Editing Level of measurement (section)

=== Scale types and Stevens's "operational theory of measurement" ===
The theory of scale types is the intellectual handmaiden to Stevens's "operational theory of measurement", which was to become definitive within psychology and the [[behavioral sciences]],{{citation needed|date=July 2012}} 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.&nbsp;245) in which Stevens's [[sone]] scale (Stevens & Davis, 1938) was an object of criticism:

{{blockquote | …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's ''[[sone]]'' scale genuinely measured the intensity of auditory sensations, then evidence for such sensations as being quantitative attributes needed to be produced. The evidence needed was the presence of ''additive structure''—a concept comprehensively treated by the German mathematician [[Otto Hölder]] (Hölder, 1901). Given that 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 (mathematics)|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's 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:

{{blockquote|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,<ref>[[Percy Bridgman]] (1957) ''[[The Logic of Modern Physics]]''</ref> the [[Nobel Prize|Nobel laureate]] physicist [[Percy Bridgman]] (1927), whose doctrine of [[operationalism]] Stevens used to define measurement. In Stevens's 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 operationalism object that it confuses the relations between two objects or events for properties of one of those of objects or events (Moyer, 1981a, b; Rogers, 1989).<ref>{{cite journal | last1 = Hardcastle | first1 = G. L. | year = 1995 | title = S. S. Stevens and the origins of operationism | journal = Philosophy of Science | volume = 62 | issue = 3| pages = 404–424 | doi=10.1086/289875| s2cid = 170941474 }}</ref><ref> Michell, J. (1999). ''Measurement in Psychology &ndash; A critical history of a methodological concept''. Cambridge: Cambridge University Press.</ref>

The Canadian measurement theorist William Rozeboom was an early and trenchant critic of Stevens's theory of scale types.<ref>{{cite journal | last1 = Rozeboom | first1 = W. W. | year = 1966 | title = Scaling theory and the nature of measurement | journal = Synthese | volume = 16 | issue = 2| pages = 170–233 | doi=10.1007/bf00485356| s2cid = 46970420 }}</ref>

==== Same variable may be different scale type depending on context ====
Another issue is that the same variable may be a different scale type depending on how it is measured and on the goals of the analysis. For example, hair color is usually thought of as a nominal variable, since it has no apparent ordering.<ref>{{cite web|url=http://www.ats.ucla.edu/stat/mult_pkg/whatstat/nominal_ordinal_interval.htm|title=What is the difference between categorical, ordinal and interval variables?|work=Institute for Digital Research and Education|publisher=University of California, Los Angeles|archive-url=https://web.archive.org/web/20160125165359/http://www.ats.ucla.edu/stat/mult_pkg/whatstat/nominal_ordinal_interval.htm|access-date=7 February 2016|archive-date=2016-01-25}}</ref> However, it is possible to order colors (including hair colors) in various ways, including by hue; this is known as [[colorimetry]]. Hue is an interval level variable.