The Variance of the Corrected Pearson Correlation Coefficient Under Correlated and Uncorrelated Additive Measurement Noise

In the presence of additive measurement noise, the Pearson moment‐product correlation coefficient between two measured quantities (variables) and is distorted and can be biased upwards or downwards depending on the interplay of the correlated and uncorrelated noise components. This bias can be removed with appropriate mathematical manipulations once the noise variance components have been estimated. In this paper, we derive expressions for the variance and standard error of the corrected sample correlation as a function of the noise variance components, which can be of utility in hypothesis testing and experimental design.