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Cyan comments on The usefulness of correlations - Less Wrong
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I don't disagree with anything in the above comment. The opening is odd, as others have noted, and I agree. I'm not sure why you're introducing confidence intervals though.
"a variable Z which is experimentally found to have a good chance of lying close to X. Let us suppose that the standard deviation of Z-X is 10% that of X".
So, you have a confidence interval for X around Z.