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More specifically, I am wondering if there is such an example satisfying the following criteria:

  1. The example happened after 1888, it would be better to be after 1900—I think few people have the conception of correlation before Galton's 1888 paper.
  2. The correlation found in the example is not easy to be investigated, but the correlation is non-trivial so that it is published first; then that correlation is investigated further, maybe with much more effort, and is finally confirmed as a result of a non-trivial causal relationship.
  3. The correlation of $A$ and $B$ is a direct result of the causal relationship between $A$ and $B$, and not induced by a common cause $C$.

I understand that correlation is not causation. Basically, I want to have examples showing that the investigation of correlations sometimes leads to the discovery of really non-trivial causal relationships, and that the conception of correlation really help for those pursuing causality.

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    $\begingroup$ "I think few people have the conception of correlation before Galton's 1888 paper." Paging 18th century Scottish philosopher David Hume… $\endgroup$ – Alexis May 19 at 19:06
  • $\begingroup$ @Alexis Pardon me. Do you mean Hume has the conception of correlation? Or ask for some references? $\endgroup$ – Eli4ph May 20 at 1:38
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    $\begingroup$ Hume is frequently credited with persuasively arguing the concept that correlation is not causation $\endgroup$ – Alexis May 20 at 3:45
  • $\begingroup$ @Alexis I see. Thanks for referring Hume. I didn't know that he had been considering the conception of correlation so long before. $\endgroup$ – Eli4ph May 20 at 3:50
  • $\begingroup$ @Alexis By the way, do you know any example showing that the conception of correlation and the use of a quantitative measure for correlation is indispensable for the discovery of a causal relationship? $\endgroup$ – Eli4ph May 20 at 3:58
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Lung cancer was not even recognised medically until the 18th century, and as recently as 1900 only about 140 cases were known in the published medical literature. ... Tobacco was apparently not even suspected as a cause of lung tumours until the final decade of the 19th century. ... Scholars started noting the parallel rise in cigarette consumption and lung cancer, and by the 1930s had begun to investigate this relationship using the methods of case-control epidemiology.

Proctor, 2012. "The history of the discovery of the cigarette–lung cancer link: evidentiary traditions, corporate denial, global toll". Tobacco Control.

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