I do not remember where I read it (probably xkcd) but it was that correlation is not casuation, though the numbers are doing big winks to you (or something like that)
As a physicist who had to endure helping biologists with statistics and cooling down their enthusiasm: it make sense to have a deeper thought about the experiment.
As parent wrote, there may be various reasons for the correlations, sometimes you have random stuff, sometimes indirect stuff and in others extraordinary stuff. Many discoveries (especially older ones) fall into the last category.
Access to, and willingness to take, flu vaccinations is the first thing that comes to mind for me. It does narrow the set somewhat to people with certain habits.
I don't think that's right? In theory you could have A and B that were naturally correlated and add a causal relationship between the two that exactly canceled that correlation but that would be infinity unlikely to happen by chance. In practice the only way that A and B can be correlated is that either A causes B, B causes A, or some C causes both A and B. Interestingly if both A and B cause C the C and A as well as C and B will be correlated but A and B won't be, allowing you to work out causation from a strictly correlational graph.
It's not by chance.
If you have a heater controlled by a thermostat, it destroys the correlation that would otherwise exist between outside temperature and inside temperature.
That particular example sounds silly because it is so obvious. But in economics you can find examples where you would be seeing a relationship, but it is masked by an active response to the cause, but it's not so obvious this is happening.
That's the thing though. A heater controlled by a thermostat will considerably reduce the correlation between outside and inside temperature but because it's imperfect it wont' eliminate it entirely.
> In theory you could have A and B that were naturally correlated and add a causal relationship between the two that exactly canceled that correlation but that would be infinit[el]y unlikely to happen by chance.
That hardly seems relevant, since we're talking about causal relationships and chance is the opposite of causation.
Just that. Variables that are causally related frequently show no correlation, or a weak correlation with the opposite sign from the one you would expect. There's already an example sidethread from me - the correlation between the temperature outside a house and the temperature inside a house would ordinarily be close to 1. But a normal modern house tampers with the indoor temperature, reducing the correlation to something close to 0 instead. This is as dramatic of a change in correlation as it's possible to see, altering "basically the same thing" (the correct answer) to "basically unrelated" (correct in an observational sense, but wildly off in a causal sense).
With this sort of thing, lots of social factors weigh in too. Access the flu shots implies regular access to healthcare and perhaps other interventions.
As a physicist who had to endure helping biologists with statistics and cooling down their enthusiasm: it make sense to have a deeper thought about the experiment.
As parent wrote, there may be various reasons for the correlations, sometimes you have random stuff, sometimes indirect stuff and in others extraordinary stuff. Many discoveries (especially older ones) fall into the last category.