Skip to main content
SpringerLink
Log in

Value assignment and uncertainty evaluation for anion and single-element reference solutions incorporating historical information

  • Research Paper
  • Published:
Analytical and Bioanalytical Chemistry Aims and scope Submit manuscript

Abstract

The National Institute of Standards and Technology, which is the national metrology institute of the USA, assigns certified values to the mass fractions of individual elements in single-element solutions, and to the mass fractions of anions in anion solutions, based on gravimetric preparations and instrumental methods of analysis. The instrumental method currently is high-performance inductively coupled plasma optical emission spectroscopy for the single-element solutions, and ion chromatography for the anion solutions. The uncertainty associated with each certified value comprises method-specific components, a component reflecting potential long-term instability that may affect the certified mass fraction during the useful lifetime of the solutions, and a component from between-method differences. Lately, the latter has been evaluated based only on the measurement results for the reference material being certified. The new procedure described in this contribution blends historical information about between-method differences for similar solutions produced previously, with the between-method difference observed when a new material is characterized. This blending procedure is justified because, with only rare exceptions, the same preparation and measurement methods have been used historically: in the course of almost 40 years for the preparation methods, and of 20 years for the instrumental methods. Also, the certified values of mass fraction, and the associated uncertainties, have been very similar, and the chemistry of the solutions also is closely comparable within each series of materials. If the new procedure will be applied to future SRM lots of single-element or anion solutions routinely, then it is expected that it will yield relative expanded uncertainties that are about 20 % smaller than the procedure for uncertainty evaluation currently in use, and that it will do so for the large majority of the solutions. However, more consequential than any reduction in uncertainty, is the improvement in the quality of the uncertainty evaluations that derives from incorporating the rich historical information about between-method differences and about the stability of the solutions over their expected lifetimes. The particular values listed for several existing SRMs are given merely as retrospective illustrations of the application of the new method, not to suggest that the certified values or their associated uncertainties should be revised.

Graphical abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Notes

  1. The IUPAC Orange Book [7, 10.3.4] recommends that the term OES be abandoned and that AES (denoting atomic emission spectroscopy/spectrometry) be used instead, while noting that both OES and AES have been advocated in IUPAC documents. This contribution concerns historical information from the analytical methods we have been using for the certification of the solutions being discussed. Considering that users of these solutions are most familiar with the usage of OES in many relevant publications, including those just cited, to avoid confusion we will continue to refer to AES methods using the traditional designation “OES.”

References

  1. Beauchamp CR, Camara JE, Carney J, Choquette SJ, Cole KD, DeRose PC, Duewer DL, Epstein MS, Kline MC, Lippa KA, Lucon E, Phinney KW, Possolo A, Sharpless KE, Sieber JR, Toman B, Winchester MR, Windover D. Metrological tools for the reference materials and reference instruments of the NIST Materials Measurement Laboratory. In: NIST Special Publication 260-136 (2020 Edition). National Institute of Standards and Technology. 2020. https://doi.org/10.6028/NIST.SP.260-136-2020

  2. Salit ML, Turk GC. A drift correction procedure. Analytical Chemistry. 1998;70(15):3184–90. https://doi.org/10.1021/ac980095b.

    Article  CAS  PubMed  Google Scholar 

  3. Salit ML, Turk GC, Lindstrom AP, Butler TA, Beck CM, Norman B. Single-element solution comparisons with a high-performance inductively coupled plasma optical emission spectrometric method. Analytical Chemistry. 2001;73(20):4821–9. https://doi.org/10.1021/ac0155097.

    Article  CAS  PubMed  Google Scholar 

  4. Salit ML, Turk GC. Traceability of single-element calibration solutions. Analytical Chemistry. 2005;77(7):136–41. https://doi.org/10.1021/ac053354n.

    Article  Google Scholar 

  5. Winchester MR, Butler TA, Turk GC. Improving the high-performance inductively coupled plasma optical emission spectrometry methodology through exact matching. Analytical Chemistry. 2010;82(18):7675–83. https://doi.org/10.1021/ac101471a.

    Article  CAS  PubMed  Google Scholar 

  6. Brennan RG, Butler TA, Winchester MR. Achieving 0.2 % relative expanded uncertainty in ion chromatography analysis using a high-performance methodology. Analytical Chemistry. 2011;83(10):3801–7. https://pubs.acs.org/doi/10.1021/ac200290y

  7. Inczedy J, Lengyel T, Ure AM, of Pure IU, Chemistry A. IUPAC Compendium on Analytical Nomenclature, Definitive Rules 1997, 3rd edn. Blackwell Science. 1998. IUPAC Orange Book. https://media.iupac.org/publications/analytical_compendium/

  8. Joint Committee for Guides in Metrology (JCGM): Evaluation of Measurement Data — Guide to the Expression of Uncertainty in Measurement. International Bureau of Weights and Measures (BIPM), Sèvres, France. 2008. BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML, JCGM 100:2008, GUM 1995 with minor corrections. https://www.bipm.org/en/publications/guides/gum.html

  9. Koepke A, Lafarge T, Toman B, Possolo A. NIST Consensus Builder — User’s Manual. National Institute of Standards and Technology. 2017. National Institute of Standards and Technology. https://consensus.nist.gov

  10. DerSimonian R, Laird N. Meta-analysis in clinical trials. Controlled Clinical Trials. 1986;7(3):177–88. https://doi.org/10.1016/0197-2456(86)90046-2.

    Article  CAS  PubMed  Google Scholar 

  11. Koepke A, Lafarge T, Possolo A, Toman B. Consensus building for interlaboratory studies, key comparisons, and meta-analysis. Metrologia. 2017;54(3):34–62. https://doi.org/10.1088/1681-7575/aa6c0e.

    Article  CAS  Google Scholar 

  12. Thompson M, Ellison SLR. Dark uncertainty. Accreditation and Quality Assurance. 2011;16:483–7. https://doi.org/10.1007/s00769-011-0803-0.

    Article  Google Scholar 

  13. Hoaglin DC. Misunderstandings about \(Q\) and ‘Cochran’s \(Q\) test’ in meta-analysis. Statistics in Medicine. 2016;35:485–95. https://doi.org/10.1002/sim.6632.

    Article  PubMed  Google Scholar 

  14. Veroniki AA, Jackson D, Viechtbauer W, Bender R, Bowden J, Knapp G, Kuss O, Higgins JPT, Langan D, Salanti G. Methods to estimate the between-study variance and its uncertainty in meta-analysis. Research Synthesis Methods. 2016;7:55–79. https://doi.org/10.1002/jrsm.1164.

    Article  PubMed  Google Scholar 

  15. Langan D, Higgins JPT, Jackson D, Bowden J, Veroniki AA, Kontopantelis E, Viechtbauer W, Simmonds M. A comparison of heterogeneity variance estimators in simulated random-effects meta-analyses. Research Synthesis Methods. 2019;10(1):83–98. https://doi.org/10.1002/jrsm.1316.

    Article  PubMed  Google Scholar 

  16. Weber F, Knapp G, Glass A, Kundt G, Ickstadt K. Interval estimation of the overall treatment effect in random-effects meta-analyses: Recommendations from a simulation study comparing frequentist, Bayesian, and bootstrap methods. Research Synthesis Methods. 2021;12(3):291–315. https://doi.org/10.1002/jrsm.1471.

    Article  PubMed  Google Scholar 

  17. Strawderman WE, Rukhin AL. Simultaneous estimation and reduction of nonconformity in interlaboratory studies. Journal of the Royal Statistical Society Series B (Statistical Methodology). 2010;72(2):219–34. https://doi.org/10.2307/40541584.

    Article  Google Scholar 

  18. Possolo A, Bodnar O, Butler TA, Molloy JL, Winchester MR. Value assignment and uncertainty evaluation in single-element reference solutions. Metrologia. 2018;55(3):404–13. https://doi.org/10.1088/1681-7575/aabd57.

    Article  CAS  Google Scholar 

  19. Possolo A, Toman B. Tutorial for metrologists on the probabilistic and statistical apparatus underlying the gum and related documents. National Institute of Standards and Technology, 2011. https://doi.org/10.13140/RG.2.1.2256.8482. https://www.itl.nist.gov/div898/possolo/TutorialWEBServer/TutorialMetrologists2011Nov09.xht

  20. Kipphardt H, Matschat R, Rienitz O, Schiel D, Gernand W, Oeter D. Traceability system for elemental analysis. Accreditation and Quality Assurance. 2006;10(11):633–9. https://doi.org/10.1007/s00769-005-0084-6.

    Article  CAS  Google Scholar 

  21. Westwood S, Choteau T, Daireaux A, Josephs RD, Wielgosz RI. Mass balance method for the SI value assignment of the purity of organic compounds. Analytical Chemistry. 2013;85(6):3118–26. https://doi.org/10.1021/ac303329k.

    Article  CAS  PubMed  Google Scholar 

  22. Vogl J, Kipphardt H, Richter S, Bremser W, Torres MRA, Manzano JVL, Buzoianu M, Hill S, Petrov P, Goenaga-Infante H, Sargent M, Fisicaro P, Labarraque G, Zhou T, Turk GC, Winchester M, Miura T, Methven B, Sturgeon R, Jährling R, Rienitz O, Mariassy M, Hankova Z, Sobina E, Krylov AI, Kustikov YA, Smirnov VV. Establishing comparability and compatibility in the purity assessment of high purity zinc as demonstrated by the CCQM-p149 intercomparison. Metrologia. 2018;55(2):211–21. https://doi.org/10.1088/1681-7575/aaa677.

    Article  CAS  Google Scholar 

  23. Linsinger TPJ, Pauwels J, Lamberty A, Schimmel HG, van der Veen AMH, Siekmann L. Estimating the uncertainty of stability for matrix CRMs. Fresenius’ Journal of Analytical Chemistry. 2001;370:183–8. https://doi.org/10.1007/s0021601007.

    Article  CAS  PubMed  Google Scholar 

  24. Cochran WG. The combination of estimates from different experiments. Biometrics. 1954;10(1):101–29. https://doi.org/10.2307/3001666.

    Article  Google Scholar 

  25. Welch BL. The generalization of ‘Student’s’ problem when several different population variances are involved. Biometrika. 1947;34:28–35. https://doi.org/10.1093/biomet/34.1-2.28.

    Article  CAS  PubMed  Google Scholar 

  26. Analytical Methods Committee. Dark uncertainty. Analytical Methods. 2012;4:2609–12. https://doi.org/10.1039/C2AY90034C. AMC Technical Briefs No. 53.

  27. Searle SR, Casella G, McCulloch CE. Variance components. John Wiley & Sons, 2006

  28. Horwitz W, Albert R. The Horwitz Ratio (HorRat): A useful index of method performance with respect to precision. Journal of AOAC International. 2006;89(4):1095–109. https://doi.org/10.1093/jaoac/89.4.1095.

    Article  CAS  PubMed  Google Scholar 

  29. Meija J. A chemical uncertainty principle challenge. Analytical and Bioanalytical Chemistry. 2007;387:1583–4. https://doi.org/10.1007/s00216-006-1059-0.

    Article  CAS  PubMed  Google Scholar 

  30. Meija J. Solution to the chemical uncertainty principle challenge. Analytical and Bioanalytical Chemistry. 2007;388:995–6. https://doi.org/10.1007/s00216-007-1312-1.

    Article  CAS  PubMed  Google Scholar 

  31. Sieber JR, Epstein MS, Possolo AM. A Retuned Horwitz procedure for upgrading certificates of older standard reference materials. NIST Special Publication 260-198. National Institute of Standards and Technology, Gaithersburg, MD, 2019. https://doi.org/10.6028/NIST.SP.260-198

  32. Horwitz W. Evaluation of analytical methods used for regulation of foods and drugs. Analytical Chemistry. 1982;54(1):67–76. https://doi.org/10.1021/ac00238a765.

    Article  Google Scholar 

  33. McCulloch CE, Searle SR, Neuhaus JM. Generalized, Linear, and Mixed Models, 2nd edn. John Wiley & Sons, 2008

  34. Balduzzi S, Rücker G, Schwarzer G. How to perform a meta-analysis with R: a practical tutorial. Evidence-Based Mental Health. 2019;22:153–60. https://doi.org/10.1136/ebmental-2019-300117.

    Article  PubMed  Google Scholar 

  35. R Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, 2021. R Foundation for Statistical Computing. https://www.R-project.org/

  36. Langan D, Higgins JPT, Simmonds M. Comparative performance of heterogeneity variance estimators in meta-analysis: a review of simulation studies. Research Synthesis Methods. 2017;8(2):181–98. https://doi.org/10.1002/jrsm.1198.

    Article  PubMed  Google Scholar 

  37. Maechler M, Rousseeuw P, Croux C, Todorov V, Ruckstuhl A, Salibian-Barrera M, Verbeke T, Koller M, Conceição ELT, di Palma MA. Robustbase: Basic Robust Statistics. 2021. R package version 0.93-9. http://CRAN.R-project.org/package=robustbase

  38. Gelman A, Hill J. Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press. 2007 https://doi.org/10.1017/CBO9780511790942.

    Article  Google Scholar 

  39. Gelman A, Carlin JB, Stern HS, Rubin DB. Bayesian data analysis, 2nd edn. Chapman & Hall / CRC, 2003

  40. Carpenter B, Gelman A, Hoffman M, Lee D, Goodrich B, Betancourt M, Brubaker M, Guo J, Li P, Riddell A. Stan: A probabilistic programming language. Journal of Statistical Software. 2017;76(1):1–32. https://doi.org/10.18637/jss.v076.i01.

    Article  PubMed  PubMed Central  Google Scholar 

  41. Freedman D, Pisani R, Purves R. Statistics, 4th edn. W. W. Norton & Company, 2007

  42. Yu LL, Butler TA, Turk GC. Effect of valence state on ICP-OES value assignment of SRM 3103a arsenic spectrometric solution. Analytical Chemistry. 2006;78:1651–6. https://doi.org/10.1021/ac051732i.

    Article  CAS  PubMed  Google Scholar 

  43. Narukawa T, Kuroiwa T, Chiba K. Mechanism of sensitivity difference between trivalent inorganic As species [As(III)] and pentavalent species [As(V)] with inductively coupled plasma spectrometry. Talanta. 2007;73:157–65. https://doi.org/10.1016/j.talanta.2007.03.021.

    Article  CAS  PubMed  Google Scholar 

  44. Narukawa T, Chiba K, Kuroiwa T, Inagaki K. Differences in sensitivity between As(III) and As(V) measured by inductively coupled plasma spectrometry and the factors affecting the incoherent molecular formation (IMF) effect in the plasma. Journal of Analytical Atomic Spectrometry. 2010;25:1682–7. https://doi.org/10.1039/C0JA00011F.

    Article  CAS  Google Scholar 

  45. Levenson MS, Banks DL, Eberhardt KR, Gill LM, Guthrie WF, Liu HK, Vangel MG, Yen JH, Zhang NF. An approach to combining results from multiple methods motivated by the ISO GUM. Journal of Research of the National Institute of Standards and Technology. 2000;105(4):571–9. https://doi.org/10.6028/jres.105.047.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  46. Vangel MG, Rukhin AL. Maximum likelihood analysis for heteroscedastic one-way random effects ANOVA in interlaboratory studies. Biometrics. 1999;55:129–36. https://doi.org/10.1111/j.0006-341X.1999.00129.x.

    Article  CAS  PubMed  Google Scholar 

  47. Rukhin A, Biggerstaff B, Vangel M. Restricted maximum likelihood estimation of a common mean and the Mandel-Paule algorithm. Journal of Statistical Planning and Inference. 2000;83:319–30. https://doi.org/10.1016/S0378-3758(99)00098-1.

    Article  Google Scholar 

  48. Toman B. Bayesian approaches to calculating a reference value in key comparison experiments. Technometrics. 2007;49(1):81–7. https://doi.org/10.1198/004017006000000273.

    Article  Google Scholar 

  49. Moody JR, Greenberg RR, Pratt KW, Rains TC. Recommended inorganic chemicals for calibration. Analytical Chemistry. 1988;60(21):1203–18. https://doi.org/10.1021/ac00172a001.

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful to their NIST colleagues who kindly provided detailed reviews of a draft, and offered useful comments and suggestions for improvement: Michael Epstein, Adam Pintar, and Michael Winchester. The authors are also highly appreciative of the suggestions for improvement offered by two anonymous reviewers, in particular for pointing out the similarity between Eq. (2) and the Horwitz equation [28].

Author information

Authors and Affiliations

  1. Inorganic Chemical Metrology Group, Chemical Sciences Division, Material Measurement Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Stop 8391, Gaithersburg, MD, 20899-8391, USA

    Brian E. Lang, John L. Molloy, Thomas W. Vetter & Shaun P. Kotoski

  2. Statistical Engineering Division, Information Technology Laboratory, National Institute of Standards and Technology, 100 Bureau Drive, Stop 8980, Gaithersburg, MD, 20899-8980, USA

    Antonio Possolo

Authors
  1. Brian E. Lang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John L. Molloy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Thomas W. Vetter
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shaun P. Kotoski
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Antonio Possolo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Brian E. Lang.

Ethics declarations

The authors declare no competing interests. The research reported herein did not involve human or animal subjects, or any biological materials, as objects of research. This research was conducted as part of the authors’ duties as employees of the National Institute of Standards and Technology, an agency of the federal government of the United States of America, under the U.S. Department of Commerce.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file 1 (pdf 115 KB)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lang, B.E., Molloy, J.L., Vetter, T.W. et al. Value assignment and uncertainty evaluation for anion and single-element reference solutions incorporating historical information. Anal Bioanal Chem 415, 1657–1673 (2023). https://doi.org/10.1007/s00216-022-04410-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00216-022-04410-y

Keywords

Search

Navigation