Causation vs Correlation

Causation vs Correlation

Journalists are constantly being reminded that “correlation doesn’t imply causation;” yet, conflating the two remains one of the most common errors in news reporting on scientific and health-related studies. In theory, these are easy to distinguish—an action or occurrence can cause another (such as smoking causes lung cancer), or it can correlate with another (such as smoking is correlated with high alcohol consumption). If one action causes another, then they are most certainly correlated. But just because two things occur together does not mean that one caused the other, even if it seems to make sense.

Unfortunately, intuition can lead us astray when it comes to distinguishing between the two. For example, eating breakfast has long been correlated with success in school for elementary school children. It would be easy to conclude that eating breakfast causes students to be better learners. Is this a causal relationship—does breakfast by itself create better students? Or is it only a correlation: perhaps not having breakfast correlates highly with other challenges in kids’ lives that make them poorer students, such as less educated parents, worse socio-economic status, less focus on school at home, and lower expectations.

It turns out that kids who don’t eat breakfast are also more likely to be absent or tardy—and absenteeism plays a significant role in their poor performance. This may lead one to believe that there is not a causal relationship. Yet breakfast may encourage kids to come to school (and on-time), which then improves their performance in school, and so perhaps encourages attendance, which then results in better performance. In a recent literature review, there were mixed results suggesting that the advantages of breakfast depend on the population, the type of breakfast provided, and the measurement of “benefit” for the kids. Breakfast seems to have an overall positive impact on cognitive performance, especially memory tasks and focus. Not surprisingly, the benefit seems greater for kids who are undernourished. But the clear message here is that a causal relationship has been extremely hard to establish, and remains in question.

Many studies are designed to test a correlation, but cannot possibly lead us to a causal conclusion; and yet, obvious “reasons” for the correlation abound, tempting us toward a potentially incorrect conclusion. People learn of a study showing that “girls who watch soap operas are more likely to have eating disorders”— a correlation between soap opera watching and eating disorders—but then they incorrectly conclude that watching soap operas gives girls eating disorders. It is entirely possible that girls who are prone to eating disorders are also attracted to soap operas.

There are several reasons why common sense conclusions about cause and effect might be wrong. Correlated occurrences may be due to a common cause. For example, the fact that red hair is correlated with blue eyes stems from a common genetic specification that codes for both. A correlation may also be observed when there is causality behind it—for example, it is well established that cigarette smoking not only correlates with lung cancer but actually causes it. But in order to establish cause, we have to rule out the possibility that smokers are more likely to live in urban areas, where there is more pollution—and any other possible explanation for the observed correlation.

In many cases, it seems obvious that one action causes another; however, there are also many cases when it is not so clear (except perhaps to the already-convinced observer). In the case of soap-opera watching anorexics, we can neither exclude nor embrace the hypothesis that the television is a cause of the problem—additional research would be needed to make a convincing argument for causality. Another hypothesis might be that girls inclined to suffer poor body image are drawn to soap operas on television because it satisfies some need related to their poor body image. Or it could be that neither causes the other, but rather there is a common trait—say, an overemphasis on appearance in the girls’ environment—that causes both an interest in soap operas and an inclination to develop eating disorders. None of these hypotheses are tested in a study that simply asks who is watching soaps and who is developing eating disorders, and finding a correlation between the two.

How, then, does one ever establish causality? This is one of the most daunting challenges of public health professionals and pharmaceutical companies. The most effective way of doing this is through a controlled study. In a controlled study, two groups of people who are comparable in almost every way are given two different sets of experiences (such one group watching soap operas and the other game shows), and the outcome is compared. If the two groups have substantially different outcomes, then the different experiences may have caused the different outcome.

There are obvious ethical limits to controlled studies: it would be problematic to take two comparable groups and make one smoke while denying cigarettes to the other in order to see if cigarette smoking really causes lung cancer. This is why epidemiological (or observational) studies are so important. These are studies in which large groups of people are followed over time, and their behavior and outcome is also observed. In these studies, it is extremely difficult (though sometimes still possible) to tease out cause and effect, versus a mere correlation.

Typically, one can only establish a causal relationship if the effects are extremely notable and there is no reasonable explanation that challenges causality. This was the case with cigarette smoking, for example. At the time that scientists, industry trade groups, activists and individuals were debating whether the observed correlation between heavy cigarette smoking and lung cancer was causal or not, many other hypotheses were considered (such as sleep deprivation or excessive drinking) and each one dismissed as insufficiently describing the data. It is now a widespread belief among scientists and health professionals that smoking does indeed cause lung cancer.

When the stakes are high, people are much more likely to jump to causal conclusions. This seems to be doubly true when it comes to public suspicion about chemicals and environmental pollution. There has been a lot of publicity over the purported relationship between autism and vaccinations, for example. As vaccination rates went up across the United States, so did autism. And if you splice the data in just the right way, it looks like some kids with autism have had more vaccinations. However, this correlation (which has led many to conclude that vaccination causes autism) has been widely dismissed by public health experts. The rise in autism rates is likely to do with increased awareness and diagnosis, or one of many other possible factors that have changed over the past 50 years.

Language further contorts the distinction, as some media outlets use words that imply causality without saying it. A recent example in Oklahoma occurred when its Governor, Mary Fallin, said there was a “direct correlation” between a recent increase in earthquakes and wastewater disposal wells. She would have liked to say that the wells caused the earthquakes, but the research only shows a correlation. Rather than misspeak, she embellished “correlation” with “direct” so that it sounds causal.

At times, a correlation does not have a clear explanation, and at other times we fill in the explanation. A recent news story reports that housing prices in D.C. correlate with reading proficiency. Many stories can be crafted to explain the phenomenon, but most people would be reluctant to conclude that a child’s reading proficiency could cause the price of their house to be higher or lower, or vice-versa. In contrast, a news story reporting that “30 years of research found a positive correlation between family involvement and a student’s academic success” in Florida feels like it has the weight of causality. The big difference between these two different correlations is our own belief in a likely mechanism for family to contribute to better grades.

In general, we should all be wary of our own bias: we like explanations. The media often concludes a causal relationship among correlated observances when causality was not even considered by the study itself. Without clear reasons to accept causality, we should only accept the existence of a correlation. Two events occurring in close proximity does not imply that one caused the other, even if it seems to makes perfect sense.


Rebecca Goldin is Professor of Mathematical Sciences at George Mason University and Director of She received her undergraduate degree from Harvard University and her Ph.D. from the Massachusetts Institute of Technology. She taught at the University of Maryland as a National Science Foundation postdoctoral fellow before joining George Mason in 2001. Her academic research is in symplectic geometry, group actions and related combinatorics. In 2007, she received the Ruth I. Michler Memorial Prize, presented by the Association for Women in Mathematics. Goldin is supported in part by NSF grant #1201458.


  1. Margaret Gorlin

    I discovered your stat stories this morning while poking around the internet looking for good examples of bad statistics. I am still reading your stories with relish an hour after starting – they are interesting, fun, thought provoking and at a level I can use in my intro stat classes this fall. Thank you for these gems – I am planning to put them to good use this term.

    • statsorg

      Thank you Margaret: We have big expansion plans in the next year!

  2. Zachary

    I’m a high school student in a college level Stats course and reading this has been so interesting. I’m starting to think about a career in Stats

    • statsorg

      Good for you Zachary! The world needs more statisticians! And it’s willing to pay too!

      • David

        See what you’ve caused!?

  3. Lexi

    This was a great source of information. I’m currently writing an essay for extra credit and this is the first clear explanation I have found that truly approaches the topic the way I need. Thank you so much.

  4. Mark

    Dr. Goldin, great piece. Is there a point where the size, scope or length of time scale of the data begins to demonstrate such an overwhelming correlation that cause and effect is much more certain? I’m thinking about this in the context of business, where most of the decisions we make each day are based on correlation v. absolute certainty re cause and effect. It seems logical, for example, that correlations in larger bodies of data over longer periods of time would be inherently more reliable and potential more indicative of cause and effect than two quarters of data. Your thoughts would be greatly appreciated. Thanks!

  5. Yawning Enthusiast

    Most readers won’t know the difference between causation and correlation. In fact, many reporters who use those two words don’t fully understand either. However, what would be the proper way to explain that not all smokers suffer from lung cancer?

    • Carey Reed

      From Rebecca Goldin: The meaning of “cause” is indeed a probabilistic one. Lung cancer is caused by smoking, but many people who smoke do not develop lung cancer. And some nonsmokers get lung cancer. To be more technical, smoking causes an increased probability (or risk) of developing lung cancer. In contrast, two correlated occurrences are happening together more than you would expect if there were no relationship between them, but one does not necessarily cause the other. For example, children’s heights are correlated with their reading ability. But it’s not that reading helps children grow nor that growing helps them read; as children grow (thanks to nutrition and genetics), they are also learning to read (likely thanks to a teacher). Correlations are also probabilistic in nature: a tall child is more likely to read better than a short child, but certainly there are many exceptions. Both causation and correlation have associated probabilities; the difference between causation and correlation has to do with why the two occurrences are related — smoking causes cancer, but height doesn’t cause improved reading skills.

  6. Shanice F-J

    Thank you for your help, the clearest example I’ve seen! I’m currently working on my dissertation and this really helped! Thanks

  7. ah ha

    go westfield, urban ed!!!

  8. morfara

    “If one action causes another, then they are most certainly correlated. “. Could you please elaborate a bit more on that, i.e. can one action cause another, and not be correlated?

    • Carey Reed

      From Rebecca Goldin: When we find an association in data, we don’t always know if one thing causes another. There may be market correlations — like the US dollar and the cost of oil — or health-related associations like a genetic marker and decreased cancer risk. But when one action causes another (directly), they are generally associated. As for whether one action can cause another, and not be correlated — the answer is that it depends on what you mean by ‘correlated’. If you mean, “related to each other in the data you collect,” the answer is yes: it is possible that we collect data that does not show an association even if there is one. If you mean “in the world,” then the answer is no: if we could collect all data with perfect instrumentation for measurement, then any causal relationship would also appear as a correlation or association. (Warning: here I am using ‘correlation’ synonymously with ‘association’, but some use ‘correlation’ in a more technical way to indicate specific kinds of associations).



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