# Correction for attenuation

© Paul Cooijmans

## Explanation

Correlations are depressed, or "attenuated", by the error components in the variances of the variables whereon they are based, such that the maximum possible correlation between two variables is the square root of the product of those variables' reliability coefficients. The true correlation between two variables is that between the true score components of those variables (assuming a variable's variance has a true score component and an error component). If the reliability coefficients (*r*_{xx} and *r*_{yy}) of the variables x and y are known, the actual correlation (*r*_{xy}) can be corrected for attenuation as follows:

True correlation = *r*_{xy} / √(*r*_{xx} × *r*_{yy})