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Annex H Common Terms and Formulas used in Uncertainty Determinations
The terms and definitions reproduced below are based on those in Guide to the Expression of Uncertainty
in Measurement (1995), International Organization for Standards.
The ISO, through Recommendation INC-1 (1980) details the expression of uncertainty:
1 The uncertainty in the result of a measurement generally consists of several components which
may be grouped into two categories according to the way in which their numerical value is estimated:
A. those which are evaluated by statistical methods,
B. those which are evaluated by other means.
There is not always a simple correspondence between the classification into categories A or B
and the previously used classification into “random” and “systematic” uncertainties. The term
“systematic uncertainty” can be misleading and should be avoided.
Any detailed report of the uncertainty should consist of a complete list of the comonents, specifying
for each the method used to obtain its numerical value.
2 The components in category A are characterized by the estimated variances (or the estimated
“standard deviations” ) and the number of degrees of freedom . Where appropriate, the
covariances should be given.
3 The components in category B should be characterised by quantities , which may be considered
as approximations to the corresponding variances, the existence of which is assumed. The quantities
may be treated like variances and the quantities like standard deviations. Where appropriate,
the covariances should be treated in a similar way.
4 The combined uncertainty should be characterized by the numerical value obtained by applying
the usual method for the combination of variances. The combined uncertainty and its components
should be expressed in the form of “standard deviations.”
5 If, for particulat applications, it is necessary to multiply the combined uncertainty by a factor to
obtaina an overall uncertainty, the multiplying factor used must always be stated.
H 1. Common Terms
Uncertainty
The uncertainty of the result of a measurement reflects the lack of exact knowledge of the value of
the measurand. The result of a measurement after correction for recognized systematic effects is still
only an estimate of the value of the measurand because of the uncertainty arising from random effects
and from imperfect correction of the result for systematic effects.
Notes:
a. The result of a measurement (after corrections) can unknowably be very close to the value of the
measurand (and hence have a negligible error) even though it may have a large uncertainty. Thus
the uncertainty of the result of a measurement should not be confused with the remaining unknown
error.
b. Possible sources of uncertainty in a measurement may include:
i. incomplete definition of the measurand
ii. imperfect realization of the definition of the measurand
iii. nonrepresentative sampling - the sample measured may not represent the defined measurand
iv. inadequate knowledge of the effects of environmental conditions on the measurement or
imperfect measurement of environmental conditions
v. finite instrument resolution or discrimination threshold
vi. inexact values of measurement standards and reference materials
vii. inexact values of constants and other parameters obtained from exteranl sources and used
in the data-reduction algorithm
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