Measurement Theory: Fallacies and Transformations (Nominal, Ordinal, Interval, Ratio)

The Winter 1993 issue of "The Statistical Consultant", published by the Section of Statistical Consulting Education of the American Statistical Association, contains excerpts from an email exchange led by Warren Sarle and Paul Velleman. The discussion started from the notion that data conform to "levels of measurement" based on S.S. Stevens' classification of Nominal, Ordinal, Interval, Ratio. Debate hinged on the extent to which analysis of such data should be controlled by the "permissible transformations" that maintain the mathematical properties of numbers reported on each level. Jack Stenner forwarded a copy of this discussion (provided by Donald Burdick) for comment.

Dear Jack:

Thank you for the copy of "The Statistical Consultant" with its discussion on Measurement Theory. It highlights an essential difference between a Rasch, theory-based approach and the usual statistical, description-based approach.

They argue about the observed "levels" of measurement and "permissible" transformations, as though the data is forced onto us with all its attributes. In nature, all things we observe are nominal. It is we who choose to order (i.e., count) them, in some way according to some theory we propose. A further step is to transform these orderings into linear measures which are more useful to us. If we construct a theory with a useful "zero" location (as opposed to zero difference), then we can measure away from that zero point and so construct a ratio scale. To say that degrees Kelvin are on a ratio scale, but degrees Celsius are not, is fallacious. They are both ratio scales, but with "zeros" defined according to different theories of heat. Frankly, I would like a temperature scale with its zero at room temperature, then "twice as hot", indicating twice as far from room temperature, would be meaningful to me.

Over the course of time, we have developed all types of measurement and counting devices to assist us in summarizing the common features of nominal nature. How these summaries relate to the linear (or ratio) relationships we require for quantitative understanding (in the context of any particular theory) is not initially clear in any situation. How does reaction time function as an indicator of physical condition? Or weight of food relate to overall health?

It is not a matter of identifying permissible transformations of time or weight. First, it is a matter of reordering the observed values so that more "time" or "weight" indicates better condition or health. Then it is a matter of linearizing so that the values provide a basis for inference. As linear measures they may have low precision and poor quality (fit) in the context of our theory, no matter how sophisticated the electronic devices employed in the data collection. Of course, it is Rasch that provides us with the linearizing mechanism.

John Michael Linacre

Measurement theory: fallacies and transformations (Nominal, Ordinal, Interval, Ratio). Linacre JM. … Rasch Measurement Transactions, 1994, 8:1 p.340

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
Rasch Books and Publications: Winsteps and Facets
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	Appliquer le modèle de Rasch: Défis et pistes de solution (Winsteps) E. Dionne, S. Béland
Introduction to Many-Facet Rasch Measurement (Facets), Thomas Eckes	Rasch Models for Solving Measurement Problems (Facets), George Engelhard, Jr. & Jue Wang	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
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

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/rmt81g.htm

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