One might wonder how civilization ever arrived at the efficient and reliable abstraction we call "weight" -- measured out, for instance, in ounces? We could not get along without this lovely abstraction. Not only physics and engineering, but also commerce would collapse. But where did the measurement of weight come from? How did it develop?
We cannot trace its full history, because most of it was never recorded. But we can reenact, right now, an experiment which shows the irresistible connection between the simplest possible comparisons and measured weight. Merely compare two objects for their heft by holding one in each hand. Record which one feels heavier. Nothing more. A psychometric construction, built from a set of these simplest of all observations, produces a linear equivalent to "objective" weight.
Ellie Choi poured different amounts of rice into 10 paper cups, sealed the cups, and labeled them "A" through "J" in random order. Then she asked each of 13 students she encountered to take pairs of cups, one in each hand, and tell her which cup felt heavier. 10 cups produce 45 pairings per student. Her experiment produced 580 independent paired comparisons with the heavier-feeling cup scored "1", each time, and the lighter-feeling cup scored "0". After Ellie had collected these data, she weighed each cup on a postal meter to determine its "official" weight in ounces.
When the simple dichotomous paired comparisons were analyzed using Facets, Ellie found that the Rasch calibrations of the 10 cups formed a statistically linear relation with their weight in ounces. Her picture of this relationship is shown.
The implications of Ellie's experiment for the history of measurement is that the linear abstraction of "weight" was resident in our simplest comparison judgements from the beginning. All we had to do over the centuries was to find out, step-by-step, how to make the implications of our simplest comparisons into objective and reproducible measures.
Choi, Sungeon "Ellie" (1995) Using Paired Comparisons to Determine Weight Perception. Unpublished paper. University of Chicago.
Rasch Invents "Ounces". Choi S. E. Rasch Measurement Transactions, 1997, 11:2 p. 557.
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