Scale-Free Measurement Revisited

The value of universal physical measures:
Until Newton noticed that Galileo's law of falling bodies applies to pendulum motion, the length of an hour varied by the seasons and by geographical latitude. Newton's work and advances in astronomy led to improved clockworks, standardizing the length of an hour, and making navigation across open seas far more accurate. Similarly, until the metric system's emergence from the French Revolution and Napoleon's subsequent desire to unify an empire, units of weight and measure in Europe varied dramatically from region to region and even from town to town. The metric system is now the standard measurement system for every country in the world but two.

Virtually every aspect of contemporary life is affected by our capacity to measure time, length, weight, volume, mass, temperature, etc., in commonly accepted and universal units. Science and the global economy are hardly conceivable without them.

Why no universal social science measures?
The crucial difference between the instruments that measure physical variables and those that measure human abilities and attitudes is usually expressed in terms of additivity and unidimensionality. But additive conjoint measurement models surmount that difference. So what barriers remain in the path of truly scientific social science measurement?

The primary barrier is indifference. It hinges on an insufficient appreciation for the possibilities offered by scale-free measurement technologies. Social scientists tolerate pre-scientific "measurement." In a manner akin to the way that the length of an hour varied by the seasons or by geographic location, the size and meaning of ability and attitude units vary not only by uncontrolled dependencies on who is measured, who is measuring, where the measuring is done, etc., but on the brand-name of the instrument used. Even when high quality measuring systems are developed using additive conjoint measurement models, instruments designed to measure the same thing do so in different units, and there is no obvious scheme for converting from one to the other.

Universal measurement possible and economical:
Application of well tested and widely applied item banking principles, however, leads to the notion of co-calibration, the derivation of a common unit of measurement for any number of instruments that can be shown to measure the same thing. The field of physical medicine and rehabilitation, for instance, has many instruments for measuring motor skills, which are typically a combination of mobility and activity of daily living skills. My study of two of these instruments has shown that they do measure the same thing, and that they can be easily co- calibrated to measure in the same unit.

The cost of arranging this situation is minuscule compared to the costs involved in the miscommunications of measurement results, which, in medicine, for instance, can lead to tragic misdiagnosis and mistreatment (as was pointed out by Michael Millenson in his recent series on medical accountability in the Chicago Tribune).

The implications of common units of measurement for the study and understanding of abilities and attitudes could be profound: does anyone have any estimate of the costs associated with our current Tower of Babel? Our hodgepodge of measuring units makes the comparison of research results needlessly complex, leads to the mistaken notion that a nationwide testing program is necessary for comparability of measures, and completely cuts off investigation of many important aspects of human variation short of being willing to mount a large and expensive study of one's own.

Mounting pressure for useful measures:
The future of Rasch measurement is probably going to depend less on its theoretical qualities than on the practical advantages it offers those who have to use measures of ability and attitude to manage their affairs. And measurement is receiving considerable attention in the work of leaders in the current philosophy of business management:

"The central problem of management in all its aspects ... is to understand better the meaning of variation, and to extract the information contained in variation."
W. Edwards Deming, Out of the Crisis, p. 20

"Measure what's important to the business.... Our systems are too complex.... Further, they fail to measure most of what's important to success today. Simple, visible measures of what's important should mark every square foot of every department in every operation."
Tom Peters, Thriving on Chaos, p. 482

"The winners' measures will emphasize the vital performance parameters - e.g., quality, service, flexibility, responsiveness, and employee skills/capabilities. True control stems from a very few, simple measures of high integrity, understood by all."
Tom Peters, Thriving on Chaos, p. 394

We typically expect commerce, not academia, to demand practical solutions to problems that theoreticians will nitpick and polish for decades. Business peoples' new interest in simple and tightly focused measurement will lead to demands for incisive breakthroughs and pragmatic applications. The Rasch measurement community is well-positioned to meet these demands. Rasch's separability theorem gives the relevant way to speak of consistent variation of items across persons and vice versa.

The establishment of something like a National Bureau of Standards for social science measures will probably be a long, drawn out, and highly politicized affair. But we prepare the ground for acceptance of its mission with every scale we calibrate, since this activity educates users in what can be demanded and achieved in measurement science, and since calibrated scales are by definition much easier to co-calibrate. But even out scales remain unscientific to the extent that our measures remain tied to our instruments, even if every individual instrument is Rasch-calibrated.

Scale-free means universal, not perfect:
The term "scale-free" does not imply errorless, perfectly reliable measurement. Scale-free denotes measurement that transcends the particulars of the situation in which measurement occurred and the brand-name of the instrument that was used. This type of measurement identifies and separates a well-defined, universally understood quantity from all the myriad details in and around the object of measurement and the measuring instrument. Only when social science measurement is scale-free will a truly scientific language of abilities and attitudes be born.

Fisher WP Jr. (1993) Scale-Free Measurement Revisited. Rasch Measurement Transactions, 7:1, p. 272-3.


Scale-free measurement revisited. Fisher WP Jr. … Rasch Measurement Transactions, 1993, 7:1 p.272

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
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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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