Analytical and Bioanalytical Chemistry

, Volume 403, Issue 2, pp 537–548 | Cite as

A Bayesian approach to the evaluation of comparisons of individually value-assigned reference materials

  • Blaza TomanEmail author
  • David L. Duewer
  • Hugo Gasca Aragon
  • Franklin R. Guenther
  • George C. Rhoderick
Original Paper


Several recent international comparison studies used a relatively novel experimental design to evaluate the measurement capabilities of participating organizations. These studies compared the values assigned by each participant to one or more qualitatively similar materials with measurements made on all of the materials by one laboratory under repeatability conditions. A statistical model was then established relating the values to the repeatability measurements; the extent of agreement between the assigned value(s) and the consensus model reflected the participants’ measurement capabilities. Since each participant used their own supplies, equipment, and methods to produce and value-assign their material(s), the agreement between the assigned value(s) and the model was a fairer reflection of their intrinsic capabilities than provided by studies that directly compared time- and material-constrained measurements on unknown samples prepared elsewhere. A new statistical procedure is presented for the analysis of such data. The procedure incorporates several novel concepts, most importantly a leave-one-out strategy for the estimation of the consensus value of the measurand, model fitting via Bayesian posterior probabilities, and posterior coverage probability calculation for the assigned 95% uncertainty intervals. The benefits of the new procedure are illustrated using data from the CCQM-K54 comparison of eight cylinders of n-hexane in methane.


Bayesian analysis Degrees of equivalence Generalized distance regression Leave-one-out analysis Posterior coverage probability 



We thank the GAWG and its members for pioneering the comparison of multiple reference materials value-assigned by different organizations using measurements made under repeatability conditions by one organization.

Supplementary material

216_2012_5847_MOESM1_ESM.pdf (496 kb)
ESM 1 (PDF 495 kb)


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Copyright information

© Springer-Verlag (outside the USA) 2012

Authors and Affiliations

  • Blaza Toman
    • 1
    Email author
  • David L. Duewer
    • 2
  • Hugo Gasca Aragon
    • 2
    • 3
  • Franklin R. Guenther
    • 2
  • George C. Rhoderick
    • 2
  1. 1.Statistical Engineering DivisionNational Institute of Science and TechnologyGaithersburgUSA
  2. 2.Analytical Chemistry DivisionNational Institute of Science and TechnologyGaithersburgUSA
  3. 3.Department of Mathematics and StatisticsUniversity of MassachusettsAmherstUSA

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