Analytical and Bioanalytical Chemistry

, Volume 390, Issue 1, pp 201–213 | Cite as

Treatment of uncorrected measurement bias in uncertainty estimation for chemical measurements

  • Bertil Magnusson
  • Stephen L. R. Ellison


Consistent treatment of measurement bias, including the question of whether or not to correct for bias, is essential for the comparability of measurement results. The case for correcting for bias is discussed, and it is shown that instances in which bias is known or suspected, but in which a specific correction cannot be justified, are comparatively common. The ISO Guide to the Expression of Uncertainty in Measurement does not provide well for this situation. It is concluded that there is a need for guidance on handling cases of uncorrected bias. Several different published approaches to the treatment of uncorrected bias and its uncertainty are critically reviewed with regard to coverage probability and simplicity of execution. On the basis of current studies, and taking into account testing laboratory needs for a simple and consistent approach with a symmetric uncertainty interval, we conclude that for most cases with large degrees of freedom, linear addition of a bias term adjusted for exact coverage (“Ue”) as described by Synek is to be preferred. This approach does, however, become more complex if degrees of freedom are low. For modest bias and low degrees of freedom, summation of bias, bias uncertainty and observed value uncertainty in quadrature (“RSSu”) provides a similar interval and is simpler to adapt to reduced degrees of freedom, at the cost of a more restricted range of application if accurate coverage is desired.


Bias Uncertainty Recovery Uncorrected bias 



The authors thank Marina Patriarca, ISS, Italy and Ivo Leito, Tartu University, Estonia and Elvar Theodorsson, University Hospital of Linköping, Sweden for stimulating and valuable discussions and contributions.


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.SP Technical Research Institute of SwedenBoråsSweden
  2. 2.Laboratory of the Government ChemistTeddingtonUK

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