Correction for attenuation (via Wikipedia)

If you are Charlotte or Yoryos (who I work for) then honestly I don’t just present work off Wikipedia and pretend it is my own. Anyone else, this article about correction for attenuation is quite good. Unless of course, by the time you read it has been edited into an entirely different form, which is always a worry, but generally I find the stuff on Wikipedia quite good.

Right. What it says is that if you have a correlation coefficient then you can multiply it by the square root of the reliability to get what the correlation coefficient would be had you measured your variable with 100% reliability. Neat, huh?

With regression, measurement error in your outcome won’t have an impact on your regression coefficient but measurement error in your exposure will. Here you need to multiply your regression coefficient by the reliability to correct it.

Gary my statistician colleague pointed out to me that I was looking at Spearman correlation coefficients, rather than Pearson so the above probably won’t quite hold, but he also kindly did a bit of simulation and said that this correction also worked in practice. Here is an interesting article about Spearman, who wrote about this in 1910.

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