53
A worldwide consensus on the evaluation and expression of uncertainty in measurement
would permit the significance of a vast spectrum of measurement results in science, engineering, commerce, industry, and regulation to be readily understood and properly interpreted. In this era of the global marketplace, it is imperative that the method for evaluating
and expressing uncertainty be uniform throughout the world so that measurements performed in different countries can be easily compared.
Such an information-oriented standpoint is the basis for a recommendation issued
in 1980 by a working group promoted by the International Bureau of Weights and
Measures (BIPM) and approved in 1981 by the International Committee of Weights
and Measures (CIPM). The traditional classification of kinds of (causes of) error as
random or systematic is replaced here with a distinction about the methods of evaluating measurement uncertainty (JCGM, 2008a, 2008b: 0.7):
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.
This change is the premise for the two key parts of the recommendation.
• First, uncertainties shall be formalized as standard deviations not only when a
statistical sample is available, i.e., for “the components in category A”, but also
in all other cases, i.e., for “the components in category B”,
11
for which the standard deviation is “based on the degree of belief that an event will occur” (JCGM,
2008a, 2008b: 3.3.5). The list of these components—each then made of a description of the evaluation method and the related standard deviation, called “standard
uncertainty” in this context
12
—is included in the uncertainty budget (JCGM,
2012: 2.33).
11 The terms chosen in the VIM are even more explicit: “Type A evaluation of measurement uncertainty” and “Type B evaluation of measurement uncertainty” (JCGM, 2012: 2.28; 2.29). The VIM
itself provides some examples of type B evaluations, “based on information (i) associated with
authoritative published quantity values, (ii) associated with the quantity value of a certified reference material, (iii) obtained from a calibration certificate, (iv) about drift, (v) obtained from the
accuracy class of a verified measuring instrument, (vi) obtained from limits deduced through personal experience” (2.29, Examples).
12 The term “standard uncertainty” was introduced by the GUM as “uncertainty of the result of a
measurement expressed as a standard deviation” (JCGM, 2008a, 2008b: 2.3.1), where the adjective
“standard” here plausibly refers to the choice of formalizing all components of measurement
uncertainty with the same mathematical tool, i.e., as standard deviations. Whether this is always a
sensible position is an open issue, and in any case for less-than-interval properties other tools need
to be adopted, for example the interquartile range for ordinal properties and the entropy for nominal properties (Mari et al., 2020). A basic justification of the choice of standard deviations is
implicitly given by the GUM itself, which defines as “parameter
[…] that characterizes the dispersion of the values that could reasonably be attributed to the measurand” (2.2.3), thus assuming that, at least in the case of measurement, uncertainty and dispersion
can be superposed. That is generally not the case is clear, as this quote shows. “Entropy measures
the uncertainty associated with a probability distribution over outcomes. It therefore also measures
surprise. Entropy differs from variance, which measures the dispersion of a set or distribution of
numerical values. Uncertainty correlates with dispersion, but the two differ. Distributions with
3.2 The quality of measurement and its results
A worldwide consensus on the evaluation and expression of uncertainty in measurement
would permit the significance of a vast spectrum of measurement results in science, engineering, commerce, industry, and regulation to be readily understood and properly interpreted. In this era of the global marketplace, it is imperative that the method for evaluating
and expressing uncertainty be uniform throughout the world so that measurements performed in different countries can be easily compared.
Such an information-oriented standpoint is the basis for a recommendation issued
in 1980 by a working group promoted by the International Bureau of Weights and
Measures (BIPM) and approved in 1981 by the International Committee of Weights
and Measures (CIPM). The traditional classification of kinds of (causes of) error as
random or systematic is replaced here with a distinction about the methods of evaluating measurement uncertainty (JCGM, 2008a, 2008b: 0.7):
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.
This change is the premise for the two key parts of the recommendation.
• First, uncertainties shall be formalized as standard deviations not only when a
statistical sample is available, i.e., for “the components in category A”, but also
in all other cases, i.e., for “the components in category B”,
11
for which the standard deviation is “based on the degree of belief that an event will occur” (JCGM,
2008a, 2008b: 3.3.5). The list of these components—each then made of a description of the evaluation method and the related standard deviation, called “standard
uncertainty” in this context
12
—is included in the uncertainty budget (JCGM,
2012: 2.33).
11 The terms chosen in the VIM are even more explicit: “Type A evaluation of measurement uncertainty” and “Type B evaluation of measurement uncertainty” (JCGM, 2012: 2.28; 2.29). The VIM
itself provides some examples of type B evaluations, “based on information (i) associated with
authoritative published quantity values, (ii) associated with the quantity value of a certified reference material, (iii) obtained from a calibration certificate, (iv) about drift, (v) obtained from the
accuracy class of a verified measuring instrument, (vi) obtained from limits deduced through personal experience” (2.29, Examples).
12 The term “standard uncertainty” was introduced by the GUM as “uncertainty of the result of a
measurement expressed as a standard deviation” (JCGM, 2008a, 2008b: 2.3.1), where the adjective
“standard” here plausibly refers to the choice of formalizing all components of measurement
uncertainty with the same mathematical tool, i.e., as standard deviations. Whether this is always a
sensible position is an open issue, and in any case for less-than-interval properties other tools need
to be adopted, for example the interquartile range for ordinal properties and the entropy for nominal properties (Mari et al., 2020). A basic justification of the choice of standard deviations is
implicitly given by the GUM itself, which defines
[…] that characterizes the dispersion of the values that could reasonably be attributed to the measurand” (2.2.3), thus assuming that, at least in the case of measurement, uncertainty and dispersion
can be superposed. That is generally not the case is clear, as this quote shows. “Entropy measures
the uncertainty associated with a probability distribution over outcomes. It therefore also measures
surprise. Entropy differs from variance, which measures the dispersion of a set or distribution of
numerical values. Uncertainty correlates with dispersion, but the two differ. Distributions with
3.2 The quality of measurement and its results