45
whereas in the example of the measurement of the reading comprehension ability of
a student by means of a test with multiple-choice questions, an example of an influence property might be human error in the scoring of the item responses. The role of
affecting properties and influence properties in a measurement is depicted in Fig. 3.1.
In a typical context these situations are not mutually exclusive, and in fact they
might co-occur to generate the multiplicity of results mentioned above. Under the
principled hypothesis that the influences described in the second situation can be
identified, the problem arises of how to deal with the incorrect results that are
obtained. Two basic strategies can be envisaged.
An empirical strategy aims at improving the behavior of the measuring instrument by reducing its sensitivity to the influence properties, and therefore the misleading variability of its results. This is a positive outcome, generally obtained at the
price of additional resources (including money, competencies, time, etc.) devoted to
the measurement. Of course this is not always feasible.
The fact that measurement is both an empirical and an informational process
makes possible a complementary, informational strategy: if the undesired variability cannot be completely removed, it can at least be modeled, evaluated, and formally expressed. The fundamental outcome is the acknowledgment that only in the
simplest cases is the information acquired on a measurand by means of a measurement entirely conveyed by a single measured value. Generally, a structurally more
complex result has to be reported instead. This is why the International Vocabulary
of Metrology (VIM) defines as a “set of quantity values being
attributed to a measurand together with any other available relevant information”
(JCGM, 2012: 2.9). This complexity is justified under the assumption that “when
reporting the result of a measurement […], it is obligatory that some quantitative
indication of the quality of the result be given so that those who use it can assess its
reliability”
2
(JCGM, 2008a: 0.1; emphasis added). In fact, one may even take it as a
definitional condition of measurement that its results include some information
about their quality.
The subject is intermingled with the development of statistics and the theory of
probability (see, e.g., Hacking, 1975, 1990; Rossi, 2014), and the diversity of interpretations of probability is reflected in the diversity of understandings of the role of
probability in measurement. In particular, according to the VIM, there are two “philosophies and descriptions of measurement”, identified as the “error approach
2 In practice, this is possibly one of the sharpest distinctions between measurement in scientific and
nonscientific contexts. Even the VIM admits that sometimes “the measurement result may be
expressed as a single measured quantity value” and then acknowledges that “in many fields, this is
the common way of expressing a measurement result” (JCGM, 2012: 2.9, Note 2).
Fig. 3.1 A black box model of the empirical behavior of a measuring instrument
3.2 The quality of measurement and its results
whereas in the example of the measurement of the reading comprehension ability of
a student by means of a test with multiple-choice questions, an example of an influence property might be human error in the scoring of the item responses. The role of
affecting properties and influence properties in a measurement is depicted in Fig. 3.1.
In a typical context these situations are not mutually exclusive, and in fact they
might co-occur to generate the multiplicity of results mentioned above. Under the
principled hypothesis that the influences described in the second situation can be
identified, the problem arises of how to deal with the incorrect results that are
obtained. Two basic strategies can be envisaged.
An empirical strategy aims at improving the behavior of the measuring instrument by reducing its sensitivity to the influence properties, and therefore the misleading variability of its results. This is a positive outcome, generally obtained at the
price of additional resources (including money, competencies, time, etc.) devoted to
the measurement. Of course this is not always feasible.
The fact that measurement is both an empirical and an informational process
makes possible a complementary, informational strategy: if the undesired variability cannot be completely removed, it can at least be modeled, evaluated, and formally expressed. The fundamental outcome is the acknowledgment that only in the
simplest cases is the information acquired on a measurand by means of a measurement entirely conveyed by a single measured value. Generally, a structurally more
complex result has to be reported instead. This is why the International Vocabulary
of Metrology (VIM) defines
attributed to a measurand together with any other available relevant information”
(JCGM, 2012: 2.9). This complexity is justified under the assumption that “when
reporting the result of a measurement […], it is obligatory that some quantitative
indication of the quality of the result be given so that those who use it can assess its
reliability”
2
(JCGM, 2008a: 0.1; emphasis added). In fact, one may even take it as a
definitional condition of measurement that its results include some information
about their quality.
The subject is intermingled with the development of statistics and the theory of
probability (see, e.g., Hacking, 1975, 1990; Rossi, 2014), and the diversity of interpretations of probability is reflected in the diversity of understandings of the role of
probability in measurement. In particular, according to the VIM, there are two “philosophies and descriptions of measurement”, identified as the “error approach
2 In practice, this is possibly one of the sharpest distinctions between measurement in scientific and
nonscientific contexts. Even the VIM admits that sometimes “the measurement result may be
expressed as a single measured quantity value” and then acknowledges that “in many fields, this is
the common way of expressing a measurement result” (JCGM, 2012: 2.9, Note 2).
Fig. 3.1 A black box model of the empirical behavior of a measuring instrument
3.2 The quality of measurement and its results