What's this nonsense I hear that
correlation doesn't imply causation? Of course it does. If there is correlation between two variables, there must be causation
somewhere. Granted, the correlation alone doesn't show which of the three types of causation it is (A causes B, B causes A, or C causes A and B*), but causation has to be there, if the correlation isn't spurious. It would be correct to say that correlation doesn't indicate the kind of causation.
In this case, causation is likely that those who've gone to the moon are alive, and those who are alive have eaten, and those who have eaten have likely eaten chicken - particularly likely if you're among those who have been in training to to go the moon.
More.
* All three cases could have intermediate variables, of course.
I suppose it's because "correlation does not imply causation" is a lot pithier than "correlation, unless spurious, implies causation but not necessarily operating directly between the two variables in question".
ReplyDeleteThere's also, I think, a possible definitional minefield with "spurious". Let's say I had perfect data on dozens of different variables regarding all US citizens. Not a subpopulation, but ALL of them. If I look at enough pairs of variables, at least one pair will be correlated with p < 0.05 simply by pure chance. Is this result "spurious"? I generally take "spurious" to mean that if you measured it again with a larger/different sample that you would not reproduce the result, but in this thought experiment we have already sampled the entire population, so no amount of resampling is going to give us a different result. And if you define a "spurious" correlation to mean "a correlation which occurred due to random chance without any causative backing, direct or indirect," then your argument has become circular: a correlation that does not imply causation is spurious by definition.
To salvage the statement, it now has to expand to, "Correlation, unless spurious, suggests (but does not necessarily prove) causation, though not necessarily direct causation operating only on the two variables in question." I'll stick with "Correlation does not imply causation", thank you ;p
After thinking about it more, I would guess that the famous line is a response to people equating "A correlates with B" with "A causes B". But the super stupid thing about that is that correlation isn't of the same sort as causation: Correlation has no direction, and causation does. "A correlates with B" is exactly the same as "B correlates with A", and once that is realized, the part about causation makes no sense whatsoever.
ReplyDeleteI was a psychology major for a few years in college, and "correlation does not equal (or imply) causation was one of the most frequent phrases I heard in my introductory classes.
ReplyDeleteI actually did quite a bit of psychology research during my summers, and one of the big things that I learned was that causation is not always contained within an experiment. That is, we would often observe correlation but have no idea what was causing it.
In such a case, I think that the phrase "correlation does not imply causation" is best understood. The experiments (measuring visual memory for faces and memory of names) had interesting correlations, but the causes, as we found later, were outside the variables we were measuring. No causation could be asserted, and just because a correlation existed, did not mean we were originally aware of it.
Interesting points though!
Perhaps the most precise and honest statement is "Correlation implies an unresolved causal structure". Take a look at Bill Shipley's and Judea Pearl's books. They are quite inspiring.
ReplyDelete