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. 2020 Jan 16;10:438. doi: 10.1038/s41598-019-57247-4

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© The Author(s) 2020

Open Access This 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 license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license 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 license, visit http://creativecommons.org/licenses/by/4.0/.

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Calculations of the correlation coefficient $ρ$ (40) as a function of the different realizations of the signal means and the size of the error components for different values of the true correlation $ρ_{0}$ . The shadowed area encloses the maximum and the minimum of the values of $ρ$ calculated in the simulation using the different error models. The dots represent the realized values of $ρ$ (only 100 of 10⁵ Monte Carlo realizations for different values of the variances of error component are shown). The solid lines represent the 5-th and the 95-th percentiles of the observed values. (A) Additive measurement error with positive correlated error. (B) Multiplicative measurement error with positive correlated error. (C) Realistic case with both additive and multiplicative measurement error with positive correlated error. (D) Additive measurement error with negative correlated error. (E) Multiplicative measurement error with negative correlated error. (F) Realistic case with both additive and multiplicative measurement error with negative correlated error. For more details on the simulations see Material and Methods section 6.5.5.