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Evaluating, Expressing, and Propagating Measurement Uncertainty for NIST Reference Materials



Antonio M. Possolo


This document is a companion of NIST Special Publication 260-136 (2020 Edition), intended for users of NIST reference materials, that explains how NIST evaluates and expresses measurement uncertainty associated with certified or with non-certified values, and exemplifies how such uncertainty may be propagated to derivative quantities that involve these values. The first few pages include navigation aids that enable direct and easy access to examples that illustrate different ways of expressing uncertainty, and to specific reference materials mentioned in this document. The document reviews the concepts of measurement, measurement uncertainty, and reference material, and includes a refresher of concepts from probability and statistics that are commonly used in certificates of NIST reference materials. The bulk of the document comprises concrete, worked out examples of how NIST evaluates measurement uncertainty for NIST reference materials, and of how this uncertainty is expressed, and how it may propagated in applications that use NIST reference materials. Illustrative computer codes are included in an appendix.
Special Publication (NIST SP) - 260-202
Report Number


bottom-up, calibration, categorical, coverage factor, coverage probability, degrees of freedom, DNA, expression, evaluation, expanded uncertainty, functional measurand, Gaussian, lognormal, measurand, measurement, measurement uncertainty, nominal, ordinal, probability, propagation, qualitative measurand, quantitative measurand, reference material, skew-normal, standard reference material, standard uncertainty, statistics, Student, top-down


Possolo, A. (2020), Evaluating, Expressing, and Propagating Measurement Uncertainty for NIST Reference Materials, Special Publication (NIST SP), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed June 24, 2024)


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Created July 28, 2020, Updated July 29, 2020