What does “correlation does not equal causation” mean, anyway?

You may have heard people respond to a study and say: “correlation does not equal causation.”

It’s a favourite line and has an important meaning.

The purpose is basically to prevent jumping to conclusions.

. . . And conclusions are jumped to All. The. Time. 🙁

In a nutshell, “correlation does not equal causation” means that when two things happen at the same time—even though they seem related and it could make sense that one caused the other—it doesn’t necessarily mean that one caused the other.

So, let’s chat about what those terms mean, and which studies show correlation and which show causation. Then I’ll share a few fascinating examples from the world of health research.

Correlation is

A connection or relationship between two or more things. (ref)

Essentially this means there’s a coincidence—two things coincide with each other. They may appear together or at the same time. They’re “associated” with each other.

Links between two seemingly related things can be found everywhere in health science.

For example, in many nutrition studies, correlations happen when people who eat more or less of something (e.g., carbs, broccoli, vitamin D) may have higher or lower levels of something else (e.g., insulin resistance, ability to fall asleep, strokes). Two things may be related, but we can’t conclude whether one caused the other, or if there are other factors involved.

The two things that are correlated may have little to do with each other or a lot to do with each other, but with the study being quoted, we can’t actually prove that one caused the other.

Don’t get me wrong. It’s great when we discover links between things, like nutrition and lifestyle choices, and risks of diseases. This is great information to have. Every study that’s well-designed to answer a health question is another puzzle piece clarifying our understanding of the complex human body. So, even if the studies show a correlation and not causation, this is great information to begin working with.

Examples of health-related correlations

• Some people who report eating more processed foods tend to feel symptoms of anxiety and depression more often than those who eat less processed foods (click here to share this study on processed foods with your audience)
• Some people who eat the MIND diet have a lower chance of developing symptoms of Alzheimer’s disease, even if they have harmful plaques and tangles in their brains (click here to share this study on the MIND diet with your audience)

You may notice one common thing between these types of studies that find correlations (and not causations). They observe things without intervening. This can mean asking people questions rather than having them start taking a supplement, for example. These observational studies are often based on surveys of thousands, or even tens- or hundreds-of-thousands of people. These studies are valuable in that they can often collect so many data points from so many people. They may even continue to collect information for months or even years.

But, because they don’t ask anyone to make a change to their nutrition or lifestyle (i.e., they’re not doing a study that measures before and after an intervention happened), they can’t conclude whether the health or lifestyle caused the disease risk to go up or down.

Is it possible that these correlations are a sign that one causes the other?

Absolutely, yes it’s possible.

BUT,

These studies that show correlations are not designed to prove causation. We need a different type of study—one that has an intervention—to see what the true causes are.

It’s not easy to prove that one thing caused something else to happen. Interventional studies are much more expensive to do and therefore are often much smaller and for shorter durations. (We’ll talk about them in the next section.)

Pro Tip: You can often easily identify a study that’s designed to look for correlations: it asks people what they do (observation), but doesn’t make them do anything different (no intervention).

Here’s a story, told by Sherry Nouraini, PhD‏, that outlines the differences between “correlation” and “causation.”

Correlation does not mean causation, we are all guilty of confusing the two from time to time. #scicomm for the rest of us pic.twitter.com/cI5mHoc9y8

— 🟣Dr. Sherry Nouraini (@snouraini) May 24, 2017

Causation is

The process of causing something to happen or exist. (ref)

Unlike correlation, causation is when you have objective confidence that, without one thing, the other would likely not happen. If A causes B, then without A, B would probably not occur. Causation is when there is fairly strong proof that one thing is responsible for the other.

In health science, causation is determined with strong (and expensive) studies that test interventions. Basically, they measure something, make an intervention, and then measure it again to see what (if anything) changed. One of these types of studies is considered to be the “gold standard” for testing treatments and is called a randomized control trial (RCT)

In an RCT, participants aren’t simply asked questions about their nutrition and/or lifestyles, they’re randomly sorted into two groups so one group can make that intervention, while the other serves as the control group with no intervention. Both groups are monitored to see what changed before and after the intervention. The two groups are then also compared to each other.

This type of study provides stronger evidence that the intervention had an effect, and therefore caused the change.

Examples of health studies that can determine causation

• When people are stressed, their levels of the hunger hormone ghrelin increase (confirmed by measuring people’s ghrelin level, putting them in a stressful situation, then testing their ghrelin level again) (click here to listen to me chat about this study about ghrelin levels and download a free mini-article to share with your audience)
• Compared to people who had no COVID-19 news, those who consumed just 2-4 minutes had a reduction in their positive affect and optimism (click here to share a mini-article about this study with your audience).
• Participants who started eating 85% dark chocolate every day for three weeks felt less negative than people who ate none or 70% dark chocolate (click here to share a mini-article about this chocolate study with your audience)

Study design has a lot to do with “correlation does not equal causation”

Science can be super-creative. I swear!

Yes, there are some (lots of!) basic types of studies used to conduct health research. For a super-simple summary, check out my favourite infographic on the internet. This infographic shows some of the most common types of studies.

Note the arrow on the left pointing down. You can see how the strength of the evidence increases as you go down this list.

Simply put, there are two main types of research that can be done (you can see these in the parenthesis under the different study types in the link above):

• “Observational” where you look at what’s going on, and
• “Experimental” where you make a change/intervention and see what happens.

Even within each study type, there really are a ton of different ways to conduct research. And this is why many studies should be done before we can be sure of something. The higher quality, the better.

For example,

• Who/what to do the study on (e.g. People? Animals? Cells?);
• How to reduce bias (e.g. Randomization? Blinding?);
• What to measure (e.g. Diagnoses? Blood/urine tests? Symptoms?);
• How to measure them (e.g. How subjective/objective? How sensitive/specific should the tests be?);
• How to statistically interpret the results of a study; and,
• How to be realistic (read: cautious) when it comes to applying the results to real life.

Yup! Scientists can be creative beings.

This is why the more studies we have, the more confident we can be. Having more studies, especially larger, longer, higher-quality ones of both the observational and experimental types can build robust body of evidence to make better health recommendations. This is especially true when different studies that look at the same thing in different ways all come to a similar conclusion. (You probably realize that many studies that look at the same thing sometimes have different results! That’s OK. That’s where we have to scrutinize the type of study and how it was done to see which ones have more weight.)

In other words, strong evidence is needed to be sure of causation.

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How do observational studies show correlations/associations/coincidences/links (and *not* causes)?

Here are a few ways to do an observational study to find correlations, links, or associations:

• We look at people who eat a certain way (based on their answers to a questionnaire) and see what types of diseases/test results/symptoms they have. It’s like a “snapshot in time.” (These are cross-sectional observational studies.)
• Or we do it the other way around. We take a group of people with a certain disease/test results/symptoms, and then ask them which/how much different foods/drinks they’ve consumed. So, we’re looking backward (retrospectively) to see if we can figure out what they may have done that may be related in some correlational/associational way. (These are case-control observational studies.)
• Or, even better, we can take a group of people, ask them what they eat, and have them give blood/urine samples, or share their medical records from time to time. We keep collecting this information regularly for many years (prospectively). Then, we see who gets which disease/test result/symptom over time. (These are cohort observational studies.)

You’ll notice that none of these have interventions. No participants have to change what they’re doing. They are free to continue living their lives as they otherwise would. No one is asked to eat a certain way for a certain time. No one starts taking a pill (active ingredient or placebo) or doing a certain amount of a certain exercise. No one is given dark chocolate to eat every day.

The information we gather from these types of studies are observations. Observations are great to know about and sometimes when we look at observations, it may make total sense that one thing caused the other.

BUT,

Without at least one interventional study, many of these observations that are very logical are later proven wrong with newer and better studies. This is why some popular health and nutrition claims are later disproven: because stronger studies have looked deeper and found more details that we didn’t ever know.

I like to think about it from the perspective of the gut-brain axis. Twenty years ago we had little, if any, evidence that it existed, let alone how strong it is. By staying up-to-date with newer and better research, over the years we’ve refined our knowledge with more understanding and can become an expert and make better health recommendations.

Why do we do “observational” studies if the results aren’t going to show causation?

First of all, observing correlations can help to find links that may be very worthwhile to study in more depth and find out what causes something. Secondly, the more observational studies we have that look at the same thing from different angles and mostly see the same correlation, the more confident we can be that one of those things may cause the other. Each study that looks at something and tries to figure out what it’s linked to sheds light on another piece of the whole puzzle. The more pieces we have, the clearer the image gets.

According to Julia Belluz at Vox:

This study design can be very valuable — it’s how scientists learned about the dangers of smoking and the benefits of exercise. But because these studies aren’t controlled like experiments, they’re a lot less precise and noisy.(ref)

How can experimental studies prove causation?

Experimental (or interventional) studies do just that: They intervene in a process or someone’s life to do an experiment. They don’t just ask questions and take measurements, they require a change or intervention.

Whether that change is to take a pill (or placebo), use a certain product, or even be admitted to a “metabolic ward” and given exact amounts of foods to eat (more on that below), it’s an intervention.

And when you intervene in someone’s life, to make that change, you can be more certain that it’s that change that caused the effect, and not just an association (or coincidence).

How? Because you can take measurements before and after the change.

Even better, when you have several experimental studies looking at the same thing in a different way and having similar results, this makes it pretty clear that there is a  cause-effect relationship.

This is where review studies come in. There are several different types of reviews, including the highest quality systematic reviews. What they have in common is that they take several studies that try to answer the same question, critically evaluate them, and come up with an overview of the topic.

PRO TIP: If you search PubMed to research a topic, start with the review studies. It is easier (and smarter, IMHO) to start your research with a smaller number of higher-quality studies (like reviews) before diving into clinical trials or observational studies.

Here’s what it looks like:

Why should we do different kinds of studies?

Scientific knowledge builds on itself. There is a foundation of health knowledge that is based on thousands of studies done over the past few centuries. In fact, there may be a bunch of different studies (of all different types) that point in the same direction. And that is pretty solid evidence.

So, before we would ever really change a health recommendation, many high-quality studies need to be done. Then, look at the results of those studies to see if they point to the same conclusion. All of that evidence—observational correlations and experimental causations—should be weighed to come to a solid conclusion.

Nutrition studies are usually observational

Because we simply can’t, and shouldn’t, force people to eat a certain way for a long time, is why nutritional science is very “correlational.” I mean, how are you going to ensure that someone sticks to a very prescribed amount of certain foods day in and day out for weeks or years to see if they eventually get high cholesterol or insulin resistance?

It can be done, but it requires a lot of oversight and is expensive. This is why the few RCTs done in nutrition are small (done in a few dozen people) and short (a few weeks long). Of course, you can do this when it comes to supplements/placebos. But, when it comes to having people stick to a new diet—that’s really, really hard!

In this blog post I talk about two high-quality nutrition trials (RCTs):

• Dr. Hall’s metabolism research
• Dr. Jacka’s nutritional psychiatry research

These kinds of experimental nutritional studies are rare because it’s very hard to get people to agree to eat a certain way and have everything measured. They’re also very expensive. But, even if they’re small studies done on one or two dozen participants, they provide stronger proof of a cause-effect relationship than most other nutrition studies.

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If you don’t require a change (or intervention); how can you prove something actually caused something else (i.e. “causation”)?

Answer: You pretty much can’t.

Hence, “correlation does not equal causation.”

Conclusion

Correlation does not equal causation.

That’s it!

(just kidding). 🙂

“Correlations” are associations that happen when two things occur at or near the same time. These results come from observational studies. These are made when we observe and measure things without purposefully intervening and seeing what happens. We’re watching, learning, and doing some math to see which things are associated with each other because they seem to happen around the same time.

“Causations” are when the research is strong enough to show that one thing made something else happen. These results are much more robust to show that a change caused something to happen differently than it normally would. These results come from experimental or interventional studies. When we make a change to see what happens.

Signing off and toasting: To rocking the “correlation does not equal causation” card.

Over to you

What do you think? Did I explain this uber-fascinating concept (or can I improve it)?

Are the differences between observational (that yield “correlational” results) and experimental/interventional studies (that yield “causational” results) clear?

Do you feel confident that you can rock the “correlation does not equal causation” card?

I’d love to know (in the comments below)!

Further reading

• Clearing up confusion between correlation and causation: Conversation
• Association is not the same as causation: Students 4 Best Evidence
• I asked 8 researchers why the science of nutrition is so messy. Here’s what they said: Vox
• The one chart you need to understand any health study: Vox
• The Evidence-Based Medicine Pyramid!: Students 4 Best Evidence