Abstract
This chapter aims to propose a general model of a measurement process, consistent with the ontological and epistemological commitments developed in the previous chapters. Starting from the premise that any measurement is grounded on an empirical process, we propose a characterization of measurement methods related to the complementary roles of empirical and informational components, by broadly distinguishing between direct and indirect methods of measurement, where indirect measurements necessarily include at least one direct measurement. The stages of direct measurement are then analyzed and exemplified in reference to both physical and psychosocial properties. This is the basis for discussing once again the quality of measurement, now described in terms of the complementary requirements of object relatedness (“objectivity”) and subject independence (“intersubjectivity”).
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Notes
- 1.
A basic reason for the complexity of this endeavor is the (usually unavoidable and in fact appropriate) specialization of the scientific and technical disciplines, which triggers the construction of specific terminologies. An interesting example of an attempt to overcome lexical hyper-specialization while maintaining scientific and technical correctness is Electropedia, “the world’s most comprehensive online terminology database on ‘electrotechnology’, containing more than 22,000 terminological entries [...] organized by subject area” (Electropedia makes the series of standards IEC 60050 freely accessible online at www.electropedia.org)
- 2.
About direct and indirect methods of measurement, see also the discussion by Boumans (2007: Sect. 9.3).
- 3.
This is related to what is referred to as the measurement model part of a structural equation model (SEM), or a measurement model for short in the context of structural equation modeling (SEM; see, e.g., Skrondal & Rabe-Hesketh, 2004). SEMs are a popular class of statistical models used in the human sciences, although such models have a number of different purposes.
- 4.
This is related to what is referred to as the structural model part of the structural equation model (SEM), or structural model for short.
- 5.
The distinction between direct measurements and processes of evaluation which are not direct is sometimes accepted as unproblematic. For example, consider this quotation from John Taylor (1997: p. 45): “Most physical quantities usually cannot be measured in a single direct measurement but are instead found in two distinct steps. First, we measure one or more quantities that can be measured directly and from which the quantity of interest can be calculated. Second, we use the measured values of these quantities to calculate the quantity of interest itself. For example, to find the area of a rectangle, you actually measure its length l and height h and then calculate its area A as A = lh. Similarly, the most obvious way to find the velocity v of an object is to measure the distance traveled, d, and the time taken, t, and then to calculate v as v = d/t” (all emphases added). Interestingly, the process of indirect evaluation is not even called a measurement here, as if only direct measurements were measurements, in opposition to Lira’s conclusion mentioned above (“no measurement can strictly be considered to be ‘direct’”).
- 6.
The fact that in some cases the transduction is repeated and the measured value is computed as a statistic of the sample of indication values does not create a third method: from the structural point of view in which we are interested here, it remains unproblematically a case of direct measurement.
- 7.
Thus, for example, when measuring the weight of foods at the supermarket, the measurand is accepted to be the weight of the object put on the scale with no further specifications, though of course the measuring instrument is expected to be appropriately calibrated, including all relevant corrections.
- 8.
Given the VIM definition of <adjustment of a measuring system> as a “set of operations carried out on a measuring system so that it provides prescribed [indication values] corresponding to given values of a quantity to be measured” (JCGM, 2012: 3.11, adapted), this action could be also called “adjustment of the measurement environment”.
- 9.
As already mentioned in Footnote 14 of Chap. 3, definitional uncertainty is sometimes understood simply as one of the components of measurement uncertainty, and as such can be combined with the other components. We follow here the other approach, and consider it as the lower bound of the result of such a combination.
- 10.
The adjective “basic” refers to the simplification of not taking uncertainty into account in scale construction.
- 11.
In the human sciences, readily transportable measurement standards are not very common. In some contexts, synthetic reference objects have been found to be useful, such as computerized chess players (Maul et al. 2019).
- 12.
By presenting public scales first and then local scales we are following a conceptual sequence from what is outside the box, i.e., a measuring instrument, to what is inside the box. But in the historical development public scales may be the outcome of the previous development of multiple local scales and the assessment of their agreement. In the example of temperature, the first public thermometric scales (e.g., Celsius and Fahrenheit) were developed only after several thermometers were discovered to be in substantial agreement in their behavior (Chang, 2007).
- 13.
For the sake of simplicity, in this initial presentation we do not distinguish between (i) the intended property (that is, the measurand), i.e., the property referred to in the Basic Evaluation Equation that reports the result of measurement, and (ii) the effective property, i.e., the property that interacts with the measuring instrument and produces an effect on it; we call both of them the property under measurement.
- 14.
This assumption of causality is at the core of the very possibility of measurement by means of these kinds of devices, which are instances of what Nancy Cartwright calls a nomological machine, “a fixed (enough) arrangement of components, or factors, with stable (enough) capacities that in the right sort of stable (enough) environment will, with repeated operation, give rise to the kind of regular behaviour that we represent in our scientific laws” (1999: p. 50).
- 15.
This is sometimes referred to as the “pilot” stage of instrument construction in the human sciences.
- 16.
Under the hypothesis that the instrument behavior is modeled by an analytical function, and the underlying structure of the evaluation is sufficiently rich (see Sect. 6.5.3), this pointwise map may be interpolated, so as to obtain pairs (local value, public value) also for public values for which the instrument was not directly calibrated. For example the thermometer could be hypothesized to behave in a linear way between the freezing and the boiling point of water—i.e., a change of the measured temperature produces a proportional change of the position of the upper surface of alcohol in the tube—so that the midpoint of the upper surface would be mapped to 50 °C, and so on. Of course, the thermometer could be calibrated even if its behavior were not linear, but this would require the availability of other public reference temperatures, intermediate between the freezing and the boiling point of water.
- 17.
We are using the contrast of direct and indirect in two distinct ways. Given the distinction between direct and indirect measurement, the reference is here to a difference about operational implementations of direct measurement, which may be performed by indirectly or directly comparing the measured property and the reference properties in the public scale. In summary, a direct measurement can be performed through an indirect (as usual) or a direct comparison.
- 18.
This case is quite rare in the human sciences, due to the already mentioned rarity of reference objects.
- 19.
- 20.
There is in fact a mathematical condition here, i.e., the mappings involved in the process can be formalized as functions, but this does not constrain the measurability of nonquantitative properties. As discussed further in Sect. 7.4, this is to be reconsidered if uncertainties are included in the model.
- 21.
This is typical of all passive instruments, which are activated by the object under measurement instead of by an external source. Also in this regard a RCA test is analogous to an alcohol thermometer, in which the upper surface of alcohol in the tube changes its position only because of the energy transferred from the object whose temperature is under measurement.
- 22.
Note that this will result in a matrix of local references Xik*.
- 23.
Complicating matters, some authors refer to error and uncertainty interchangeably (Kirkup & Frenkel, 2006), as noted by Taylor: “In science, the word error does not carry the usual connotations of the terms mistake or blunder. Error in a scientific measurement means the inevitable uncertainty that attends all measurements. [… Here] error is used exclusively in the sense of uncertainty, and the two words are used interchangeably” (1997: p. 3). More or less explicitly, this denies that there is anything new in what has happened on this matter in the last decades, as witnessed in particular by the publication in 1993 of the Guide to the expression of uncertainty in measurement (GUM) (JCGM, 2008).
- 24.
Several cases of this phenomenon are proposed by Jerzy Muller in his book so explicitly titled The Tyranny of Metrics. An example: “In England, in an attempt to reduce wait times in emergency wards, the Department of Health adopted a policy that penalized hospitals with wait times longer than 4 h. The program succeeded—at least on the surface. In fact, some hospitals responded by keeping incoming patients in queues of ambulances, beyond the doors of the hospital, until the staff was confident that the patient could be seen within the allotted 4 h of being admitted” (2018: p. 5).
- 25.
- 26.
Sometimes the distinction between objectivity and intersubjectivity is not maintained, and they are conflated in a single concept of <non-subjective>. An explicit example is: “A highly disciplined discourse helps to produce knowledge independent of the particular people who make it. This last phrase points to my working definition of objectivity. It is, from the philosophical standpoint, a weak definition. It implies nothing about truth to nature. It has more to do with the exclusion of judgment, the struggle against subjectivity” (Porter, 1995: p. ix).
- 27.
As noted above, the concept of validity in human science measurement is closely related to definitional uncertainty. However, it is an expansive concept, and hence, there are aspects of it that also overlap with other parts of objectivity and intersubjectivity.
- 28.
Interestingly, these dimensions correspond to the two main stages of a measurement process of (a) transduction and matching and (b) calibration mapping, as connected by the local scale application. The idea that measurement is to be modeled on the basis of such two stages is not unusual, though the terms may be different. For example, Roman Morawski calls them “conversion” and “reconstruction” (Morawski, 2013) and Giovanni Battista Rossi and Francesco Crenna call them “observation” and “restitution” (Rossi & Crenna, 2018).
- 29.
This implies that <measurement> cannot be defined in terms of objectivity and intersubjectivity, as instead sometimes suggested (e.g., “the result of measurement must meet the condition of objective truth”, Piotrowski, 1992: p. 1), also, mistakenly, by one of the present authors (Mari et al., 2012: p. 2109).
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Mari, L., Wilson, M., Maul, A. (2021). Modeling measurement and its quality. In: Measurement across the Sciences. Springer Series in Measurement Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-030-65558-7_7
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