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Comparison of statistical consistency and metrological consistency



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


The conventional concept of consistency in multiple evaluations of the same measurand is based on statistical error analysis. This concept is based on regarding the evaluations as realizations from sampling probability distributions of potential evaluations which might be obtained in contemplated replications. The expected values of the sampling distributions are regarded as unknown but the standard deviations are assumed to be known. The multiple evaluations are said to be statistically consistent if their dispersion agrees with the hypothesis that the sampling distributions of potential evaluations have equal expected values. As the science and technology of measurement advanced, the limitations of the statistical error analysis view of uncertainty in measurement became a hindrance to communication of scientific and technical measurements. Therefore, a new concept of uncertainty in measurement was established by the Guide to the Expression of Uncertainty in Measurement (GUM). In the GUM view, an evaluation and uncertainty are, respectively, measures of centrality and dispersion of a state-of-knowledge probability distribution for the measurand. Statistical consistency is not compatible with the GUM concept of uncertainty in measurement; however, metrologists continue to use it as an approximate rule of thumb because no suitable alternative has been available until recently. The concept of metrological consistency is compatible with the GUM concept of uncertainty in measurement. It is a pair-wise concept. A pair of state-of-knowledge distributions are said to be metrologically consistent if the ratio of the absolute difference between evaluations and the standard uncertainty of the difference is less than some chosen benchmark. As the concept of metrological consistency becomes more widely known and its benefits realized, it should become the dominant approach to test consistency of multiple evaluations of the same measurand.
Proceedings Title
XIX IMEKO World Congress 2009
Conference Dates
September 6-11, 2009
Conference Location


Kacker, R. , Kessel, R. , , K. and Bian, X. (2008), Comparison of statistical consistency and metrological consistency, XIX IMEKO World Congress 2009, Lisbon, -1, [online], (Accessed June 21, 2024)


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Created September 6, 2008, Updated February 19, 2017