What examples are there of scientific effects or correlations that we now know to be real, and were known about for a long time but thought to be coincidences?

To give an example of the kind of thing that I have in mind (but I don't necessarily know if these are real or the best examples):

  1. People used to know that there was a relationship between the moon and the tides, but expert opinion was that this was just a superstition. Now we know the moon really does influence tides.

  2. The "hot hand" effect in basketball. Originally this was claimed to be the result of random chance and a psychological bias to see patterns, later some papers claimed that this was a real effect. I'm not sure what the current state of the debate is.

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    $\begingroup$ I think the problem with your examples is that the first (tides) was in an epoch before methods of scientific validation had been developed, vs. the second case where it's next to impossible to run a "double-blind" test. $\endgroup$ – Carl Witthoft Oct 11 '18 at 12:42

Dunno, how about

-- equivalence of gravitational and inertial mass

-- transmission of disease via contact. Well-known, but not proven until well after microscopes came along.

You could contrast with effects long-thought to be real but which were disproven, such as night air carrying disease

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  • $\begingroup$ Is there a source for anyone specifically saying that these effects were coincidences? If so those are great answers $\endgroup$ – user7951 Oct 12 '18 at 2:21

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