Correlation does not imply causation, but causation causes correlation. By correlation I do not mean exclusively linear correlation, it could be arbitrarily shaped, as long as it is consistent and reflects dependency.

Does correlation correlate with causation?

At first I thought: "Yes, because every causation implies correlation hence there definitely is a correlation between correlation and causation."

But then I thought: "Wait, the answer is no because for every correlation that is truly causal there are an infinite number of correlations that are not causal, hence the correlation between correlation and causation is not significant."

Which is right, the first answer or the second answer? Or neither?

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    $\begingroup$ Causation does not imply correlation because the causal relationship might be nonlinear. $\endgroup$ – Richard Hardy Aug 25 '17 at 15:58
  • $\begingroup$ I reworded the question to state that by correlation I'm not referring to linear relationships exclusively. $\endgroup$ – MathuSum Mut Aug 25 '17 at 16:06
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    $\begingroup$ You still need to define what exactly you mean by correlation. Because if you make your definition too wide or vague, it won't be different from causation. If you say "any kind of relationship" that's basically wide enough to include causation. $\endgroup$ – Aksakal Aug 25 '17 at 17:50
  • $\begingroup$ Doesn't this boil down to a tautology? "Correlation implies correlation". $\endgroup$ – Nate Diamond Aug 26 '17 at 0:31
  • $\begingroup$ You’ve applied the word “correlation” to two concepts without measurement, which makes this question hard to interpret. By “does correlation correlate with causality,” do you mean do people infer causality when they infer correlation? Do you mean that research on causality or correlation tend to come from the same people? Do you mean that if you create a dataset of literally every bivariate relationship that exists or will ever exist, if it is correlational, is it also likely causal? $\endgroup$ – RickyB Nov 8 '17 at 15:15

The sentence "correlation does not imply causation" is usually understood much broader than it should be. If two variables A and B are highly correlated, then something is causing something else. You just cannot conclude that A causes B because there are a number of other possibilities:

  • B causes A
  • A and B are both caused by C
  • Only if D is given, does A cause B
  • A causes E which in turn causes B
  • (An error of type I occured and the correlation is not significant, but this one is dealt with by talking about strong correlations.)

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