Attenuation

Attenuation refers to the correlation between two different measures being reduced due to measurement error. Of course, no test has scores that are perfectly reliable. Therefore, having unreliable scores results in poor predictability of the criterion. To obtain an estimate of the correlation, given predictor and criterion scores, with perfect reliability, Spearman (1904) proposed the following formula known as the correction for attenuation:

This formula has also been referred to as the double correction because both the predictor (x) and criterion [Page 40](y) scores are being corrected. Suppose that we are examining the correlation between depression and job satisfaction. The correlation between the two measures (rxy) is .20. If the reliability (e.g., CRONBACH'S ALPHA) of the scores from the depression inventory (rxx) is .80 and the reliability of the scores from the job satisfaction scale (ryy) is .70, then the correlation corrected for attenuation would be equal to the following:

In this case, there is little correction. However, suppose the reliabilities of the scores for depression and job satisfaction are .20 and .30, respectively. The correlation corrected for attenuation would now be equal to .81. The smaller the reliabilities or sample sizes (N < 300), the greater the correlation corrected for attenuation (Nunnally, 1978). It is even possible for the correlation corrected for attenuation to be greater than 1.00 (Nunnally, 1978).

There are cases, however, when one might want to correct for unreliability for either the predictor or the criterion scores. These would incorporate the single correction. For example, suppose the correlation between scores on a mechanical skills test (x) and job performance ratings (y) is equal to .40, and the reliability of the job performance ratings is equal to .60. If one wanted to correct for only the unreliability of the criterion, the following equation would be used:

In this case, the correlation corrected for attenuation would be equal to .51. It is also feasible, albeit less likely for researchers, to correct for the unreliability of the test scores only. This correction would occur when either the criterion reliability is measured perfectly or if the criterion reliability is unknown (Muchinsky, 1996). Hence, the following formula would be applied:

Muchinsky (1996) summarized the major tenets of the correction for attenuation. First, the correction for attenuation does not increase the predictability of the test scores (Nunnally, 1978). Furthermore, the corrected correlations should neither be tested for statistical significance (Magnusson, 1967), nor should corrected and uncorrected validity coefficients be compared to each other (American Educational Research Association, 1985). Finally, the correction for attenuation should not be used for averaging different types of validity coefficients in meta-analysis that use different estimates of reliabilities (e.g., internal consistencies, test-retest) (Muchinsky, 1996).