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 .
The effects of range restriction on estimates of criterion interrater reliability: Implications for validation research
Jan 01, 2002; This paper explores the implications of the fact that range restriction affects reliability coefficients as well as validity...
The effect of mean and differential attenuation on the precision and accuracy of the estimates of reflectivity and differential reflectivity
Mar 01, 2003; (Manuscript received 18 February 2002, in final form 18 July 2002) ABSTRACT Error propagation analysis is applied to evaluate the...