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Correction for attenuation is a statistical procedure developed by Charles Spearman in 1904 that is used to "rid a correlation coefficient from the weakening effect of measurement error" (Jensen, 1998), a phenomenon known as regression dilution. In measurement and statistics, the correction is also called disattenuation. The correction assures that the correlation across data units (for example, people) between two sets of variables is estimated in a manner that accounts for error contained within the measurement of those variables.[1]

## Background

Estimates of correlations between variables are diluted (weakened) by measurement error. Disattenuation provides for a more accurate estimate of the correlation by accounting for this effect.

## Formula

Let ${\displaystyle \beta }$ and ${\displaystyle \theta }$ be the true values of two attributes of some person or statistical unit. These values are variables by virtue of the assumption that they differ for different statistical units in the population. Let ${\displaystyle {\hat {\beta }}}$ and ${\displaystyle {\hat {\theta }}}$ be estimates of ${\displaystyle \beta }$ and ${\displaystyle \theta }$ derived either directly by observation-with-error or from application of a measurement model, such as the Rasch model. Also, let

Let ${\displaystyle \beta }$ and