Analytical and Bioanalytical Chemistry

, Volume 410, Issue 3, pp 1061–1069 | Cite as

Uncertainty evaluation in normalization of isotope delta measurement results against international reference materials

  • Juris Meija
  • Michelle M. G. Chartrand
Research Paper
Part of the following topical collections:
  1. ABCs 16th Anniversary.


Isotope delta measurements are normalized against international reference standards. Although multi-point normalization is becoming a standard practice, the existing uncertainty evaluation practices are either undocumented or are incomplete. For multi-point normalization, we present errors-in-variables regression models for explicit accounting of the measurement uncertainty of the international standards along with the uncertainty that is attributed to their assigned values. This manuscript presents framework to account for the uncertainty that arises due to a small number of replicate measurements and discusses multi-laboratory data reduction while accounting for inevitable correlations between the laboratories due to the use of identical reference materials for calibration. Both frequentist and Bayesian methods of uncertainty analysis are discussed.


Isotope delta Normalization Uncertainty evaluation Random effects model 



The authors have benefited from discussions with Blaza Toman, National Institute of Standards and Technology, USA.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.

Supplementary material

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216_2017_659_MOESM2_ESM.xlsm (71 kb)
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Copyright information

© Crown 2017

Authors and Affiliations

  1. 1.Measurement Science and StandardsNational Research Council CanadaOttawaCanada

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