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# Publication Citation: Assessing differences between results determined according to the Guide to the Expression of Uncertainty in Measurement

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Author(s): Raghu N. Kacker; Ruediger Kessel; Klaus-Dieter Sommer; Assessing differences between results determined according to the Guide to the Expression of Uncertainty in Measurement December 01, 2010 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. Journal of Research (NIST JRES) - 115 6 pp. 453 - 459 Birge test, Interlaboratory evaluations, Predictive p-value, Uncertainty Math Click here to retrieve PDF version of paper (146KB)