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

How do you establish a causal relationship using statistical procedures? That’s a trick question. Statistical tests can determine whether an effect is statistically significant, but they cannot determine whether the treatment causes the effect.

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

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

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

## Correlation, Causation, and Confounding Variables

As a critical component of the scientific method, experiments typically set up contrasts between a control group and one or more treatment groups. The idea is to determine whether the effect, which is the difference between a treatment group and the control group, is statistically significant. If the effect is significant, group assignment correlates with different outcomes.

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

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

**Related posts**: Understanding Correlation in Statistics and Causation versus Correlation

## Example of Confounding in an Experiment

An example will help clarify how confounding can obscure your results. Imagine that we’re performing an experiment to determine whether regular vitamin consumption improves health outcomes. To keep things simple, we have the following two experimental groups:

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

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

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

**Related post**: Confounding Variables in Regression Analysis

## Alternative Explanations for Differences in Outcomes

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

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

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

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

## Experiments Must Account for Confounding Variables

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

- Statistically control for them in an observational study.
- Use random assignment to reduce the likelihood that systematic differences exist between experimental groups when the study begins.

I’ll cover observational studies in a future post. For now, let’s take a look at how random assignment works in an experimental design.

## Random Assignment Can Reduce the Impact of Confounding Variables

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

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

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

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

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

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

## Comparing the Vitamin Study With and Without Random Assignment

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

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

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

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

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

## Drawbacks of Random Assignment

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

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

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

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

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

Floyd Patterson says

Hi Jim,

I have a question of randomly assigning participants to one of two conditions when it is an ongoing

study and you are not sure of how many participants there will be.

I am using this random assignment tool for factorial experiments. http://methodologymedia.psu.edu/most/rannumgenerator

It asks you for the total number of participants but at this point, I am not sure how many there will be.

Thanks for any advice you can give me,

Floyd

Marty Shudak says

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

Anoop says

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

Jim Frost says

Thank you, Anoop!

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