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

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

## References

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