for improving singlet classifications via method combinations

After identifying the demultiplexing and doublet detecting methods that performed well individually, we next sought to test whether using intersectional combinations of multiple methods would enhance droplet classifications and provide a software platform— Demuxafy —capable of supporting the execution of these intersectional combinations.

We recognise that different experimental designs will be required for each project. As such, we considered this when testing combinations of methods. We considered multiple experiment designs and two different intersectional methods: (1) more than half had to classify a droplet as a singlet to be called a singlet and (2) at least half of the methods had to classify a droplet as a singlet to be called a singlet. Significantly, these two intersectional methods only differ when an even number of methods are being considered. For combinations that include demultiplexing methods, the individual called by the majority of the methods is the individual used for that droplet. When ties occur, the individual is considered ‘unassigned’.

Combining multiple doublet detecting methods improve doublet removal for non-multiplexed experimental designs

For the non-multiplexed experimental design, we considered all possible method combinations (Additional file 1 : Table S12). We identified important differences depending on the number of droplets captured and have provided recommendations accordingly. We identified that DoubletFinder , Scrublet , ScDblFinder and Scds is the ideal combination for balanced droplet calling when less than 2,000 droplets are captured. Scds and ScDblFinder or Scrublet , Scds and ScDblFinder is the best combination when 2,000–10,000 droplets are captured. Scds , Scrublet, ScDblFinder and DoubletDetection is the best combination when 10,000–20,000 droplets are captured and Scrublet , Scds , DoubletDetection and ScDblFinder . It is important to note that even a slight increase in the MCC significantly impacts the number of true singlets and true doublets classified with the degree of benefit highly dependent on the original method performance. The combined method increases the MCC compared to individual doublet detecting methods on average by 0.11 and up to 0.33—a significant improvement in the MCC ( t -test FDR < 0.05 for 95% of comparisons). For all combinations, the intersectional droplet method requires more than half of the methods to consider the droplet a singlet to classify it as a singlet (Fig. 5 ).

Recommended Method Combinations Dependent on Experimental Design. Method combinations are provided for different experimental designs, including those that are not multiplexed (left) and multiplexed (right), including experiments that have reference SNP genotypes available vs those that do not and finally, multiplexed experiments with different numbers of individuals multiplexed. The each bar represents either a single method (shown with the coloured icon above the bar) or a combination of methods (shown with the addition of the methods and an arrow indicating the bar). The proportion of true singlets, true doublets, false singlets and false doublets for each method or combination of methods is shown with the filled barplot and the MCC is shown with the black points overlaid on the barplot. MCC: Matthew’s Correlation Coefficient

Demuxafy performs better than Chord

Chord is an ensemble machine learning doublet detecting method that uses Scds and DoubletFinder to identify doublets. We compared Demuxafy using Scds and DoubletFinder to Chord and identified that Demuxafy outperformed Chord in pools that contained at least eight donors and was equivalent in pools that contained less than eight donors (Additional file 2 : Fig S14). This is because Chord classifies more droplets as false singlets and false doublets than Demuxafy . In addition, Chord failed to complete for two of the pools that contained 128 multiplexed donors.

Combining multiple demultiplexing and doublet detecting methods improve doublet removal for multiplexed experimental designs

For experiments where 16 or fewer individuals are multiplexed with reference SNP genotypes available, we considered all possible combinations between the demultiplexing and doublet detecting methods except ScDblFinder with known doublets due to its highly similar performance to ScDblFinder (Fig 3 ; Additional file 1 : Table S13). The best combinations are DoubletFinder , Scds , ScDblFinder , Vireo and Demuxalot (refined) (<~5 donors) and Scrublet , ScDblFinder , DoubletDetection , Dropulation and Demuxalot (refined) (Fig. 5 ). These intersectional methods increase the MCC compared to the individual methods ( t -test FDR < 0.05), generally resulting in increased true singlets and doublets compared to the individual methods. The improvement in MCC depends on every single method’s performance but, on average, increases by 0.22 and up to 0.71. For experiments where the reference SNP genotypes are unknown, the individuals multiplexed in the pool with 16 or fewer individuals multiplexed, DoubletFinder , ScDblFinder, Souporcell and Vireo (<~5 donors) and Scds , ScDblFinder , DoubletDetection , Souporcell and Vireo are the ideal methods (Fig. 5 ). These intersectional methods again significantly increase the MCC up to 0.87 compared to any of the individual techniques that could be used for this experimental design ( t -test FDR < 0.05 for 94.2% of comparisons). In both cases, singlets should only be called if more than half of the methods in the combination classify the droplet as a singlet.

Combining multiple demultiplexing methods improves doublet removal for large multiplexed experimental designs

For experiments that multiplex more than 16 individuals, we considered the combinations between all demultiplexing methods (Additional file 1 : Table S14) since only a small proportion of the doublets would be undetectable by demultiplexing methods (droplets that are homogenic; Fig 3 b). To balance doublet removal and maintain true singlets, we recommend the combination of Demuxalot (refined) and Dropulation . These method combinations significantly increase the MCC by, on average, 0.09 compared to all the individual methods ( t -test FDR < 0.05). This substantially increases true singlets and true doublets relative to the individual methods. If reference SNP genotypes are not available for the individuals multiplexed in the pools, Vireo performs the best (≥ 16 multiplexed individuals; Fig. 5 ). This is the only scenario in which executing a single method is advantageous to a combination of methods. This is likely due to the fact that most of the methods perform poorly for larger pool sizes (Fig. 3 c).

These results collectively demonstrate that, regardless of the experimental design, demultiplexing and doublet detecting approaches that intersect multiple methods significantly enhance droplet classification. This is consistent across different pool sizes and will improve singlet annotation.

Demuxafy improves doublet removal and improves usability

To make our intersectional approaches accessible to other researchers, we have developed Demuxafy ( https://demultiplexing-doublet-detecting-docs.readthedocs.io/en/latest/index.html ) - an easy-to-use software platform powered by Singularity. This platform provides the requirements and instructions to execute each demultiplexing and doublet detecting methods. In addition, Demuxafy provides wrapper scripts that simplify method execution and effectively summarise results. We also offer tools that help estimate expected numbers of doublets and provide method combination recommendations based on scRNA-seq pool characteristics. Demuxafy also combines the results from multiple different methods, provides classification combination summaries, and provides final integrated combination classifications based on the intersectional techniques selected by the user. The significant advantages of Demuxafy include a centralised location to execute each of these methods, simplified ways to combine methods with an intersectional approach, and summary tables and figures that enable practical interpretation of multiplexed datasets (Fig. 1 a).

Demultiplexing and doublet detecting methods have made large-scale scRNA-seq experiments achievable. However, many demultiplexing and doublet detecting methods have been developed in the recent past, and it is unclear how their performances compare. Further, the demultiplexing techniques best detect heterogenic doublets while doublet detecting methods identify heterotypic doublets. Therefore, we hypothesised that demultiplexing and doublet detecting methods would be complementary and be more effective at removing doublets than demultiplexing methods alone.

Indeed, we demonstrated the benefit of utilising a combination of demultiplexing and doublet detecting methods. The optimal intersectional combination of methods depends on the experimental design and capture characteristics. Our results suggest super loaded captures—where a high percentage of doublets is expected—will benefit from multiplexing. Further, when many donors are multiplexed (>16), doublet detecting is not required as there are few doublets that are homogenic and heterotypic.

We have provided different method combination recommendations based on the experimental design. This decision is highly dependent on the research question.

Conclusions

Overall, our results provide researchers with important demultiplexing and doublet detecting performance assessments and combinatorial recommendations. Our software platform, Demuxafy ( https://demultiplexing-doublet-detecting-docs.readthedocs.io/en/latest/index.html ), provides a simple implementation of our methods in any research lab around the world, providing cleaner scRNA-seq datasets and enhancing interpretation of results.

PBMC scRNA-seq data

Blood samples were collected and processed as described previously [ 17 ]. Briefly, mononuclear cells were isolated from whole blood samples and stored in liquid nitrogen until thawed for scRNA-seq capture. Equal numbers of cells from 12 to 16 samples were multiplexed per pool and single-cell suspensions were super loaded on a Chromium Single Cell Chip A (10x Genomics) to capture 20,000 droplets per pool. Single-cell libraries were processed per manufacturer instructions and the 10× Genomics Cell Ranger Single Cell Software Suite (v 2.2.0) was used to process the data and map it to GRCh38. Cellbender v0.1.0 was used to identify empty droplets. Almost all droplets reported by Cell Ranger were identified to contain cells by Cellbender (mean: 99.97%). The quality control metrics of each pool are demonstrated in Additional file 2 : Fig S15.

PBMC DNA SNP genotyping

SNP genotype data were prepared as described previously [ 17 ]. Briefly, DNA was extracted from blood with the QIAamp Blood Mini kit and genotyped on the Illumina Infinium Global Screening Array. SNP genotypes were processed with Plink and GCTA before imputing on the Michigan Imputation Server using Eagle v2.3 for phasing and Minimac3 for imputation based on the Haplotype Reference Consortium panel (HRCr1.1). SNP genotypes were then lifted to hg38 and filtered for > 1% minor allele frequency (MAF) and an R 2 > 0.3.

Fibroblast scRNA-seq data

The fibroblast scRNA-seq data has been described previously [ 18 ]. Briefly, human skin punch biopsies from donors over the age of 18 were cultured in DMEM high glucose supplemented with 10% fetal bovine serum (FBS), L-glutamine, 100 U/mL penicillin and 100 μg/mL (Thermo Fisher Scientific, USA).

For scRNA-seq, viable cells were flow sorted and single cell suspensions were loaded onto a 10× Genomics Single Cell 3’ Chip and were processed per 10× instructions and the Cell Ranger Single Cell Software Suite from 10× Genomics was used to process the sequencing data into transcript count tables as previously described [ 18 ]. Cellbender v0.1.0 was used to identify empty droplets. Almost all droplets reported by Cell Ranger were identified to contain cells by Cellbender (mean: 99.65%). The quality control metrics of each pool are demonstrated in Additional file 2 : Fig S16.

Fibroblast DNA SNP genotyping

The DNA SNP genotyping for fibroblast samples has been described previously [ 18 ]. Briefly, DNA from each donor was genotyped on an Infinium HumanCore-24 v1.1 BeadChip (Illumina). GenomeStudioTM V2.0 (Illumina), Plink and GenomeStudio were used to process the SNP genotypes. Eagle V2.3.5 was used to phase the SNPs and it was imputed with the Michigan Imputation server using minimac3 and the 1000 genome phase 3 reference panel as described previously [ 18 ].

Demultiplexing methods

All the demultiplexing methods were built and run from a singularity image.

Demuxalot [ 6 ] is a genotype reference-based single cell demultiplexing method. Demualot v0.2.0 was used in python v3.8.5 to annotate droplets. The likelihoods, posterior probabilities and most likely donor for each droplet were estimated using the Demuxalot Demultiplexer.predict_posteriors function. We also used Demuxalot Demultiplexer.learn_genotypes function to refine the genotypes before estimating the likelihoods, posterior probabilities and likely donor of each droplet with the refined genotypes as well.

The Popscle v0.1-beta suite [ 16 ] for population genomics in single cell data was used for Demuxlet and Freemuxlet demultiplexing methods. The popscle dsc-pileup function was used to create a pileup of variant calls at known genomic locations from aligned sequence reads in each droplet with default arguments.

Demuxlet [ 3 ] is a SNP genotype reference-based single cell demultiplexing method. Demuxlet was run with a genotype error coefficient of 1 and genotype error offset rate of 0.05 and the other default parameters using the popscle demuxlet command from Popscle (v0.1-beta).

Freemuxlet [ 16 ] is a SNP genotype reference-free single cell demultiplexing method. Freemuxlet was run with default parameters including the number of samples included in the pool using the popscle freemuxlet command from Popscle (v0.1-beta).

Dropulation

Dropulation [ 5 ] is a SNP genotype reference-based single cell demultiplexing method that is part of the Drop-seq software. Dropulation from Drop-seq v2.5.1 was implemented for this manuscript. In addition, the method for calling singlets and doublets was provided by the Dropulation developer and implemented in a custom R script available on Github and Zenodo (see “Availability of data and materials”).

ScSplit v1.0.7 [ 7 ] was downloaded from the ScSplit github and the recommended steps for data filtering quality control prior to running ScSplit were followed. Briefly, reads that had read quality lower than 10, were unmapped, were secondary alignments, did not pass filters, were optical PCR duplicates or were duplicate reads were removed. The resulting bam file was then sorted and indexed followed by freebayes to identify single nucleotide variants (SNVs) in the dataset. The resulting SNVs were filtered for quality scores greater than 30 and for variants present in the reference SNP genotype vcf. The resulting filtered bam and vcf files were used as input for the s cSplit count command with default settings to count the number of reference and alternative alleles in each droplet. Next the allele matrices were used to demultiplex the pool and assign cells to different clusters using the scSplit run command including the number of individuals ( -n ) option and all other options set to default. Finally, the individual genotypes were predicted for each cluster using the scSplit genotype command with default parameters.

Souporcell [ 4 ] is a SNP genotype reference-free single cell demultiplexing method. The Souporcell v1.0 singularity image was downloaded via instructions from the gihtub page. The Souporcell pipeline was run using the souporcell_pipeline.py script with default options and the option to include known variant locations ( --common_variants ).

Vireo [ 2 ] is a single cell demultiplexing method that can be used with reference SNP genotypes or without them. For this assessment, Vireo was used with reference SNP genotypes. Per Vireo recommendations, we used model 1 of the cellSNP [ 20 ] version 0.3.2 to make a pileup of SNPs for each droplet with the recommended options using the genotyped reference genotype file as the list of common known SNP and filtered with SNP locations that were covered by at least 20 UMIs and had at least 10% minor allele frequency across all droplets. Vireo version 0.4.2 was then used to demultiplex using reference SNP genotypes and indicating the number of individuals in the pools.

Doublet detecting methods

All doublet detecting methods were built and run from a singularity image.

DoubletDecon

DoubletDecon [ 9 ] is a transcription-based deconvolution method for identifying doublets. DoubletDecon version 1.1.6 analysis was run in R version 3.6.3. SCTransform [ 21 ] from Seurat [ 22 ] version 3.2.2 was used to preprocess the scRNA-seq data and then the Improved_Seurat_Pre_Process function was used to process the SCTransformed scRNA-seq data. Clusters were identified using Seurat function FindClusters with resolution 0.2 and 30 principal components (PCs). Then the Main_Doublet_Decon function was used to deconvolute doublets from singlets for six different rhops—0.6, 0.7, 0.8, 0.9, 1.0 and 1.1. We used a range of rhop values since the doublet annotation by DoubletDecon is dependent on the rhop parameter which is selected by the user. The rhop that resulted in the closest number of doublets to the expected number of doublets was selected on a per-pool basis and used for all subsequent analysis. Expected number of doublets were estimated with the following equation:

where N is the number of droplets captured and D is the number of expected doublets.

DoubletDetection

DoubletDetection [ 14 ] is a transcription-based method for identifying doublets. DoubletDetection version 2.5.2 analysis was run in python version 3.6.8. Droplets without any UMIs were removed before analysis with DoubletDetection . Then the doubletdetection.BoostClassifier function was run with 50 iterations with use_phenograph set to False and standard_scaling set to True. The predicted number of doublets per iteration was visualised across all iterations and any pool that did not converge after 50 iterations, it was run again with increasing numbers of iterations until they reached convergence.

DoubletFinder

DoubletFinder [ 10 ] is a transcription-based doublet detecting method. DoubletFinder version 2.0.3 was implemented in R version 3.6.3. First, droplets that were more than 3 median absolute deviations (mad) away from the median for mitochondrial per cent, ribosomal per cent, number of UMIs or number of genes were removed per developer recommendations. Then the data was normalised with SCTransform followed by cluster identification using FindClusters with resolution 0.3 and 30 principal components (PCs). Then, pKs were selected by the pK that resulted in the largest BC MVN as recommended by DoubletFinder. The pK vs BC MVN relationship was visually inspected for each pool to ensure an effective BC MVN was selected for each pool. Finally, the homotypic doublet proportions were calculated and the number of expected doublets with the highest doublet proportion were classified as doublets per the following equation:

ScDblFinder

ScDblFinder [ 11 ] is a transcription-based method for detecting doublets from scRNA-seq data. ScDblFinder 1.3.25 was implemented in R version 4.0.3. ScDblFinder was implemented with two sets of options. The first included implementation with the expected doublet rate as calculated by:

where N is the number of droplets captured and R is the expected doublet rate. The second condition included the same expected number of doublets and included the doublets that had already been identified by all the demultiplexing methods.

Scds [ 12 ] is a transcription-based doublet detecting method. Scds version 1.1.2 analysis was completed in R version 3.6.3. Scds was implemented with the cxds function and bcds functions with default options followed by the cxds_bcds_hybrid with estNdbl set to TRUE so that doublets will be estimated based on the values from the cxds and bcds functions.

Scrublet [ 13 ] is a transcription-based doublet detecting method for single-cell RNA-seq data. Scrublet was implemented in python version 3.6.3. Scrublet was implemented per developer recommendations with at least 3 counts per droplet, 3 cells expressing a given gene, 30 PCs and a doublet rate based on the following equation:

where N is the number of droplets captured and R is the expected doublet rate. Four different minimum number of variable gene percentiles: 80, 85, 90 and 95. Then, the best variable gene percentile was selected based on the distribution of the simulated doublet scores and the location of the doublet threshold selection. In the case that the selected threshold does not fall between a bimodal distribution, those pools were run again with a manual threshold set.

Solo [ 15 ] is a transcription-based method for detecting doublets in scRNA-seq data. Solo was implemented with default parameters and an expected number of doublets based on the following equation:

where N is the number of droplets captured and D is the number of expected doublets. Solo was additionally implemented in a second run for each pool with the doublets that were identified by all the demultiplexing methods as known doublets to initialize the model.

In silico pool generation

Cells that were identified as singlets by all methods were used to simulate pools. Ten pools containing 2, 4, 8, 16, 32, 64 and 128 individuals were simulated assuming a maximum 20% doublet rate as it is unlikely researchers would use a technology that has a higher doublet rate. The donors for each simulated pool were randomly selected using a custom R script which is available on Github and Zenodo (see ‘Availability of data and materials’). A separate bam for the cell barcodes for each donor was generated using the filterbarcodes function from the sinto package (v0.8.4). Then, the GenerateSyntheticDoublets function provided by the Drop-seq [ 5 ] package was used to simulate new pools containing droplets with known singlets and doublets.

Twenty-one total pools—three pools from each of the different simulated pool sizes (2, 4, 8, 16, 32, 64 and 128 individuals) —were used to simulate different experimental scenarios that may be more challenging for demultiplexing and doublet detecting methods. These include simulating higher ambient RNA, higher mitochondrial percent, decreased read coverage and imbalanced donor proportions as described subsequently.

High ambient RNA simulations

Ambient RNA was simulated by changing the barcodes and UMIs on a random selection of reads for 10, 20 or 50% of the total UMIs. This was executed with a custom R script that is available in Github and Zenodo (see ‘Availability of data and materials’).

High mitochondrial percent simulations

High mitochondrial percent simulations were produced by replacing reads in 5, 10 or 25% of the randomly selected cells with mitochondrial reads. The number of reads to replace was derived from a normal distribution with an average of 30 and a standard deviation of 3. This was executed with a custom R script available in Github and Zenodo (see ‘Availability of data and materials’).

Imbalanced donor simulations

We simulated pools that contained uneven proportions of the donors in the pools to identify if some methods are better at demultiplexing pools containing uneven proportions of each donor in the pool. We simulated pools where 50, 75 or 95% of the pool contained cells from a single donor and the remainder of the pool was even proportions of the remaining donors in the pool. This was executed with a custom R script available in Github and Zenodo (see ‘Availability of data and materials’).

Decrease read coverage simulations

Decreased read coverage of pools was simulated by down-sampling the reads by two-thirds of the original coverage.

Classification annotation

Demultiplexing methods classifications were considered correct if the droplet annotation (singlet or doublet) and the individual annotation was correct. If the droplet type was correct but the individual annotation was incorrect (i.e. classified as a singlet but annotated as the wrong individual), then the droplet was incorrectly classified.

Doublet detecting methods were considered to have correct classifications if the droplet annotation matched the known droplet type.

All downstream analyses were completed in R version 4.0.2.

Availability of data and materials

All data used in this manuscript is publicly available. The PBMC data is available on GEO (Accession: GSE196830) [ 23 ] as originally described in [ 17 ]. The fibroblast data is available on ArrayExpress (Accession Number: E-MTAB-10060) [ 24 ] and as originally described in [ 18 ]. The code used for the analyses in this manuscript are provided on Github ( https://github.com/powellgenomicslab/Demuxafy_manuscript/tree/v4 ) and Zenodo ( https://zenodo.org/records/10813452 ) under an MIT Open Source License [ 25 , 26 ]. Demuxafy is provided as a package with source code available on Github ( https://github.com/drneavin/Demultiplexing_Doublet_Detecting_Docs ) and instructions on ReadTheDocs ( https://demultiplexing-doublet-detecting-docs.readthedocs.io/en/latest/ ) under an MIT Open Source License [ 27 ]. Demuxafy is also available on Zenodo with the link https://zenodo.org/records/10870989 [ 28 ].

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Wenjing She was the primary editor of this article and managed its editorial process and peer review in collaboration with the rest of the editorial team.

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This work was funded by the National Health and Medical Research Council (NHMRC) Investigator grant (1175781), and funding from the Goodridge foundation. J.E.P is also supported by a fellowship from the Fok Foundation.

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Drew Neavin, Anne Senabouth, Himanshi Arora & Joseph E. Powell

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Himanshi Arora

Wellcome Sanger Institute, Wellcome Genome Campus, Hinxton, UK

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DRN and JEP conceived the project idea and study design. JTHL, AR, LF, SP, CJY, DJM, MM and MH provided feedback on experimental design. DRN carried out analyses with support on coding from AS. JTHL and AR tested Demuxafy and provided feedback. DRN and JEP wrote the manuscript. All authors reviewed and provided feedback on the manuscript.

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Briefly, all work was approved by the Royal Hobart Hospital, the Hobart Eye Surgeons Clinic, Human Research Ethics Committees of the Royal Victorian Eye and Ear Hospital (11/1031), University of Melbourne (1545394) and University of Tasmania (H0014124) in accordance with the requirements of the National Health & Medical Research Council of Australia (NHMRC) and conformed with the Declaration of Helsinki [ 29 ].

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C.J.Y. is founder for and holds equity in DropPrint Genomics (now ImmunAI) and Survey Genomics, a Scientific Advisory Board member for and holds equity in Related Sciences and ImmunAI, a consultant for and holds equity in Maze Therapeutics, and a consultant for TReX Bio, HiBio, ImYoo, and Santa Ana. Additionally, C.J.Y is also newly an Innovation Investigator for the Arc Institute. C.J.Y. has received research support from Chan Zuckerberg Initiative, Chan Zuckerberg Biohub, Genentech, BioLegend, ScaleBio and Illumina.

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Neavin, D., Senabouth, A., Arora, H. et al. Demuxafy : improvement in droplet assignment by integrating multiple single-cell demultiplexing and doublet detection methods. Genome Biol 25 , 94 (2024). https://doi.org/10.1186/s13059-024-03224-8

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DOI : https://doi.org/10.1186/s13059-024-03224-8

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