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

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.