Measuring and Counting

Every morning I squeeze the orange juice ­ two glassfuls ­ one for Claire ­ one for me. Oranges are very much themselves, each orange an individual in size, color, fragrance, softness. I can count oranges. How many shall I get out of the icebox to fill the two glasses? The trouble is that there is no constant number of oranges that makes a glassful. Sometimes it's only three. Other times it can take six. How on earth can I regularize this procedure?

Well, as I am sure you've already guessed, the solution is embarrassingly simple. The store sells oranges in 4 pound bags. No matter how many oranges it takes, the bag always weighs 4 pounds. Now "a pint's a pound the world around" and an orange is about half juice, by weight. By experiment and/or calculation I establish that 2 pounds of oranges make two glassfuls ­ no more no less. This is always so, no matter how few or how many oranges it takes to weigh the 2 pounds.

The result of this abstract science is that I have a simple, fool-proof, infinitely reproducible, inferentially stable rule: "Take one 4 pound bag of oranges out of the icebox and squeeze half of whatever number of oranges happen to be in it." Two glassfuls are always produced - no matter how many or how few the oranges.

Weighing oranges is vastly superior to counting them ­ perhaps not for art or even literature, but certainly for routinely obtaining a glassful of orange juice. But counting each orange is so immediate, so fulsome, so personal, so individually appreciative, so richly qualitative. While weighing bags of oranges is so impersonal, so meagerly singular, so general, so unappreciative of the true unique, individual nature of each orange, so niggardly quantitative. How dare I reduce the lovely, charming, richly multidimensional orange to a mere cold, stingy weight in lifeless, uncaring pounds ­ what a travesty of nature!

But what a triumph for obtaining a glassful of orange juice every time. You might decry my reduction of the gorgeous orange to such a brutal simplicity as its weight. But you have to admit that for routinizing the production of glassfuls of orange juice you will never in a million years invent an approach that is as simple or as reliable. That's the difference between art and science, between counting right answers and constructing measures.

Ben Wright


Measuring and counting. Wright BD. … Rasch Measurement Transactions, 1994, 8:3 p.371

Please help with Standard Dataset 4: Andrich Rating Scale Model



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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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