The NIST Reference on Constants, Units and Uncertainty

Uncertainty of Measurement Results
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The following definitions are given in the ISO Guide to the Expression of Uncertainty in Measurement. Many additional terms relevant to the field of measurement are given in a companion publication to the ISO Guide, entitled the International Vocabulary of Basic and General Terms in Metrology, or VIM. Both the ISO Guide and VIM may be readily purchased.

Uncertainty (of measurement)

parameter, associated with the result of a measurement, that characterizes the dispersion of the values that could reasonably be attributed to the measurand

  • The parameter may be, for example, a standard deviation (or a given multiple of it), or the half-width of an interval having a stated level of confidence.

  • Uncertainty of measurement comprises, in general, many components. Some of these components may be evaluated from the statistical distribution of the results of a series of measurements and can be characterized by experimental standard deviations. The other components, which also can be characterized by standard deviations, are evaluated from assumed probability distributions based on experience or other information.

  • It is understood that the result of the measurement is the best estimate of the value of the measurand, and that all components of uncertainty, including those arising from systematic effects, such as components associated with corrections and reference standards, contribute to the dispersion.
Standard uncertainty uncertainty of the result of a measurement expressed as a standard deviation
Type A evaluation (of uncertainty) method of evaluation of uncertainty by the statistical analysis of series of observations
Type B evaluation (of uncertainty) method of evaluation of uncertainty by means other than the statistical analysis of series of observations
Combined standard uncertainty standard uncertainty of the result of a measurement when that result is obtained from the values of a number of other quantities, equal to the positive square root of a sum of terms, the terms being the variances or covariances of these other quantities weighed according to how the measurement result varies with changes in these quantities
Expanded uncertainty

quantity defining an interval about the result of a measurement that may be expected to encompass a large fraction of the distribution of values that could reasonably be attributed to the measurand.

  • The fraction may be viewed as the coverage probability or level of confidence of the interval.

  • To associate a specific level of confidence with the interval defined by the expanded uncertainty requires explicit or implicit assumptions regarding the probability distribution characterized by the measurement result and its combined standard uncertainty. The level of confidence that may be attributed to this interval can be known only to the extent to which such assumptions may be justified.
Coverage factor
numerical factor used as a multiplier of the combined standard uncertainty in order to obtain an expanded uncertainty

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