Editing Psychometrics (section)

== Definition of measurement in the social sciences ==
The definition of measurement in the social sciences has a long history. A current widespread definition, proposed by [[Stanley Smith Stevens]], is that measurement is "the assignment of numerals to objects or events according to some rule." This definition was introduced in a 1946 ''[[Science (journal)|Science]]'' article in which Stevens proposed four [[levels of measurement]].<ref name="Stevens 1946">{{cite journal|last=Stevens|first=S. S.|author-link=Stanley Smith Stevens|date=7 June 1946|title=On the Theory of Scales of Measurement|journal=[[Science (journal)|Science]]|volume=103|issue=2684|pages=677–680|bibcode=1946Sci...103..677S|doi=10.1126/science.103.2684.677|pmid=17750512|s2cid=4667599}}</ref> Although widely adopted, this definition differs in important respects from the more classical definition of measurement adopted in the physical sciences, namely that scientific measurement entails "the estimation or discovery of the ratio of some magnitude of a quantitative attribute to a unit of the same attribute" (p.&nbsp;358)<ref>{{cite journal|last1=Michell|first1=Joel|title=Quantitative science and the definition of measurement in psychology|journal=British Journal of Psychology|date=August 1997|volume=88|issue=3|pages=355–383|doi=10.1111/j.2044-8295.1997.tb02641.x}}</ref>

Indeed, Stevens's definition of measurement was put forward in response to the British Ferguson Committee, whose chair, A. Ferguson, was a physicist. The committee was appointed in 1932 by the British Association for the Advancement of Science to investigate the possibility of quantitatively estimating sensory events. Although its chair and other members were physicists, the committee also included several psychologists. The committee's report highlighted the importance of the definition of measurement. While Stevens's response was to propose a new definition, which has had considerable influence in the field, this was by no means the only response to the report. Another, notably different, response was to accept the classical definition, as reflected in the following statement:

:Measurement in psychology and physics are in no sense different. Physicists can measure when they can find the operations by which they may meet the necessary criteria; psychologists have to do the same. They need not worry about the mysterious differences between the meaning of measurement in the two sciences (Reese, 1943, p. 49).<ref>Reese, T.W. (1943). The application of the theory of physical measurement to the measurement of psychological magnitudes, with three experimental examples. ''Psychological Monographs, 55'', 1–89. {{doi|10.1037/h0061367}}</ref>

These divergent responses are reflected in alternative approaches to measurement. For example, methods based on [[covariance matrix|covariance matrices]] are typically employed on the premise that numbers, such as raw scores derived from assessments, are measurements. Such approaches implicitly entail Stevens's definition of measurement, which requires only that numbers are ''assigned'' according to some rule. The main research task, then, is generally considered to be the discovery of associations between scores, and of factors posited to underlie such associations.<ref>{{Cite web|url=http://www.assessmentpsychology.com/psychometrics.htm|title=Psychometrics|website=Assessmentpsychology.com|access-date=28 June 2022}}</ref>

On the other hand, when measurement models such as the [[Rasch model]] are employed, numbers are not assigned based on a rule. Instead, in keeping with Reese's statement above, specific criteria for measurement are stated, and the goal is to construct procedures or operations that provide data that meet the relevant criteria. Measurements are estimated based on the models, and tests are conducted to ascertain whether the relevant criteria have been met.{{citation needed|date=March 2015}}