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Re: st: how to derive standard error of correlation coefficient

From   Nick Cox <>
Subject   Re: st: how to derive standard error of correlation coefficient
Date   Tue, 04 Aug 2009 08:52:59 -0500

If that is really all you know, I doubt that you can do it. To a good first approximation the se of r depends mainly on the sample size, so long as correlations are near zero. The original standard deviations are immaterial, given that the correlation is necessarily scale-free. But even given a p-value, you need sample size as well.

Also watch out: if correlations are interestingly non-zero, then the usual kind of rule that uncertainty is captured by intervals of the form estimate +/- multiplier * se breaks down, as the bounds +1 or -1 impart asymmetry to the problem. It's better to do calculations on a transformed scale. For more, see

SJ-8-3 pr0041 . Speaking Stata: Corr. with confidence, Fisher's z revisited (help corrci, corrcii if installed) . . . . . . . . . . . . N. J. Cox
        Q3/08   SJ 8(3):413--439
        reviews Fisher's z transformation and its inverse, the
        hyperbolic tangent, and reviews their use in inference
        with correlations


Miranda Kim wrote:

How can I derive the standard error of the correlation coefficient when I have only a correlation coefficient, p-value, and the standard deviations of both variables?

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