The late John A. Simpson was a physicist and metrologist associated with the University of Chicago, the Enrico Fermi Institute, and the US National Institute for Standards and Technology.
In the following definition of measurement, taken from the Metrology subject heading in the Encyclopedia of Physics, note that Simpson makes repeated explicit references to the concept of quantity without specifically invoking any tests of additivity or divisibility, though these, along with other similar tests, are indeed implicit in the concept of a "continuous scale of magnitude."
Simpson places far more emphasis on common units, and common methods of obtaining them and determining ordinal relations, than he does on knowing how and when additive relations have been established. He goes so far as to hold that "a proper measurement" is one that is "universally reproducible" "wherever and whenever the measurement process is repeated."
Psychometricians might then do well to shift some of their resources toward deployment of common units and methods for each major measurable variable, and away from the generation of ever more different units and methods. In what follows, the emphasis is mine.
Simpson, J. A. (1991). Metrology. In R. G. Lerner & G. L. Trigg (Eds.), Encyclopedia of physics, 2d Ed. (pp. 723-5). New York, New York: VCH Publishers, Inc.
p. 723-4: "A measurement is a series of manipulations of physical objects or systems according to defined protocols that result in a number. The objects or systems involved are test objects, measuring devices, and computational operations. The objects and devices exist in and are influenced by some environment. The value obtained is purported to represent uniquely the magnitude, or intensity, of some quantity embodied in the test object. This number is acquired to form the basis of a decision affecting some human goal or satisfying some human need that depends on the properties of the test object.
In order to attain this goal of useful decision making, metrology has focused on the task of assuring that the value obtained for a given quantity of a given object is functionally identical wherever and whenever the measurement process is repeated. Only then can all parties to the decision work from a concordant data base. Such a universally reproducible measurement is called a proper measurement.
An analysis of the logical conditions that must be satisfied to achieve a proper measurement shows that three independent arbitrary axioms must be universally agreed upon:
1. All parties must agree upon and have access to a common unit in which the results will be expressed.
2. There must be an agreed-upon physically realizable method of obtaining a continuous scale of magnitude based on the unit.
3. There must be an agreed-upon physically realizable method of determining when the quantity of interest, as embodied in a physical object or system, is equal to, less than, or greater than, some fixed point on this realized scale.
The principal activity of metrologists consists of generating, propagating, testing, and applying to an object or system of interest sets of these measurement axioms for all quantities and all useful magnitudes of those quantities...
Fundamental to the success of such a system is the development, at each transfer [points through which the unit is traceable to the reference standard from secondary standards and the point of use], of realistic estimates of uncertainty."
p. 725: "By far the greatest activity in metrology is that performed in the service of quality control. Manufacturing establishments of any size maintain standards laboratories and/or metrology laboratories. The laboratories maintain the company master standards, gauges, and measuring instruments, which are periodically calibrated against the national standards. The working measuring equipment on the shop floor is calibrated by the metrology laboratory on a scheduled basis. ... In this manner the measurements made for quality control are considered `traceable' to national standards."
William P. Fisher, Jr.
"Measurement lies at the heart of genuine quality improvement,
the kind that healthcare organizations undertake on behalf of their
patients and communities, not simply to ensure accreditation. When
delivery systems get ready to transition from talking about
continuous quality improvement to really practicing it, learning to
measure and manage care processes and outcomes becomes the first
priority. If quality is Job One, measurement is Job Zero."
Carl Stevens, M.D. (UCLA Medical Center) in the Foreword to Statistical Process Control for Healthcare, Marilyn K. Hart & Robert F. Hart, Brooks Cole, 2001
And it is now agreed that measurement is not merely, as S.S. Stevens mistakenly leads people to believe, the arbitrary assignment of numbers to observations.
William P. Fisher, Jr.
Proper Measurement is Universally Reproducible, Fisher W.P. Jr., Rasch Measurement Transactions, 2004, 18:1 p.967
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