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 (rxx and ryy) of the variables x and y are known, the actual correlation (rxy) can be corrected for attenuation as follows:
True correlation = rxy / √(rxx × ryy)
In practice this correction is rarely applied, and one finds the raw correlations more informative. It is good to be aware of circumstances that attenuate correlations though, and in high-range testing the important ones are (1) the severe restriction of range (about I.Q. 120 and higher, as opposed to the full range of say I.Q. 55 and higher), (2) incomplete or dishonest reporting of scores by candidates, and (3) the lack of high-range validity of mainstream tests. All of these may depress the correlations one finds between and with high-range tests.