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.
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 Measurement Transactions (free, online)||Rasch Measurement research papers (free, online)||Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch||Applying the Rasch Model 3rd. Ed., Bond & Fox||Best Test Design, Wright & Stone|
|Rating Scale Analysis, Wright & Masters||Introduction to Rasch Measurement, E. Smith & R. Smith||Introduction to Many-Facet Rasch Measurement, Thomas Eckes||Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr.||Statistical Analyses for Language Testers, Rita Green|
|Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar||Journal of Applied Measurement||Rasch models for measurement, David Andrich||Constructing Measures, Mark Wilson||Rasch Analysis in the Human Sciences, Boone, Stave, Yale|
|in Spanish:||Análisis de Rasch para todos, Agustín Tristán||Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez|
|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.
|Coming Rasch-related Events|
|March 21, 2019, Thur.||13th annual meeting of the UK Rasch user group, Cambridge, UK, http://www.cambridgeassessment.org.uk/events/uk-rasch-user-group-2019|
|April 4 - 8, 2019, Thur.-Mon.||NCME annual meeting, Toronto, Canada,https://ncme.connectedcommunity.org/meetings/annual|
|April 5 - 9, 2019, Fri.-Tue.||AERA annual meeting, Toronto, Canada,www.aera.net/Events-Meetings/Annual-Meeting|
|April 12, 2019, Fri.||On-line course: Understanding Rasch Measurement Theory - Master's Level (G. Masters), https://www.acer.org/au/professional-learning/postgraduate/rasch|
|July 2-5, 2019, Tue.-Fri.||2019 International Measurement Confederation (IMEKO) Joint Symposium, St. Petersburg, Russia,https://imeko19-spb.org|
|July 11-12 & 15-19, 2019, Thu.-Fri.||A Course in Rasch Measurement Theory (D.Andrich), University of Western Australia, Perth, Australia, flyer - http://www.education.uwa.edu.au/ppl/courses|
|Aug 5 - 10, 2019, Mon.-Sat.||6th International Summer School "Applied Psychometrics in Psychology and Education", Institute of Education at HSE University Moscow, Russia.https://ioe.hse.ru/en/announcements/248134963.html|
|Aug. 9 - Sept. 6, 2019, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Aug. 14 - 16, 2019. Wed.-Fri.||An Introduction to Rasch Measurement: Theory and Applications (workshop led by Richard M. Smith) https://www.hkr.se/pmhealth2019rs|
|August 25-30, 2019, Sun.-Fri.||Pacific Rim Objective Measurement Society (PROMS) 2019, Surabaya, Indonesia https://proms.promsociety.org/2019/|
|Oct. 11 - Nov. 8, 2019, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|Nov. 3 - Nov. 4, 2019, Sun.-Mon.||International Outcome Measurement Conference, Chicago, IL,http://jampress.org/iomc2019.htm|
|Jan. 24 - Feb. 21, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|May 22 - June 19, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 26 - July 24, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
|Aug. 7 - Sept. 4, 2020, Fri.-Fri.||On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com|
|Oct. 9 - Nov. 6, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|June 25 - July 23, 2021, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com|
The URL of this page is www.rasch.org/rmt/rmt81g.htm