Attenuation

Attenuation is a statistical concept that refers to underestimating the correlation between two different measures because of measurement error. Because no test or other measurement of any construct has perfect reliability, the validity of the scores between predictor and criterion will decrease. Hence, when correlating scores from two survey instruments, the obtained correlation may be substantively lower if the score reliabilities from both instruments are suspect. Therefore, Charles Spearman proposed the following "correction for attenuation" formula, estimating the correlation between two measures if the scores on both had perfect reliability:

In this formula, rxyc is the correlation between the predictor (x) and the criterion (y) corrected for attenuation; rxy is the correlation between the predictor and criterion scores; rxx is the reliability of the predictor ...