Comment by rwilson4

4 years 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.

8 comments

rwilson4

KarlKemp 4 years ago

This 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 4 years ago

That's s bit unnecessarily pedantic, I think we all understand in which context we are talking about correlation.
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_...
- csee 4 years ago
  
  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.
  
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popcube 4 years ago

sorry, 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 4 years ago

I 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 4 years ago

I 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.