# Making Standard Measures

In the course of time metrology has moved from man -the measure (utilizing a foot, hand or digit) to man - the measurer. The goal for measuring was a standard unit with the characteristics of utility, constancy and generality. The evolution of units can be shown with an example of relationships emanating from the digit of one finger. Hence the following:
One digit
Two digits equal a half-hand
Two half-hands equal one hand
Two hands equal a span
Two spans equal a cubit (elbow to the end of the middle finger)
Two cubits equal an arm (chin to extended middle finger)
Two arms equal a fathom, or two full striding steps (including heal to toe): about 5.9 feet
100 steps equal a Greek stade: 528 feet
10 stades equal a Roman mile: 5,280 feet (US)

Hence, we see the evolution from a human attribute, the digit, to an external one, the Greek stadion and Roman mile. (See further Stone, 1997)

Still further transition has occurred. In the endless pursuit for an objective unit, the history of the meter illustrates another evolution. By 1889, the unit meter was defined as the distance between two marks on a particular bar of platinum-iridium kept in a vault in Troyes, France. Local copies served as regional standards. By 1927, 1,553,164.13 wavelengths of red cadmium defined the standard meter, and by 1960 it was 1,650,763.73 vacuum wave-lengths of orange radiation under specific conditions using Krypton mass 86. Uncertainty was reduced from one in five million to one in 100 million. But even more useful was the fact that this standard could be constructed locally. There was no need to make copies. Anyone following the exact specifications could produce their own standard unit. The convenience of portability-of-unit no longer required a specified haven in which the unit need reside. The unit can be produced anywhere. Whereas the meter bar initially required a detailed copy, the new unit could now be produced upon demand by simply reproducing its specifications.

The history of man is a history of measuring. Successful measuring requires standard units. These units were first bound to a specific human one, a kingly arm or foot. Kingly units provided standards, but these units often required extraordinary influence for them to be implemented. The Julian calendar and the Gregorian are not simply calendars named after individuals; their implementation required the absolute power of position (a Caesar or Pope) to produce a standard or a change.

The implementation of the metric system illustrates the historically slow transition to new units. Napoleon was able to implement the metric system in France only by imposing the threat of death! Nor were the English going to follow the dictates of the French! Representatives from England attending the discussions in France concerning metric units quickly returned home. England retained its own units and America followed. In the USA we find ourselves caught between the two systems. Consequently, a garage mechanic is required to own two sets of wrenches, one in English units and one in metric, in order to work.

A more recent example of the consequences of using two measurement units was reported in the newspapers. Both metric and English values were found to exist in the flight plans of the Mars Climate Orbiter. One team used English units, the other metric. This resulted in miscommunication at the measurement level, and then disaster.

The transition from arbitrary human units to arbitrary conceptual ones has been a long and rocky road. The story is not over. In a sense it will never be completed. We construct measures, but we must also monitor the measuring process. To make accurate measures we require a unit whose own error is under control. In this sense, the history of science can be said to be a history of measurement precision.

Standardization is a hallmark of science. When we speak of objectivity in science we are addressing standardization. Communication requires objectivity in order to accurately exchange information. Portability is essential to this enterprise. The unit must be accessible to everyone or it lacks generality. In portability we achieve abstraction. The unit as a natural phenomenon has been replaced by an idea, an abstraction. This development increases the utility of making measures. No longer does the unit reside in the dimensions of a potentate; it can exist anywhere we desire. But measures can be compromised whenever we relax our attention. Constant monitoring is necessary and a quality control procedure is required.

Science pursues questions and the answers are derived from theory and data. Knowledge is constructed by bringing together theory and data in meaningful ways. Measurement in the sciences requires units that possess utility and portability if communication is to be achieved. Rasch models and their accompanying measurement strategies support this pursuit. The widening application of Rasch measurement to more and problems in the sciences furthers the goal of increasing knowledge by producing standard units with utility and portability.

Mark Stone, Adler School of Professional Psychology

Stone, M. (1997). Man the measure - the measurer. Journal of Outcome Measurement, 2, (1), 25-32.

Making Standard Measures. Stone M. … Rasch Measurement Transactions, 2001, 15:1 p.792-3

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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