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Correlation typically means y is a linear function of x, but people usually interpet it (incorrectly) as: knowing x tells you something about y. If y = x^2, the
by rwilson4 5y ago
Correlation typically means y is a linear function of x, but people usually interpet it (incorrectly) as: knowing x tells you something about y. If y = x^2, then y is determined completely by x, but since it's nonlinear the correlation may actually be zero depending on the distribution of x. This paper proposes a statistic that will indicate if y is related to any function of x, linear or nonlinear.
- KarlKemp 5y agoThis is... quite wrong? The dictionary says: 1. a mutual relationship or connection between two or more things 2. [Statistics] interdependence of variable quantities. 3. [Statistics] a quantity measuring the extent of the interdependence of variable quantities. The most sympathetic to your definition is Wikipedia: In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. In the broadest sense correlation is any statistical association, though it actually refers to the degree to which a pair of variables are linearly related. And that's the mathematical formulation. Correlation also has a meaning in everyday speech, and mathematics doesn't have the authority to just adopt terms and then claim people are wrong after they've changed the meaning. Also correlation very definitely means that knowing <x> tells you something about <y>. And vice versa. Like, for example: its value. Or at least a better idea of it than pure guessing without correlation.
- doovd 5y agoThat's s bit unnecessarily pedantic, I think we all understand in which context we are talking about correlation.
- UncombedCoconut 5y agoHello, see here for an explanation: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient 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_coefficient https://en.wikipedia.org/wiki/Spearman%27s_rank_correlation_...
- csee 5y agoI 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.
- mattkrause 5y agoThat 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.
- popcube 5y agosorry, scientists always use nomal English words in their region and then it will get meaning in this specific region. It maybe is confused, but the advantage that most people understand English is enough.
- PopeUrbanX 5y agoI think it's safe to say you're not the intended audience for anything math-related, given that you're going to a dictionary to try to figure things out...
- ouid 5y agoI don't think that there's a standard enough mathematical definition of correlation to say that. Perhaps the word has been coopted but the paper linked suggests that the cooprion isn't accepted.