Is Error Fatal to Interval Measurement?

Norman Cliff: "One is dubious that any convincing evidence exists, such as provided by conjoint measurement, that would allow the equating of intervals along the [raw] score variable. Either it is treated ordinally, or as a pro forma interval scale. There exist, of course, models that attempt to convert the ordinal test data provided by test items into some more strictly defined scale (e.g., Birnbaum, 1968; Lord & Novick, 1968; Rasch, 1966), but the evidence that supports the interval-scale status of the derived variables is not compelling because of the amount of error involved." (1993, p.87)

Cliff here takes the position that interval-scaling must be proved empirically, which was Norman Campbell's argument as to why fundamental measurement can't exist in the social sciences, summarized as "you can't concatenate heads." But Cliff makes the point with physical measurement (p. 62) that "measuring length is much more effectively and efficiently done if it is embedded in a larger system, in this instance the science of geometry." For social science measurement, the larger system is algebra. With algebra, it is easy to demonstrate that, however error-ridden the empirical data and however great the error in the resultant measures, there is only one method of transforming ordinal data that accords with conjoint measurement and so can possibly produce interval scales, the Rasch model.

Once the hurdle of interval scaling is overcome, social science can then advance in the same way as has physical science. "What is clear about physical measurement is its intimate entanglement with the science itself. Somehow, someone hits upon a way of taking observations that results in regular relations of a quantifiable sort. Someone else finds a way of making observations that are highly correlated with the first sort, but whose relations are even more precise. It is thus that empirical variables are defined operationally and theoretical variables are born" (p. 63).

John Michael Linacre

Cliff, N. (1993) What is and isn't measurement. In G. Keren & C. Lewis (Eds.), A Handbook for Data Analysis in the Behavioral Sciences: Methodological Issues. Hillsdale, NJ: Lawrence Erlbaum Assoc.

Is Error Fatal to Interval Measurement? Cliff, N. … Rasch Measurement Transactions, 1999, 13:3 p. 702

Rasch Books and Publications
Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, 2nd Edn. George Engelhard, Jr. & Jue Wang	Applying the Rasch Model (Winsteps, Facets) 4th Ed., Bond, Yan, Heene	Advances in Rasch Analyses in the Human Sciences (Winsteps, Facets) 1st Ed., Boone, Staver	Advances in Applications of Rasch Measurement in Science Education, X. Liu & W. J. Boone	Rasch Analysis in the Human Sciences (Winsteps) Boone, Staver, Yale
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	Statistical Analyses for Language Testers (Facets), Rita Green	Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments (Facets), George Engelhard, Jr. & Stefanie Wind	Aplicação do Modelo de Rasch (Português), de Bond, Trevor G., Fox, Christine M	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Exploring Rating Scale Functioning for Survey Research (R, Facets), Stefanie Wind	Rasch Measurement: Applications, Khine	Winsteps Tutorials - free Facets Tutorials - free	Many-Facet Rasch Measurement (Facets) - free, J.M. Linacre	Fairness, Justice and Language Assessment (Winsteps, Facets), McNamara, Knoch, Fan
Other Rasch-Related Resources: Rasch Measurement YouTube Channel
Rasch Measurement Transactions & Rasch Measurement research papers - free	An Introduction to the Rasch Model with Examples in R (eRm, etc.), Debelak, Strobl, Zeigenfuse	Rasch Measurement Theory Analysis in R, Wind, Hua	Applying the Rasch Model in Social Sciences Using R, Lamprianou	El modelo métrico de Rasch: Fundamentación, implementación e interpretación de la medida en ciencias sociales (Spanish Edition), Manuel González-Montesinos M.
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar	Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch	Rasch Models for Measurement, David Andrich	Constructing Measures, Mark Wilson	Best Test Design - free, Wright & Stone Rating Scale Analysis - free, Wright & Masters
Virtual Standard Setting: Setting Cut Scores, Charalambos Kollias	Diseño de Mejores Pruebas - free, Spanish Best Test Design	A Course in Rasch Measurement Theory, Andrich, Marais	Rasch Models in Health, Christensen, Kreiner, Mesba	Multivariate and Mixture Distribution Rasch Models, von Davier, Carstensen

Forum

Rasch Measurement Forum to discuss any Rasch-related topic

Go to Top of Page
Go to index of all Rasch Measurement Transactions
AERA members: Join the Rasch Measurement SIG and receive the printed version of RMT
Some back issues of RMT are available as bound volumes
Subscribe to Journal of Applied Measurement

Go to Institute for Objective Measurement Home Page. The Rasch Measurement SIG (AERA) thanks the Institute for Objective Measurement for inviting the publication of Rasch Measurement Transactions on the Institute's website, www.rasch.org.

The URL of this page is www.rasch.org/rmt/rmt133f.htm

Website: www.rasch.org/rmt/contents.htm