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. 2020 Oct 15;10:17372. doi: 10.1038/s41598-020-74057-1

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© The Author(s) 2020

Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Illustration of how the variance in estimating X is inversely related to the maximum measurable Pearson correlation coefficient $ρ (X, Y) = c o v (X, Y) / σ_{X} σ_{Y}$ ^11–15, while the bias in estimating X does not affect the correlation. Therefore, one should seek to find a minimal variance estimator of X. Note that in the upper panel points were individually shifted in the X dimension to modify the variance of X while points in the lower panel were shifted by the same amount and direction in the X dimension to modify bias. Points have the same Y value across all plots.