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Lumifer comments on Be Skeptical of Correlational Studies - Less Wrong
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Well, we have to be careful about definitions here. People generally don't talk about correlations when there is a known underlying mechanism.
I guess technically the phrase should look like this: Correlation by itself without known connecting mechanisms or relationships does not imply causation.
The bayesian approach would suggest that we assign a causation-credence to every correlation we observe. Of course detecting confounders is very important since it provides you with updates. However, a correlation without known connecting mechanisms does imply causation. In particular it does it probabilistically. A bayesian updater would prefer talking about credences in causation which can be shifted up and downwards. It would be a (sometimes dangerous) simplification to in our map deal with discrete values like "just correlation" and "real causation". However, such a simplification may be of use as a heuristic in everyday life, still I'd suggest not to overgeneralize it.
This does separate out the "getting run over by a car" case, but it doesn't handle the handwashing one. Germ theory hadn't been invented yet and Semelweiss' proposed mechanism was both medically unlikely and wrong. With sickle cell anemia it kind of handles it, in that you can think of all sorts of ways weirdly shaped blood cells might be a problem, but I think it's a stretch to say that the first people looking at the blood and saying "that's weird, it's probably the problem" understood the "connecting mechanisms or relationships".
More generally, correlation is some evidence and if it's not expected someone should probably look more closely to try to understand why we're seeing it, which generally means some kind of controlled experiment.
Well, to start with correlation is data. This data might be used to generate hypotheses. Once you have some hypotheses you can start talking about evidence and yes, correlation can be promoted to the rank of evidence supporting some hypothesis.
I don't think any of that is controversial. The only point is that pure correlation without anything else is pretty weak evidence, that's all. However if you want to use it to generate hypotheses, sure, no problems with it whatsoever.