We have a thread, Real life examples of difference between independence and correlation, which currently reads:
It is well known that independence implies zero correlation but zero correlation need not imply independence.
I came across plenty of examples using random variables supporting the latter result. Are there any real life examples to support this fact?
[Edit: @amoeba, @gung and I have performed some editing, so the second paragraph now reads:
I came across plenty of mathematical examples demonstrating dependence despite zero correlation. Are there any real life examples to support this fact?
But this does not seem to have been deemed a sufficient change for a successful reopen review.]
The thread is currently closed as a duplicate of Simplest example of uncorrelated but not independent X and Y?, which is itself closed as a duplicate of How to show operations on two random variables (each Bernoulli) are dependent but not correlated? I'm not sure how much sense it makes to close a question as a duplicate of a duplicate in general, but can see some logic behind doing so in this case.
However, I think it's clear that, at its heart, the "real life examples" thread is getting at a different point to the other threads, which are rather more oriented towards mathematical statistics. Moreover it has two nice "real-life" examples posted in the answers, which wouldn't quite seem to fit as answers in the "simplest example of uncorrelated but not independent X and Y" that it's closed as duplicate of, and certainly wouldn't fit in the Bernoulli thread that the "simplest example" thread was closed as a duplicate of.
I seem to have been the only person who wanted to reopen in the thread's last reopen review, which suggests in its current state it is not viewed as sufficiently distinctive. But it does seem clear, at least to me, that the original poster (OP) was hoping for a thread quite different in character to our existing ones. Could someone suggest to what extent the wording of the question would need to be clarified/strengthened to emphasise the question's distinctive character, so that it could return as an open thread?
Alternatively, if this question is to be viewed as essentially indistinguishable from the "simplest example" question, then perhaps this thread should be merged into that one (and presumably that one would be reopened, since if "real life example" answers were deemed acceptable there, then that thread is not redundant to the Bernoulli variable one). Personally, I don't find this alternative particularly attractive, because it strikes me there is worthwhile distinction between a minimalist mathematically simple example, and a more heuristic/intuitive real life example, but I think it would be more consistent than the current situation.