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Standard
Uncertainty and Relative Standard Uncertainty
- Definitions
- The standard uncertainty u(y) of a measurement result y is the estimated
standard deviation of y.
The relative standard uncertainty ur(y) of a measurement
result y is defined by ur(y) = u(y)/|y|, where y is not equal
to 0.
Meaning of uncertainty
If the
probability distribution characterized by the measurement result y and its standard
uncertainty u(y) is approximately normal (Gaussian),
and u(y) is a reliable estimate of the standard
deviation of y, then the interval y – u(y) to
y + u(y) is
expected to encompass approximately 68 % of the distribution of values that could
reasonably be attributed to the value of the quantity Y of which y is an estimate. This implies that it is
believed with an approximate level of confidence of 68 % that Y is greater than or equal
to y - u(y), and is less than or equal
to y + u(y), which is commonly written
as Y= y ± u(y).
Use of concise notation
If, for
example, y = 1 234.567 89 U and u(y) = 0.000 11 U, where U is the unit of y, then Y = (1 234.567 89 ± 0.000 11) U. A more concise form of this expression,
and one that is in common use, is Y = 1 234.567 89(11) U, where it understood that the number in
parentheses is the numerical value of the standard uncertainty referred to the corresponding last
digits of the quoted result.
Additional information
See Uncertainty of Measurement Results.
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