Disattenuating Correlation Coefficients

Schumacker R E (1996) Disattenuating Correlation Coefficients. Rasch Measurement Transactions 10:1 p.479.

When two sets of measures, {x} and {y}, are correlated, measurement error lowers the correlation coefficient below the level it would have reached had the measures been precise. The reliability of a set of measures is the proportion of observed variance not due to measurement error, rxx for set {x} and ryy for set {y}. Measurement error can be removed from a correlation coefficient, rxy, to estimate the correlation coefficient disattenuated of measurement error, Rxy, by the formula (Spearman 1904, 1910):

Rxy = rxy / sqrt (rxx ryy)

Disattenuated values greater than 1.00 indicate that measurement error is not randomly distributed.

Muchinsky (1996) summarizes features of the disattenuated correlation coefficient:

1.Disattenuation does not change the quality of the measures or their predictive power.

2.Disattenuated correlations are not directly comparable with uncorrected correlations.

3.Disattenuated correlations are not suited to statistical hypothesis testing.

4.Disattenuation is not a substitute for precise measurement.

5.But, disattenuation tells us whether the correlation between two sets of measures is low because of measurement error or because the two sets are really uncorrelated.

Randall E. Schumacker

Muchinsky P.M. (1996) The correction for attenuation. Educational & Psychological Measurement 56:1, 63-75.

Spearman C. (1904) The proof and measurement of association between two things. American Journal of Psychology, 15, 72-101.

Spearman C. (1910) Correlation calculated from faulty data. British Journal of Psychology, 3, 271-295

Zimmerman, D. W., & Williams, R. H. (1997). Properties of the Spearman correction for attenuation for normal and realistic non-normal distributions. Applied Psychological Measurement, 21, 253-270.

Table of Disattenuated of Correlation Coefficients
Reliability (Test 1)
multiplied by
Reliability (Test 2)		 Reported Test 1 x Test 2 Correlation Coefficient
.05.10.15.20.25.30.35.40.45.50.55.60.65.70.75.80.85.90.95
.05.22.45.67.89---------------
.10.16.32.47.63.79.95-------------
.15.13.26.39.52.65.77.90------------
.20.11.22.34.45.56.67.78.89-----------
.25.10.20.30.40.50.60.70.80.90----------
.30.09.18.27.37.46.55.64.73.82.91---------
.35.08.17.25.34.42.51.59.68.76.85.93--------
.40.08.16.24.32.40.47.55.63.71.79.87.95-------
.45.07.15.22.30.37.45.52.60.67.75.82.89.97------
.50.07.14.21.28.35.42.49.57.64.71.78.85.92.99-----
.55.07.13.20.27.34.40.47.54.61.67.74.81.88.94-----
.60.06.13.19.26.32.39.45.52.58.65.71.77.84.90.97----
.65.06.12.19.25.31.37.43.50.56.62.68.74.81.87.93.99---
.70.06.12.18.24.30.36.42.48.54.60.66.72.78.84.90.96---
.75.06.12.17.23.29.35.40.46.52.58.64.69.75.81.87.92.98--
.80.06.11.17.22.28.34.39.45.50.56.61.67.73.78.84.89.95--
.85.05.11.16.22.27.33.38.43.49.54.60.65.71.76.81.87.92.98-
.90.05.11.16.21.26.32.37.42.47.53.58.63.69.74.79.84.90.95-
.95.05.10.15.21.26.31.36.41.46.51.56.62.67.72.77.82.87.92.97

Disattenuating correlation coefficients. Schumacker RE, Muchinsky PM. … Rasch Measurement Transactions, 1996, 10:1 p.479

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