Meaning of 'Correlation Does Not Imply Causation': Explained Here

Meaning of 'Correlation Does Not Imply Causation' Explained
The phrase 'correlation does not imply causation' is used in science, sociology, psychology, economics, and philosophy to show the distinction between the causal relation of two variables. PsycholoGenie explains the phrase 'correlation does not imply causation' with its meaning and examples.
PsycholoGenie Staff
Last Updated: Feb 27, 2018
"Correlation doesn't imply causation, but it does waggle its eyebrows suggestively and gesture furtively while mouthing 'look over there.'
― Randall Munroe from xkcd, A webcomic of romance, sarcasm, math, and language.
Have you ever experienced morning headaches after sleeping with your shoes on? It may have happened once, but repeated occurrence of headaches may cause someone to think that there is a relationship between wearing one's shoes to bed and a headache next morning. We tend to form a relationship between two phenomena. We form a logical relationship between them believing that if one phenomenon precedes another, then it is the cause of the second phenomenon. The second phenomenon is an effect or a consequence of the first one. However, is it true every time?

To understand the difference between causation and correlation, let us see the definitions of both.
According to the Merriam-Webster dictionary, correlation means a relation existing between phenomena or things or between mathematical or statistical variables which tend to vary, be associated, or occur together in a way not expected on the basis of chance alone.

Causation means the act or process of causing something to happen or exist; the relationship between an event or situation and a possible reason or cause.
There are two Latin phrases that are used to support this type of cause-and-effect relation between two things. Those phrases are cum hoc ergo propter hoc, meaning "with this, therefore because of this" and post hoc ergo propter hoc, meaning "after this, therefore because of this." These are logical fallacies that convince us that if two things are happening simultaneously, there is a causal relationship between them. In addition, if a particular thing occurred after another, it is an effect of the previous one. However, it may not always be the case.
Meaning
The phrase correlation does not imply causation is used to emphasize the fact that if there is a correlation between two things, that does not imply that one is necessarily the cause of the other. Even though with the logical fallacies, the way to find the cause behind its effect is false, the result itself is usually not. Researchers test to calculate correlation between two variables and the true causal relationship between them.
► There are several possibilities of a causation vs. correlation relation. If we consider "A" and "B" as two variables, then first and foremost, there can be a direct relationship where A causes B to occur. Secondly, B can be the cause of A in a reverse relationship. A and B both might be the consequences of some unknown factor. The causal relationship can go in a circular fashion where A is the cause of B and B is the cause of A.

► In some cases, there might be a third factor apart from the original two variables that contributes in the effect. Let us take the previously discussed example of sleeping with your shoes on and having a headache the next morning. It may happen that both the things happened simultaneously more than once in a person's life. As that person had slept wearing shoes before experiencing a headache the next morning, he might believe that wearing shoes to his bed caused the headache. However, there might be a third hidden factor that he chose to ignore. Every time that person goes to bed with his shoes on, he might be drunk. That is the reason he forgot to take his shoes off, and that is the reason he had a headache the next morning. This third factor is called confounding factor or confounding variable.

► In some other cases, there might be no connection between the two things. The correlation between the two variables may be a pure coincidence. It is known as a risk factor as well. For example, obesity is a risk factor for type 2 diabetes. We might confuse the "risk factor" in the sentence as a "cause"; however, it is means that both the factors are correlated to each other. If obesity is a risk factor of type 2 diabetes, then type 2 diabetes is a risk factor of obesity.
Examples
► According to a 1991 observational study, hormone replacement therapy, apart from treating menopause symptoms, had a potential to reduce risks of a coronary heart disease. However, later, controlled studies showed that there is no such connection between them. It was socioeconomic strata of some women, who received better quality of food and exercise, which contributed in reducing the risk of coronary heart disease.
► Take a look at this statement―"When the rotation of windmills are faster, there is usually more wind. Therefore, faster rotations of windmills cause more wind." The juxtaposition of the speed of windmills and the velocity of wind does not mean that a windmill causes wind. In fact, it is the reverse. The velocity of wind causes windmills to rotate faster.
► According to the Church of the Flying Spaghetti Monster, which was first introduced in 2005, global warming is caused by a decreasing number of pirates. In this case as well, correlation of increasing temperature and decreasing number of pirates do not imply causation. The fact that the number of pirates has decreased over the years and rising temperature coincide with each other.
In the end, we need to remember that not every two things appearing together will have a causal relationship. The relation will have several explanations, which we will need to unearth.
Windmills on Crete island Greece