correction for attenuation

Correction for attenuation is a statistical procedure, due to Spearman, to "rid a correlation coefficient from the weakening effect of measurement error" (Jensen, 1998). Given two random variables

X

and

Y

, with correlation

r_{xy}

, and a known reliability for each variable,

r_{xx}

and

r_{yy}

, the correlation between

X

and

Y

corrected for attenuation is

r_{x'y'} = \frac{r_{xy}}{\sqrt{r_{xx}r_{yy}}}

. If

X

and

Y

are taken to be imperfect measurements of underlying variables

X'

and

Y'

with independent errors, then

r_{x'y'}

measures the true correlation between

X'

and

Y'

Derivation

References

*Jensen, A.R. (1998). The g Factor. Praeger, Connecticut, USA.

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