Advertisement

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
Review

Abstract

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.

Keywords

Bias Uncertainty Recovery Uncorrected bias 

Notes

Acknowledgement

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.

References

  1. 1.
    Hund E, Luc Massart D, Smeyers-Verbeke J (2001) TRAC 20(8):394–406Google Scholar
  2. 2.
    Thompson M (2000) Analyst 11:2020–2025CrossRefGoogle Scholar
  3. 3.
    Hasselbarth W (2004) Accred Qual Assur 9:509–514Google Scholar
  4. 4.
    Lira IH, Wögler W (1998) Meas Sci Technol 9:1010–1011CrossRefGoogle Scholar
  5. 5.
    BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, OIML: Guide to the expression of uncertainty in measurement (1993) ISO, GenevaGoogle Scholar
  6. 6.
    Menditto A, Patriarca M, Magnusson B (2007) Accred Qual Assur 12:45–47CrossRefGoogle Scholar
  7. 7.
    ISO Guide 99 International vocabulary of metrology-basic and general concepts and associated terms VIM 3rd edn (2007) ISO, GenevaGoogle Scholar
  8. 8.
    Thompson M, Ellison SLR (2005) Accred Qual Assur 10:82TCrossRefGoogle Scholar
  9. 9.
    Thompson M, Ellison SLR, Fajgeli A, Willetts P, Wood R (1999) Pure Appl Chem 71:337–348CrossRefGoogle Scholar
  10. 10.
    Barwick VJ, Ellison SLR (1999) Analyst 124:981–990CrossRefGoogle Scholar
  11. 11.
    Ellison SLR, Barwick VJ, Norris P, Griffiths M (2003) Analyst 128:493–498CrossRefGoogle Scholar
  12. 12.
    Dybkaer R (2005) Accred Qual Assur 10:302–303CrossRefGoogle Scholar
  13. 13.
    Magnusson B, Naykki T, Hovind H, Krysell M (2003) Handbook for calculation of measurement uncertainty. NORDTEST report TR 537 Internet version 2003. Can be obtained from http://www.nordicinnovation.net/nordtest.cfm under link Rapporter. Cited June 2007
  14. 14.
    EN 10315 (2006) Routine method for analysis of high alloy steel by X-ray fluorescence spectrometry (XRF) by using a near by techniqueGoogle Scholar
  15. 15.
    Kallner A, Khorovskaya L, Petterson T (2005) Scand J Clin Lab Invest 65:551–558CrossRefGoogle Scholar
  16. 16.
    Commission Regulations (EC) 333–2007, Laying down the method of sampling and analysis for the official control of the levels of lead, cadmium, mercury, inorganic tin, 3-MPCD, benzo(a)pyrene in food stuffGoogle Scholar
  17. 17.
    Synek V (2005) Talanta 65:829–837CrossRefGoogle Scholar
  18. 18.
    O’Donnell GE, Hibbert DB (2005) Analyst 130:721–729CrossRefGoogle Scholar
  19. 19.
    Maroto A, Boqué R, Riu J, Rius X (2002) Accred Qual Assur 7:90–94CrossRefGoogle Scholar
  20. 20.
    Phillips SD, Eberhardt KR, Parry B (1997) J Res Nat Inst Stand Technol 102:577–585Google Scholar
  21. 21.
    Franson MAH (1989) American Public Health Association. Standard methods for examination of water and wastewater, Washington DCGoogle Scholar
  22. 22.
    Eurachem/Citac guide (2000) Quantifying uncertainty in analytical measurement, 2nd edn. http://www.eurachem.org (Cited June 2007)

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

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

Personalised recommendations