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We know many different statistical tests to find if there is an association (correlation) between the variables. But sometimes the correlation does not imply any causation. This could be in such cases, when some events A and B are correlated, and the following might be:
- B causes A
- A causes B
- A and B caused by some common event C, but they do not cause each other
- No connection between B and A
A significant correlation between two random variables is always evidence of the existence of a statistical association in this sample, but this relationship does not have to be observed for the other samples and have a cause-and-effect nature. Most attractive simplicity of the correlation study encourages researchers to make false intuitive conclusions about a causal connection between the pairs of signs, while the correlation coefficients are set only statistical relationships. For example, considering the fires in a particular city, you can uncover a very high correlation between the damage that caused the fire, and the number of firefighters involved in extinguishing the fire, and this correlation is positive. From this, however, not be concluded "there is more number of fire leads to more damage," and certainly not make sense to try to minimize the damage from fires by removing fire brigades. At the same time, the lack of correlation between two variables does not mean that between them there is no connection.
Or, another example:
Sleeping with one’s sock on is strongly correlated with having a headache in the morning.
So, the one sock on causes headache.
Of course, this is fallacy. A more realistic explanation of this correlation is that both – one sock on and headache in the morning are caused by a third factor, for example, being drunk.
Sources
- Aldrich, John (1995). "Correlations Genuine and Spurious in Pearson and Yule". Statistical Science 10 (4): 364–376. doi:10.1214/ss/1177009870. JSTOR 2246135.
