Correction for Attenuation

Correction for attenuation (CA) is a method that allows researchers to estimate the relationship between two constructs as if they were measured perfectly reliably and free from random errors that occur in all observed measures. All research seeks to estimate the true relationship among constructs; because all measures of a construct contain random measurement error, the CA is especially important in order to estimate the relationships among constructs free from the effects of this error. It is called the CA because random measurement error attenuates, or makes smaller, the observed relationships between constructs. For correlations, the correction is as follows:

where δxy is the corrected correlation between variables x and y, rxy is the observed correlation between variables x and y, rxx is the reliability estimate ...