Comment by UncombedCoconut
4 years ago
Hello, see here for an explanation: https://en.wikipedia.org/wiki/Pearson_correlation_coefficien... It's widely understood that the words "correlation" and "uncorrelated", when used in the context of statistics and not otherwise qualified, are shorthand for this definition in particular. By "otherwise qualified" I mean, for example, saying "Spearman's correlation" (in in the OP's abstract) to specify this one: https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_...
I think that depends on context. Sometimes, in a technical setting correlation just means dependence as an abstract concept, and this includes non-linear dependence. Similar how in financial circles, volatility doesn't mean standard deviation, but in colloquial settings it does.
That matches my experience too.
Correlation, in general, just means some sort of statistical dependence: knowing x tells you something about y. It's often "operationalized" by computing Pearson's r: it's easy to do and there's lots of associated theory.
However, I would find it absolutely bizarre if someone showed a plot with obvious non-linear dependence and described it as "uncorrelated". In that case, the low r reflects a failure of the measuring tool rather than something being measured.