Measurement With Persons

Theory, Methods, and Implementation Areas

Birgitta Berglund, Giovanni B. Rossi, James T. Townsend, Leslie R. Pendrill

• Publisher: Psychology Press
• Year: 2013
• ISBN:
  9781136723735
• Edition: 1
• Topic: Psychology
• Subtopic: History & Theory in Psychology
• Index: Psychology

Measurements with persons are those in which human perception and interpretation are used for measuring complex, holistic quantities and qualities, which are perceived by the human brain and mind. Providing means for reproducible measurement of parameters such as pleasure and pain has important implications in evaluating all kind of products, services, and conditions.

This book inaugurates a new era for this subject: a multi- and inter-disciplinary volume in which world-renowned scientists from the psychological, physical, biological, and social sciences reach a common understanding of measurement theory and methods.

In the first section, generic theoretical and methodological issues are treated, including the conceptual basis of measurement in the various fields involved; the development of formal, representational, and probabilistic theories; the approach to experimentation; and the theories, models, and methods for multidimensional problems. In the second section, several implementation areas are presented, including sound, visual, skin, and odor perception, functional brain imagining, body language and emotions, and, finally, the use of measurements in decision making

Measurement with Persons will appeal to a wide audience across a range of sciences, including general psychology and psychophysics, measurement theory, metrology and instrumentation, neurophysiology, engineering, biology, and chemistry.

1 Measurement across physical and behavioral sciences

Birgitta Berglund, ¹ Giovanni Battista Rossi,² and Andrew Wallard³

¹ Department of Psychology

Stockholm University

and

Institute of Environmental Medicine, Karolinska Institutet

Stockholm, Sweden

² DIMEC

Università degli Studi di Genova

Genova, Italy

³ Bureau International des Poids et Mesures

Sèvres, France

1.1 The origins

Although measurement has been a key factor in the development of modern science, studies on its foundations appeared relatively late, in the second half of the nineteenth century. They concerned, at the same time, both physical and behavioral sciences and they paralleled the constitution of the international system of metrology, with the signing of the Metre Convention. It is important to be aware of such common roots for understanding and putting in the right perspective what happened later, up to the present day. So, a historical overview of these crucial nineteenth century developments is presented in the first part of this chapter, up to the division that arose among the two communities—physicists and engineers on the one side, psychological and behavioral scientists on the other—in the first part of the twentieth century. With lack of communication such division led to an essentially parallel development on the two sides. Nevertheless, noteworthy developments in measurement science and technology, as well as recent measurement needs emerging in science and society, call for a common effort toward reaching a common view, enabling interdisciplinary collaboration and ensuring a common development. This is the subject of the second part of the chapter. Lastly, in the third and final part, new trends are presented and discussed and research needs addressed.

1.2. In search of a theory for physical measurement

1.2.1 Helmholtz: The analogy between measuring and counting

Helmholtz, in a Memoire published in 1887 (Helmholtz, 1971), investigated “the objective meaning of the fact that we express as quantities, through concrete numbers, situations of real objects” and he wanted to discuss “under what circumstances we are allowed to do so.” “Concrete numbers,” in his language, are those arising from the counting of real objects. He found a brilliant solution to the problem by establishing an analogy between measurement and counting.

The key idea is that, in many cases, the characteristic we want to measure is a quantity, in that it is the amount of something, and thus it may be thought of as the sum of a number of elementary parts, or units, of that something. In those cases measurement is equivalent to the counting of such units. From this analogy it is possible to derive the conditions that must be met in order for measurement to make sense, that is, the conditions for measurability. Counting is possible thanks to the properties of natural numbers, which undergo an order, based on the relation “greater than or equal to,” and may be added to each other. Similarly, measurement is possible and well founded whenever it is possible to identify the empirical counterparts of the order relation and of the addition operation for the objects carrying the characteristic of interest. For example, in the case of mass measurement, order may be established by comparing objects by an equal-arms balance and addition of two objects consists in putting them on the same pan of the balance. Thanks to these properties it is possible to construct a measurement scale, which supports the practice of measurement, as we soon show. An important question is now whether it is possible to establish the above properties for all kinds of measurement. Helmholtz admits it is not and mentions an indirect approach as an approach. This idea was developed afterwards by Campbell, yielding the distinction between fundamental and derived quantities.

1.2.2 Campbell: The foundation of physical measurement

The first organic presentation of a theory for physical measurement was by Campbell, in the second part of his book, Physics—The Elements, published in 1920 (Campbell, 1957). Like Helmholtz, he considers the problem of

… why can and do we measure some properties of bodies while we do not measure others?… I have before my table [he writes] a tray containing several similar crystals. These crystals possess many properties among which may be included the following: Number, weight, density, hardness, colour, beauty. The first three of these qualities are undoubtedly capable of measurement—unless it be judged the number is to be excluded as being more fundamental than any measurement; concerning hardness it is difficult to say whether or not it can be measured, for though various systems of measuring hardness are in common use, it is generally felt that none of them are wholly satisfactory. Colour cannot be measured as the others can, that is to say it is impossible to denote the colour of an object by a single number which can be determined with the same freedom from arbitrariness which characterises the assigning of a number to represent weight or density. The last property, beauty, can certainly not be measured, unless we accept the view which is so widely current that beauty is determined by the market value. What is the difference between the properties which determine the possibility or impossibility of measuring them? (Campbell, 1957)

To answer this question, he considers two kinds of quantities,

• Fundamental (e.g., mass)

• Derived (e.g., density)

Both of these require an empirical property of order, which is (according to Helmholtz) the basic requirement for measurement. But fundamental quantities allow for a physical-addition operation also. Why is this operation so important? Because it is key in permitting the general procedure for fundamental measurement to be applied. Such a procedure consists in constructing a measurement scale, that is, a series of standards with properly assigned numerical values, and then in comparing any unknown object r to it, in order to select the element in the series that is equivalent to it. Then it will be possible to assign to r the same number (measure) as the selected element.

Let us see this in more detail, considering again the mass-measurement case. For the construction of the measurement scale, we first arbitrarily select one object, u, which will serve as the unit of the scale, and we assign the number 1 to it, that is, m(u) = 1, where m is the measure function. Then we look for another element u′, equivalent to u, such that, put in the opposite pan of the balance, it will balance it. We now sum the two elements by putting them on the same pan of the balance and we look for a third element that balances with them. Clearly, we may assign the number 2. So we have constructed a multiple of the unit, and we may proceed similarly for the other multiples. Submultiples may also be constructed in a similar way. Once the scale is available, mass measurement may be performed by comparing an unknown object r, with the elements of the scale, with the balance, up to finding the element of the series, say s, equivalent to it: then we assign m(r) = m(s). The scheme of the direct-measurement procedure just considered may be depicted as in Figure 1.1.

Noteworthy, in the process of construction of the scale, the only arbitrary choice concerns the selection of the unitary element; afterwards, the values to be assigned to the other elements are fully constrained by the need for conformity with the results of the summing operation. As a consequence of this, the measure may be interpreted as the ratio between the value of the characteristic in object r and in the unitary element u. In other words, m(r) = p/q implies that the sum of q “copies” of r balances with the sum of p unitary elements. Note that q copies of r may be realized by proper amplification devices, for example, by using an unequal-arm balance, with arms in a ratio q:1 to each other.

Figure 1.1 Basic scheme for the direct measurement of a quantity.

Now we may understand Campbell’s statement that only qualities “which can be determined with the same freedom from arbitrariness which characterises the assigning of a number to represent weight” fully qualify as measurable, and we may also comprehend the rationale behind it. What has been considered so far applies to fundamental quantities, yet there is another way of measuring something, the way that applies to derived quantities. Consider the case of density, ρ. For this quantity we may find a meaningful criterion for order, because we may say that a is denser than b, if we may find a liquid in which b floats, whereas a sinks, but we do not have any criterion of empirical summation. Yet density “can be determined with the same freedom from arbitrariness which characterises the assigning of a number to represent weight,” because we may identify density as the ratio of mass to volume: ρ = M/V, and we can measure mass and volume. So, given an object a, assuming we are able to measure its mass, obtaining m_M (a), and its volume, obtaining m_v (a), we may assign a measure to its density as m_ρ(a) = m_M(a)/m_v(a). The other way to found measurement—the way that applies to derived quantities—thus consists in finding some physical law that allows expressing the measure of the characteristic of our interest as a function of the measure of other quantities whose measurability has already been assessed.

To sum up, Campbell holds that measurability may be established first by proving that the characteristic under investigation involves an empirical order relation and then either by finding a physical addition operation that allows the construction of a reference measurement scale and the performing of measurement by comparison with it, or by finding some physical law that allows the measure to be expressed as a function of other quantities. The first procedure applies to fundamental quantities, the second to derived ones and is illustrated in Figure 1.2.

In the case of derived measurement the foundation of measurement is subject to the physical (more generally we could say “natural”) law that is invoked. In this regard, we may consider two possibilities: either it is also possible to measure the quantity directly, and so we only have to check whether the direct and the indirect approaches produce consistent results, or the law has an intrinsic validity and, if the same magnitude appears in two or more laws accepted in the same scientific domain, the consistency of the system may be invoked to support the measurability of the quantity under consideration and so plays a foundational role.

Figure 1.2 Basic scheme for the indirect measurement of a quantity.

In the first case, derived measurements are essentially reduced to fundamental ones and do not have an independent foundation. In the second, quantities are considered as a part of a system and the focus is shifted toward the performance of the overall system rather than on the individual properties. This concept of quantities as a part of a system was clearly affirmed, in about the same period, with the constitution of the Metre Convention.

1.3 The constitution of the international system of metrology

The need for reference standards for measurement in trade, agriculture, and construction has been recognized by mankind from ancient times. Metrological activities have been developed on a regional basis, following the evolution of the geopolitical scenario, up to relatively recent times. Only in the nineteenth century has international coordination been achieved, as a consequence of a process that started near the end of the previous century. At the time of the French Revolution, the decimal metric system was instituted and two platinum standards representing the meter and the kilogram were deposed in the Archives de la République in Paris (1799). This rationalization of the system of units may perhaps have been explained by the concurrence of a few factors. At that time modern science had been firmly established and the need of accurate measurements for its development had been clearly recognized. Philosophers of the Enlightenment were in search of a rational foundation of knowledge, which has a natural counterpart in science in the search for universal reference standards, independent of place and time.

This process continued in the nineteenth century and ultimately led to the Metre Convention, a treaty that was signed in Paris in 1875 by representatives of sevent...

Table of contents

• Cover
• Halftitle
• Title
• Copyright
• Dedication
• Contents
• Preface
• Contributors
• 1 Measurement across physical and behavioral sciences
• 2 Measurement in psychology
• 3 Measurements of physical parameters in sensory science
• 4 Meaningful and meaningless statements in epidemiology and public health
• 5 Toward a probabilistic theory of measurement
• 6 Multivariate measurements
• 7 The prospects for measurement in infinite-dimensional psychological spaces: Modern notions for geometric person measurements in finite and infinite dimensional spaces
• 8 Psychophysical linguistics
• 9 Mathematical foundations of Universal Fechnerian Scaling
• 10 Neural networks and fuzzy systems
• 11 Psychological measurement for sound description and evaluation
• 12 Nociception and pain in thermal skin sensitivity
• 13 Measurement-related issues in the investigation of active vision
• 14 Electrical and functional brain imaging
• 15 Body language: Embodied perception of emotion
• 16 Risk assessment and decision making
• Author Index
• Subject Index