# Correction for attenuation

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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 and , with correlation , and a known reliability for each variable, and , the correlation between and corrected for attenuation is .

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 and are taken to be imperfect measurements of underlying variables and with independent errors, then measures the true correlation between and .

## Derivation Edit

## References Edit

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

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