Editing Guttman scale (section)

== Reproducibility ==
In practice, perfect ("deterministic") Guttman scales are rare, but approximate ones have been found in specific populations with respect to attributes such as religious practices, narrowly defined domains of knowledge, specific skills, and ownership of household appliances.<ref name=":0">{{cite book|title=Theory Construction and Data Analysis in the Behavioral Sciences|last1=Coombs|first1=Clyde|last2=Coombs|first2=Lolagene|last3=Lingoes|first3=James|publisher=San Francisco: Jossey-Bass|isbn=0-87589-379-1|editor-last=Shye|editor-first=Samuel|pages=280–298|chapter=Chapter 11: Stochastic Cumulative Scales|year=1978}}</ref> When data do not conform to a Guttman scale, they may either represent a Guttman scale with noise (and treated stochastically<ref name=":0" />), or they may have a more complex structure requiring multiple scaling for identifying the scales intrinsic to them.

The extent to which a data set conforms to a Guttman scale can be estimated from the coefficient of reproducibility <ref name="Stouffer">Stouffer, S.A., Guttman, L., Suchman, E.A., Lazarsfeld, P.F., Star, S.A., Clausen, J.A. (1950) [https://academic.oup.com/sf/article/29/2/207/2225654 Measurement and Prediction] Princeton University Press</ref><ref name=":1">{{Cite journal|last=Guttman|first=Louis|date=1944|title=A basis for scaling qualitative data|journal=American Sociological Review|volume=9|issue=2|pages=139–150|doi=10.2307/2086306|jstor=2086306}}</ref> of which there are a few versions, depending on statistical assumptions and limitations. Guttman's original definition of the reproducibility coefficient, C<sub>R</sub> is simply 1 minus the ratio of the number of errors to the number of entries in the data set. And, to ensure that there is a range of responses (not the case if all respondents only endorsed one item) the coefficient of scalability is used.<ref name="Menzel">Menzel, H. (1953) A new coefficient for scalogram analysis in Educational and ''Public Opinion Quarterly'' Volume: 15 issue: 2, page(s): 268-280</ref>

In Guttman scaling is found the beginnings of [[item response theory]] which, in contrast to [[classical test theory]], acknowledges that items in [[questionnaires]] do not all have the same level of difficulty. Non-deterministic (i.e., stochastic) models have been developed such as the [[Mokken scale]] and the [[Rasch model]]. Guttman scale has been generalized to the theory and procedures of "multiple scaling" which identifies the minimum number of scales needed for satisfactory reproducibility.

As a procedure that ties substantive contents with logical aspects of data, Guttman scale heralded the advent of facet theory developed by Louis Guttman and his associates.