Widely-defined measurement – An analysis of challenges
Introduction
Measurement, that is the descriptive representation of the attributes of objects and events of the real world by symbols on the basis of an objective empirical process, is a basic tool of modern human thought. It is the way in which we describe and reason about the world.
Measurement has been developed through the physical sciences, which serve as a paradigm. From this basis its application has been extended to virtually all domains of human knowledge and discourse. However, the concepts and methods of measurement in this wider and more diverse range of disciplines offer significant conceptual problems, compared with measurement in the physical sciences that is the normative view of much metrological discourse.
Some of these problems will be outlined in the present paper as a starting point of discussion and an agenda for research.
Section snippets
Historical development
The present concepts and principles of measurement are the product of a long historical development. An understanding of this process of development is very necessary to help the extension of the application of measurement to new domains, or to areas where measurement is still problematic. The literature of the history of mathematics and science does not, in general, treat the development of measurement explicitly in its general account. Some critical historical philosophical studies of the
Measurement theory
Modern logical and philosophical understanding of the fundamental concepts of measurement is based on the representational theory. The theory is based on the viewing of the real world as empirical relational systems and measurement as a process of mapping them into symbolic relational systems.
The theory has been extensively presented in the literature [13], [14], [15], [16], [17], [18]. An outline has been presented in [19]. The theory has been extensively considered and important contributions
Properties of measurement
The properties of measurement arising from the above wide-sense definition will now be analysed and discussed to provide an explanation of the usefulness of its wide and diverse applications.
Measurement provides an objective description of the measurand. The description is not merely a matter of opinion or feeling. It is invariant in rational discourse.
Measurement is verifiable. Given a specification of the measurement process the same symbolic description of a measurand should in principle be
Applications of measurement
As was discussed above, measurement is extensively applied outside the physical sciences, in domains where widely-defined concepts of measurement are used. This outline of the range and diversity of applications illustrates the significance of measurement outside the physical sciences.
Measurement in psychology is the first example to be cited. It is the endeavour to apply measurement in psychology that first challenged the restrictive view of measurement of the physical sciences and led to the
Philosophical considerations
The wide application of measurement is driven by philosophical considerations. It is based on a belief that empirical observation represents the only secure basis of knowledge and that objectivity is possible.
In this outline it is not possible to review the relevant philosophical discussions adequately. Relevant entries in [54], [55], [56] are recommended for further reading. A good summary discussion is presented in [27].
There is a wide adoption of the programme of Galileo to measure what is
Measurand concept formation
The establishment of a process and scale of measurement requires the formation of the concept of the measurand. This has been a central problem of the establishment of measurement concepts of such attributes as temperature, or electrical current, which unlike length and weight are not simply perceived by the human senses.
The process of measurand concept formation has been discussed in the literature of logical positivism [63] and considered in [64].
The consideration of widely-defined
Experiment and observation
Measurement theory relies on an ability to perform experiments for the purpose of establishing the existence of empirical relational systems.
In many cases direct observation of the measurand is not possible and it must be indirectly observed. Such indirect experiments consist of exciting the system under test and observing the response. In many cases of widely-defined measurement, such experiments are not possible, because the system under observation cannot be significantly disturbed.
This is
Replicable relations
The establishment of a scale of measurement for a quality is based on the existence among the quality manifestations of empirical relations that can be observed to be replicable. Such relations are termed nomological, or law like.
In many systems, however, there are no replicable relations for the measurand.
As has been discussed in the section dealing with philosophical considerations humans are autonomous intelligent actors and may behave differently under apparently identical conditions. They
Reliability, validity and generalisability
The concepts of reliability, validity and generalisability are central to widely-defined measurement. A good summary account is given in [27].
Reliability is the term used to describe the extent to which a measurement procedure yields the same result on repeated trials. It is thus the same concept as that of uncertainty used in strictly defined measurement. This is well discussed in the literature [72]. Reliability may be difficult to achieve in practice in many applications of measurement, but
Theories
The aim of scientific inquiry is, in general, to establish a well-defined theory for a domain of knowledge. Such a theory consists of a system of quantities and relations between them. It provides descriptive, explanatory and predictive power. In the physical sciences such a system is well established.
Such theories are not well developed in the psychological and social sciences and, as been discussed above, the possibility of such theories for systems incorporating human actors is widely
Verifiability
One of the principal pragmatic strengths of measurement is that measurement statements are verifiable. A measurement statement consists of a symbol assigned to the measurand, together with the specification of the scale of measurement employed. Given such a statement the measurement can be replicated by any other observer.
In the strongly defined measurement in the physical sciences a measurement result consists of a number and the specification of the unit.
In physical and chemical measurements
Conclusions
Measurement is applied in a wide range of human inquiry and discourse. Measurement in the physical sciences is the dominant paradigm. However, in significant areas of application of measurement that paradigm is inapplicable and a wide-sense definition of measurement is necessary.
Measurement science should address the whole range of applications of measurement. It should endeavour to provide a universal framework of concepts and principles to address all applications of measurement.
Measurement
Acknowledgements
The author thanks his colleagues Professors K.T.V. Grattan and S.H. Khan for their support. He is also grateful to Professors D. Hofmann, R. Morawski and L. Mari for creating the environment in which fundamental measurement science ideas can be discussed.
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