Correction for Attenuation

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Correction for attenuation is a statistical procedure, due to Spearman (1904), to "rid a correlation coefficient from the weakening effect of measurement error" (Jensen, 1998), a phenomenon also known as regression dilution. Given two random variables X and Y, with correlation rxy, and a known reliability for each variable, rxx and ryy, the correlation between X and Y corrected for attenuation is . How well the variables are measured affects the correlation of X and Y. The correction for attenuation tells you what the correlation would be if you could measure X and Y with perfect reliability. If X and Y are taken to be imperfect measurements of underlying variables X' and Y' with independent errors, then rx'y' measures the true correlation between X' and Y'.

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