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**Correction for attenuation** is a statistical procedure, due to Spearman, to "rid a correlation coefficient from the weakening effect of measurement error" (Jensen, 1998).

Given two random variables $ X $ and $ Y $, with correlation $ r_{xy} $, and a known reliability for each variable, $ r_{xx} $ and $ r_{yy} $, the correlation between $ X $ and $ Y $ corrected for attenuation is $ r_{x'y'} = \frac{r_{xy}}{\sqrt{r_{xx}r_{yy}}} $.

How well the variables are measured affects the correlation of *X* and *Y*. The correction for attenuation tells you what the correlation would be if you could measure *X* and *Y* with perfect reliability.

If $ X $ and $ Y $ are taken to be imperfect measurements of underlying variables $ X' $ and $ Y' $ with independent errors, then $ r_{x'y'} $ measures the true correlation between $ X' $ and $ Y' $.

## Derivation Edit

## References Edit

- Jensen, A.R. (1998).
*The*g*Factor.*Praeger, Connecticut, USA.

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