Counts or Measures? Which Communicate Best?

"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 Publications
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
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