Expected Values of Correlated Measurements and Correction for Attenuation

Abstract

The correlation between scores on two measurements or test procedures in a population is attenuated by variability of the individual measurements. If an individual's scores are uncorrected random variables, X_j and Y_j, the “correction for attenuation” provides an estimate of the correlation between the expected values, EX_j and EY_j, in the population. However, if an individuals scores are correlated random variables, a plausible alternative in some situations, the usual correction formula is not applicable. This paper derives a general formula which includes correlation between expected values of correlated measurements and which reduces to the usual correction for attenuation in the case of uncorrected measurements.