An approach to combining results from multiple methods motivated by the ISO GUM

Abstract

The problem of determining a consensus value and its uncertainty from the results of multiple methods or laboratories is discussed. Desirable criteria of a solution are presented. A solution motivated by the ISO Guide to the Expression of Uncertainty in Measurement (ISO GUM) is introduced and applied in a detailed worked example. A Bayesian hierarchical model motivated by the proposed solution is presented and compared to the solution.

Determination of polychlorinated biphenyl congeners and chlorinated pesticides in a fish tissue standard reference material

“…Wise et al [3] provide a review of the various modes of value assignment of SRMs for chemical composition (i.e., certified versus reference values) with examples (organic contaminants in natural-matrix SRMs) to illustrate their use. Each concentration value for SRM 1946 is expressed as the value ± the uncertainty, these are defined in Table 5 [41,42,43,44]. Certified concentration values are available for 30 PCB congeners and 15 chlorinated pesticides (Table 5).…”

“…The certified values are a weighted mean of the results from four to seven analytical methods; the uncertainty listed with each value is an expanded uncertainty about the mean value, with coverage factor 2 (approximately 95% confidence) calculated by combining a between-source variance incorporating inter-method bias with a pooled within-source variance following the ISO/NIST Guide to the Expression of Uncertainty in Measurement [41,42] b PCB congeners are numbered according to Table 4 c The certified value is an unweighted mean of the results from three analytical methods; the uncertainty listed is an exapanded uncertainty about the mean, with coverage factor 2, calculated by combining a between-method variance [43] with a pooled, withinmethod variance [41,42] d The certified value is an unweighted mean of the results from five analytical methods; the uncertainty listed is an expanded uncertainty about the mean, with coverage factor 2, calculated by combining a between-method variance [43] with a pooled, withinmethod variance [41,42] e Each reference value is a weighted mean of the results from three to five analytical methods [44]; the uncertainty listed with each value is an expanded uncertainty about the mean value, with coverage factor 2 (approximately 95% confidence) calculated by combining a between-source variance incorporating inter-method bias with a pooled within-source variance [41,42] f Reference values are unweighted means of the results from two or more analytical methods; the uncertainty listed is an expanded uncertainty about the mean, with coverage factor 2, calculated by combining a between-method vairance [43] with a pooled,withinmethod variance [41,42] g These represent PCB congeners not previously examined in NIST natural-matrix SRMs…”

Phase Analysis of Portland Cement by Combined Quantitative X-Ray Powder Diffraction and Scanning Electron Microscopy

“…The method is designed to handle cases where the number of analytical methods is small (two to five), and the ordinary sample standard deviation is an inadequate estimate of the uncertainty of the systematic effects [37]. The method combines a pooled estimate of within-method uncertainty with a between-method error estimate in quadrature, and multiplies by an expansion factor of k = 2.…”

Certification of natural isotopic abundance inorganic mercury reference material NIMS-1 for absolute isotopic composition and atomic weight

“…17 The following equation was used: Fourteen bottles were randomly sampled for the analysis of relative variations in the isotopic composition of mercury. Of these, one bottle was randomly chosen as an internal standard and isotope ratios, 196 Hg/ 198 Hg… 204 Hg/ 198 Hg were determined (in triplicate) with respect to this standard bottle using a standard-sample-standard bracketing approach.…”