Scale Types and Stevens' "operational Theory of Measurement"
The theory of scale types is the intellectual handmaiden to Stevens' "operational theory of measurement", which was to become definitive within psychology and the behavioral sciences, despite Michell's characterization as its being quite at odds with measurement in the natural sciences (Michell, 1999). Essentially, the operational theory of measurement was a reaction to the conclusions of a committee established in 1932 by the British Association for the Advancement of Science to investigate the possibility of genuine scientific measurement in the psychological and behavioral sciences. This committee, which became known as the Ferguson committee, published a Final Report (Ferguson, et al., 1940, p. 245) in which Stevens' sone scale (Stevens & Davis, 1938) was an object of criticism:
| “ | …any law purporting to express a quantitative relation between sensation intensity and stimulus intensity is not merely false but is in fact meaningless unless and until a meaning can be given to the concept of addition as applied to sensation. | ” |
That is, if Stevens' sone scale was genuinely measuring the intensity of auditory sensations, then evidence for such sensations as being quantitative attributes must be produced. The evidence needed was the presence of additive structure - a concept comprehensively treated by the German mathematician Otto Hölder (Hölder, 1901). Given the physicist and measurement theorist Norman Robert Campbell dominated the Ferguson committee's deliberations, the committee concluded that measurement in the social sciences was impossible due to the lack of concatenation operations. This conclusion was later rendered false by the discovery of the theory of conjoint measurement by Debreu (1960) and independently by Luce & Tukey (1964). However, Stevens' reaction was not to conduct experiments to test for the presence of additive structure in sensations, but instead to render the conclusions of the Ferguson committee null and void by proposing a new theory of measurement:
| “ | Paraphrasing N.R. Campbell (Final Report, p.340), we may say that measurement, in the broadest sense, is defined as the assignment of numerals to objects and events according to rules (Stevens, 1946, p.677). | ” |
Stevens was greatly influenced by the ideas of another Harvard academic, the Nobel laureate physicist Percy Bridgman (1927), whose doctrine of operationism Stevens used to define measurement. In Stevens' definition for example, it is the use of a tape measure that defines length (the object of measurement) as being measurable (and so by implication quantitative). Critics of operationism object that it confuses the relations between two objects or events for properties of one of those of objects or events (Hardcastle, 1995; Michell, 1999; Moyer, 1981a,b; Rogers, 1989).
The Canadian measurement theorist William Rozeboom (1966) was an early and trenchant critic of Stevens' theory of scale types. But it was not until much later with the work of mathematical psychologists Theodore Alper (1985, 1987), Louis Narens (1981a, b) and R. Duncan Luce (1986, 1987, 2001) did the concept of scale types receive the mathematical rigour that it lacked at its inception. As Luce (1997, p. 395) bluntly stated:
| “ | S.S. Stevens (1946, 1951, 1975) claimed that what counted was having an interval or ratio scale. Subsequent research has given meaning to this assertion, but given his attempts to invoke scale type ideas it is doubtful if he understood it himself…no measurement theorist I know accepts Stevens' broad definition of measurement…in our view, the only sensible meaning for 'rule' is empirically testable laws about the attribute. | ” |
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