Why does correlation not mean causation

For example, if we observe that the faster the windmill rotates, the more wind there is, we might falsely conclude that the windmills rotating causes the wind. However, we know that it is the wind that causes the windmills to rotate. In some cases, there may be a hidden, underlying variable that causes events that appear to be correlated. We might assume that event A causes event B when in reality, there is another event C that causes both events A and B.

For example, many researchers have previously found that alcohol consumption is associated with an increased risk for lung cancer. However, smoking was later shown to be a confounding factor. Individuals who consume more alcohol also happen to smoke more, which increases their risk for lung cancer. While correlation is easily observable, determining causation is much more complicated and requires an appropriate experimental design. Ideally, we would want to conduct experiments in the lab, where we tightly control all variables except for the one that we are interested in.

However, this is nearly impossible in human studies. To conduct a most rigorous randomized-controlled experiment, we probably would need participants to live in the same place, eat the same food, exercise and sleep at the same time, just to name a few variables. As a result, most human microbiome research has been largely observational.

By analyzing differences in the microbiome between individuals suffering from disease and healthy individuals, we can find correlations between microbiome composition and the disease of interest Figure 3. Specifically, scientists have found that patients, such as those suffering from inflammatory bowel disease, have different gut bacteria compared to healthy individuals. We are often quick to assume the former, that the bacteria have caused the disease, though the direction of this causal relationship is not so easily determined.

Furthermore, lifestyle is a big confounding factor. Patients who suffer from diseases often change their diet upon diagnosis or take drugs for treatment, which can change their gut microbiome composition.

In an attempt to solve the problem of confounding variables, a recent publication in Nature by Ivan Vujkovic-Cvijin and co-workers picked out lifestyle differences that might be associated with microbiome composition. When we talk about a common-causal variable, we are referring to a variable that is hidden and lurking in some way. We might not be able to see it or the impact that it's having, but it can skew our view of a particular correlation.

The fallacy here is looking at the correlation and assuming causation without taking into account the active variable that is actually causing the correlation that we can see. One example of how this works is during a hot summer. If there is a hot summer and a particular politician got elected as the leader of the country during this summer, and ice cream sales also break records, there are three things happening.

If the hot summer is ignored, one could incorrectly see a causal relationship between the election of a politician and an increase in ice cream sales. In fact, the hot weather is the common variable that accounts for the increase in ice cream sales. Coincidental Relationships. Sometimes things happen by pure coincidence.

If two things happen at the same time, it doesn't necessarily prove that they have a direct link. This is different from a common-causal relationship because there isn't necessarily one variable that is skewing the results. It can be more complex than that and the correlation you're seeing can be a complete coincidence, even if the pattern occurs repeatedly over years or decades.

This is how many conspiracy theories are generated. If it's suggested that a terrorist attack often occurs days after the police carry out training, that doesn't mean that there is a link between these events. Conspiracy theorists extrapolate even more nonsense and use it to suggest proof of undercover operations and inside jobs when these things simply aren't happening.

That's why you have to be careful and examine all variables when determining cause and effect relationships. Bidirectional Causation. Bidirectional causations apply to situations where the two things being looked at have an effect on one another. If there are two things happening and the causation goes both ways, it can be easy to misinterpret the data and view it as a more conventional form of cause and effect.

The most obvious example of this is in the animal kingdom. The number of prey that predators eat directly affects the number of predators that can survive. But at the same time, if the number of predators increase, the number of prey will decrease because more of them will become food for the predators. Although correlation and causation can sometimes be linked, it's not enough to prove causation.

Search ABS. Statistical Language - Correlation and Causation. Correlation and Causation What are correlation and causation and how are they different? Two or more variables considered to be related, in a statistical context, if their values change so that as the value of one variable increases or decreases so does the value of the other variable although it may be in the opposite direction.

For example, for the two variables "hours worked" and "income earned" there is a relationship between the two if the increase in hours worked is associated with an increase in income earned. If we consider the two variables "price" and "purchasing power", as the price of goods increases a person's ability to buy these goods decreases assuming a constant income.

Correlation is a statistical measure expressed as a number that describes the size and direction of a relationship between two or more variables. A correlation between variables, however, does not automatically mean that the change in one variable is the cause of the change in the values of the other variable. Causation indicates that one event is the result of the occurrence of the other event; i. This is also referred to as cause and effect. Arguably the most well known and important example of a correlation being clear but caustion being in doubt concerned smoking and lung cancer in the s.

There had been a sixfold increase in the rate of lung cancer in the preceding two decades. Nobody disputed that there was a correlation between lung cancer and smoking, but to prove that one caused the other would be no mean feat. There might be a confounder that was responsible for the correlation between smoking and lung cancer. The increased rate could have been the result of better diagnosis, more industrial pollution or more cars on the roads belching noxious fumes.

Perhaps people who were more genetically predisposed to want to smoke were also more susceptible to getting cancer?