Accreditation and Quality Assurance

, Volume 5, Issue 12, pp 464-469

First online:

Uncertainty calculations in the certification of reference materials. 1. Principles of analysis of variance

  • A.M.H. van der VeenAffiliated withNederlands Meetinstituut, Schoemakerstraat 97, 2600 AR Delft, The Netherlands e-mail: Tel.: +31-15-2691 733 Fax: +31-15-261 2971
  • , J. PauwelsAffiliated withEuropean Commission, Joint Research Centre, Institute for Reference Materials and Measurements, Retieseweg, 2440 Geel, Belgium e-mail: Tel.: +32-14-571 722 Fax: +32-14-590 406

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 The preparation and certification of reference materials is a rapidly developing area. Many innovative reference materials have limited homogeneity and stability, and, additionally, the uncertainty estimation of the property values must be brought in agreement with the principles of the “Guide to the expression of uncertainty in measurement” (GUM). The results of the homogeneity and stability studies must be included to a certain extent in the uncertainty of the property values of the reference material, in order to comply with these requirements. The basic theory needed to accomplish this is essentially the theory of analysis of variance (ANOVA). As GUM also allows alternative evaluations other than Type A evaluations, a reinterpretation of the theory of ANOVA is necessary to establish a model for the certification of reference materials that is widely applicable. For this, analysis of variance can be used as a statistical technique to derive standard uncertainties from homogeneity, stability and characterisation data.

Keywords Reference materials Measurement uncertainty Analysis of variance Homogeneity study Stability study