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**Physics, Astronomy & Cosmology / Re: Correlation vs association**

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**Today**at 00:56:18 »

Hi.

Good general discussion from @evan_au above.

Essentially it depends on your target audience - the people who you expect to read your statements.

The phrase "X and Y are uncorrelated" has a precise meaning to a Statistician or Mathematician. It means precisely r(X,Y) = 0 (the correlation coefficient = 0) and nothing more. They won't jump to any other conclusions, in particular they won't assume that X and Y are completely unrelated or independent variables. They know that X could still be entirely determined by Y, they just aren't linearly related.

The phrase "X and Y are correlated" would just mean that r(x,Y) equals anything else other than 0. To be honest, that's a rare phrase to use for statisticians. It would be more common to take more lines and state that r(X,Y) cannot be zero but its not clear that a linear relationship exists or else just leave it written in symbols r(X,Y) ≠ 0. If you did leave that phrase "X and Y are correlated" as if it was some sort of final conclusion then they might reasonably assume you meant that X and Y are strongly correlated, or that |r(x,Y)| ≈ 1. To say that in plain English - they might assume that X is (or is almost entirely explained by) a linear function of Y.

If your target audience is not a group of statisticians, then you "know" that when people hear the words "correlated" or "uncorrelated" they will jump to conclusions about whether X and Y are independent or unrelated. They might make even bigger jumps than that and assume one thing is actually the cause of the other. So if your target audience isn't a group of statisticians, then you really must do as @evan_au suggested and choose your phrases more carefully.

Best Wishes.

Good general discussion from @evan_au above.

is it wrong to say that they are correlated to each otherNo it's not "wrong" it's just a bit dangerous or could be misunderstood.

Essentially it depends on your target audience - the people who you expect to read your statements.

The phrase "X and Y are uncorrelated" has a precise meaning to a Statistician or Mathematician. It means precisely r(X,Y) = 0 (the correlation coefficient = 0) and nothing more. They won't jump to any other conclusions, in particular they won't assume that X and Y are completely unrelated or independent variables. They know that X could still be entirely determined by Y, they just aren't linearly related.

The phrase "X and Y are correlated" would just mean that r(x,Y) equals anything else other than 0. To be honest, that's a rare phrase to use for statisticians. It would be more common to take more lines and state that r(X,Y) cannot be zero but its not clear that a linear relationship exists or else just leave it written in symbols r(X,Y) ≠ 0. If you did leave that phrase "X and Y are correlated" as if it was some sort of final conclusion then they might reasonably assume you meant that X and Y are strongly correlated, or that |r(x,Y)| ≈ 1. To say that in plain English - they might assume that X is (or is almost entirely explained by) a linear function of Y.

If your target audience is not a group of statisticians, then you "know" that when people hear the words "correlated" or "uncorrelated" they will jump to conclusions about whether X and Y are independent or unrelated. They might make even bigger jumps than that and assume one thing is actually the cause of the other. So if your target audience isn't a group of statisticians, then you really must do as @evan_au suggested and choose your phrases more carefully.

Best Wishes.