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Figure 1

From: Corruption of the Pearson correlation coefficient by measurement error and its estimation, bias, and correction under different error models

Figure 1

(A) Correlation plot of two variables \(x\) and \(y\) (\({\sigma }_{{x}_{0}}^{2}={\sigma }_{{y}_{0}}^{2}=1\)) generated without (\({\sigma }_{a{u}_{x}}^{2}={\sigma }_{a{u}_{y}}^{2}=0\)) and with uncorrelated additive error (\({\sigma }_{a{u}_{x}}^{2}={\sigma }_{a{u}_{y}}^{2}=0.75\)) with underlying true correlation \({\rho }_{0}=0.8\) (model 8). (B) Distribution of the sample correlation coefficient for different levels of measurement error (\({\sigma }_{au}^{2}={\sigma }_{a{u}_{x}}^{2}={\sigma }_{a{u}_{y}}^{2}\)) for a true correlation \({\rho }_{0}=0.8\). (C) The attenuation coefficient \(A\) from Eq. (10) as a function the measurement error for different level of the variance \({\sigma }^{2}={\sigma }_{{x}_{0}}^{2}={\sigma }_{{y}_{0}}^{2}\) of the variables \({x}_{0}\) and \({y}_{0}\). See Material and Methods section 6.5.1 for details on the simulations.

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