46
(sometimes called traditional approach or true value approach)” and the “uncertainty approach” (JCGM, 2012: Introduction). While for some purposes this might
be too rough a classification, and some cases may be intermediate (see, e.g., Giordani
& Mari, 2014), or even of a different kind (see, e.g., Ferrero & Salicone, 2006), we
adopt this distinction to introduce the informational strategy and therefore the pivotal concepts of measurement error and measurement uncertainty.
3
However, before
discussing such concepts, we first consider the framework in which they may be
understood.
3.2.1 A sketch of the framework
“Measurement is essentially a production process, the product being numbers”
(Speitel, 1992). The quality of the products and the quality of the process are in
principle distinct, though related, entities, and as such each of them deserves some
consideration. First of all, it is clear that the users’ focus is on the quality of what is
produced: in general, users would like to have trustworthy, useful values for the
measurands in which they are interested. Were it possible to disentangle the quality
of the process from the quality of the products, the former would become immaterial. But, as for any production process, the quality of the products—measurement
results in this case—depends on the quality of the process, which is why both need
to be taken into account.
The quality of a measurement has to do with the features of the experimental
setup, which includes the measuring instrument(s) and everything that is exploited
to control the environment with the aim of reducing its effects on the behavior of the
instrument(s). In the traditions of both physical and psychosocial measurement a
wealth of models and accompanying parameters have been developed. In these traditions, measurements are sometimes modeled as black boxes that transform an
input property, i.e., the property being measured, to an output property, i.e., the
instrument indication, under the acknowledgment that the transformation is usually
affected by some influence properties.
As mentioned in Sect. 2.3, the transformation performed by the measuring
instrument is modeled by the instrument calibration function, whose inverse maps
values of the instrument indication to values of the measurand. On this basis we can
define some parameters characterizing the behavior of the instrument, and therefore
the quality of the process. The definitions are exemplified by the simple case of a
spring dynamometer, which transforms the applied weight force (the property being
measured) to a spring elongation (the instrument indication); however, the defined
parameters are modeled as structural features of instruments, and as such they can
3 Like most of the contents of this chapter, what follows generally applies to both quantitative and
nonquantitative properties, even though the mathematical aspects are mainly introduced here in
reference to quantities. The issue of uncertainty in nonquantitative evaluations is further considered in Chap. 6.
3 Technical and cultural contexts for measurement systems
(sometimes called traditional approach or true value approach)” and the “uncertainty approach” (JCGM, 2012: Introduction). While for some purposes this might
be too rough a classification, and some cases may be intermediate (see, e.g., Giordani
& Mari, 2014), or even of a different kind (see, e.g., Ferrero & Salicone, 2006), we
adopt this distinction to introduce the informational strategy and therefore the pivotal concepts of measurement error and measurement uncertainty.
3
However, before
discussing such concepts, we first consider the framework in which they may be
understood.
3.2.1 A sketch of the framework
“Measurement is essentially a production process, the product being numbers”
(Speitel, 1992). The quality of the products and the quality of the process are in
principle distinct, though related, entities, and as such each of them deserves some
consideration. First of all, it is clear that the users’ focus is on the quality of what is
produced: in general, users would like to have trustworthy, useful values for the
measurands in which they are interested. Were it possible to disentangle the quality
of the process from the quality of the products, the former would become immaterial. But, as for any production process, the quality of the products—measurement
results in this case—depends on the quality of the process, which is why both need
to be taken into account.
The quality of a measurement has to do with the features of the experimental
setup, which includes the measuring instrument(s) and everything that is exploited
to control the environment with the aim of reducing its effects on the behavior of the
instrument(s). In the traditions of both physical and psychosocial measurement a
wealth of models and accompanying parameters have been developed. In these traditions, measurements are sometimes modeled as black boxes that transform an
input property, i.e., the property being measured, to an output property, i.e., the
instrument indication, under the acknowledgment that the transformation is usually
affected by some influence properties.
As mentioned in Sect. 2.3, the transformation performed by the measuring
instrument is modeled by the instrument calibration function, whose inverse maps
values of the instrument indication to values of the measurand. On this basis we can
define some parameters characterizing the behavior of the instrument, and therefore
the quality of the process. The definitions are exemplified by the simple case of a
spring dynamometer, which transforms the applied weight force (the property being
measured) to a spring elongation (the instrument indication); however, the defined
parameters are modeled as structural features of instruments, and as such they can
3 Like most of the contents of this chapter, what follows generally applies to both quantitative and
nonquantitative properties, even though the mathematical aspects are mainly introduced here in
reference to quantities. The issue of uncertainty in nonquantitative evaluations is further considered in Chap. 6.
3 Technical and cultural contexts for measurement systems