"Sijtsma and Hemker (2000) extensively discussed the practical usefulness of [the test score] as opposed to the theoretical
usefulness of [the ability measure].... They argue that [the test score] is better suited than [the ability measure] for
communicating test results to measurement practitioners and laymen, because [the test score] has an interpretation closely
related to solving problems correct or incorrect (dichotomous items) or the number of points earned (polytomous items),
whereas [the ability measure] has a complicated interpretation in terms of logits. .... For test practitioners [the total score] is
quick and simple, and allows immediate feedback to testees."
(Hemker et al. 2000. Italics authors'.)
Which is more meaningful? A test score of "16 out of 20"? Or an ability measure of 2.37 logits? Expressed this way, the test score!
The first step to comprehensibility is simple. Match the numbering of the linear measures to the numbering of the non-linear raw scores in a convenient manner. For instance, their operational range could be aligned. Then "16 out of 20" raw scores could become "15 out 20" units. Or match the central slope of the raw score ogive. Then, from about 5 to 15 the raw scores and the measures will have the same numbers, but they will diverge at the extremes.
More useful, however, is to linearly transform the logits onto a meaningful scale of "Academic Achievement Units" where, say, 0 = entry into 1st Grade and 1000 = admission to College. Now 2.37 logits becomes, say, 673 AAU. Immediately test practitioners, teachers, parents and students know accurately where the student stands; how much the student has advanced; how much is yet to go; and the difficulty level of the material to teach next. The total score gives us none of this.
Experiments with pilot whales have shown that teaching too slowly is boring and the whales stop learning. Is it the same with our children? Is school "boring" because we teach too slowly? Do we teach too slowly because we want our children to attain perfect raw scores (i.e., experience over-learned easy tests), rather than experience maximal increase in ability (i.e., experience challenging targeted tests)?
Benjamin D. Wright
Hemker B.T., van der Ark L.A., Sijtsma K. (2000) On Measurement Properties of Continuation Ratio Models. Measurement and Research Department Reports 2000-6. Arnhem, the Netherlands: Citogroep. p. 12-13.
Sijtsma, K., & Hemker, B.T. (2000). A taxonomy for ordering persons and items using simple sum scores. Journal of Educational and Behavioral Statistics, 25, 391-415.
Wright B.D. (2001) Counts or Measures? Which Communicate Best? Rasch Measurement Transactions 14:4 p.784
Counts or Measures? Which Communicate Best? Wright B.D. Rasch Measurement Transactions, 2001, 14:4 p.784
|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|
|Jan. 30-31, 2020, Thu.-Fri.||A Course on Rasch Measurement Theory - Part 1, Sydney, Australia, course flyer|
|Feb. 3-7, 2020, Mon.-Fri.||A Course on Rasch Measurement Theory - Part 2, Sydney, Australia, course flyer|
|Jan. 24 - Feb. 21, 2020, Fri.-Fri.||On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com|
|Apr. 14-17, 2020, Tue.-Fri.||International Objective Measurement Workshop (IOMW), University of California, Berkeley, https://www.iomw.org/|
|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|
|June 29 - July 1, 2020, Mon.-Wed.||Measurement at the Crossroads 2020, Milan, Italy , https://convegni.unicatt.it/mac-home|
|July 1 - July 3, 2020, Wed.-Fri.||International Measurement Confederation (IMEKO) Joint Symposium, Warsaw, Poland, http://www.imeko-warsaw-2020.org/|
|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/rmt144g.htm