Assessing differences between results determined according to the Guide to the Expression of Uncertainty in Measurement

Published

December 1, 2010

Author(s)

Raghu N. Kacker, Ruediger Kessel, Klaus-Dieter Sommer

Abstract

When the data consist of multiple results of measurement for a common measurand, often one needs to determine whether the results agree with each other. A result of measurement based on the Guide to the Expression of Uncertainty in Measurement (GUM) consists of a measured value together with its associated standard uncertainty. In the GUM, the measured value is regarded as the expected value and the standard uncertainty is regarded as the standard deviation, both known values, of a state-of-knowledge probability distribution. A state-of-knowledge distribution represented by a result is not required to be completely known. Then how can one assess the differences between the results based on the GUM? Metrologists have for many years used the Birge chi-square test as a rule of thumb to assess the differences between two or more measured values for the same measurand by pretending that the standard uncertainties were the standard deviations of the presumed sampling probability distributions from random variation of the measured values. We point out that this is misuse of the standard uncertainties; the Birge test and the concept of statistical consistency motivated by it do not apply to the results of measurement based on the GUM. In 2008, the International Vocabulary of Metrology, third edition (VIM3) introduced the concept of metrological compatibility. We show that the concept of metrological compatibility can be used to assess the differences between results based on the GUM for the same measurand. A pairwise Birge test of statistical consistency and a test of metrological compatibility do not conflict.

Citation

Journal of Research (NIST JRES) -

Volume

115

Issue

6

NIST Pub Series

Journal of Research (NIST JRES)

Pub Type

NIST Pubs

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Keywords

Birge test, Interlaboratory evaluations, Predictive p-value, Uncertainty

Citation

Kacker, R. , Kessel, R. and , K. (2010), Assessing differences between results determined according to the Guide to the Expression of Uncertainty in Measurement, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=906548 (Accessed October 2, 2025)