Scales of Measurement

Any set of geographic information can be disassembled into a collection of observations. In almost any case, these observations follow the rules of a particular measurement scheme. A scale of measurement is a way to document such rules. The archetype of a measurement scale has a fixed zero and an established unit of measure, but not all geographic information conforms to this format. This entry discusses taxonomies of measurement, particularly a system of “levels” of measurement in an ordered hierarchy, with the labels nominal, ordinal, interval, and ratio, that has become a common element of instruction in cartography, geography, and many of the social sciences. Some attention to measurement is critical to understanding the utility and limitations of geographic data.

Measurement is an old technology. The traces of ancient measurement can be found in preliterate society in the form of knotted ropes to count sheep or days in a lunar cycle. In medieval markets, measures of volume were instituted by creating a hollow in a surface in the market square. Grain was poured into this space and thus measured—in other words, its quantity was turned into a number that represents the ratio between the standard volume and the quantity of grain to be sold. One of the earliest functions of a centralized government was to promote trade by ensuring a common set of weights and measures. The king's foot set a standard for linear measurement. For convenience, copies were made so the king could tend to other business. In the modern world, measurement is increasingly prevalent and to some extent so routine that it passes without much notice.

Rules of measurement apply to all aspects of geographic information science. The geometric rules that deal with location have specific requirements to relate to the surface of the earth. The description of the earth's shape has created a scientific enterprise called geodesy, which goes back for centuries and has come to a high degree of sophistication with recent advances in measurement equipment. Coupled with some rules of geometry, geodetic measurements are organized into spatial reference systems, a distinct topic in this volume. Consequently, this entry concentrates on the wide diversity of measurements applied to all other geographic data, the so-called attributes attached to spatial objects.

A straightforward example of standardizing a measurement scale involves mass, a property of an object that does not change from place to place. The international standard scale (SI) for mass produces a number, the ratio of the object to a specific tangible object, the international kilogram. This metal cylinder is kept [Page 381]under highly controlled conditions in Sevres, France, with copies spread around the world. It is impractical to go to Sevres to weigh your purchase of meat, so a whole set of practices are maintained to ensure that the measurement devices in the store are calibrated against a sufficiently reliable standard. In some countries, there are other mass scales in common usage, including pounds or ounces. One is no more correct than another, and there are conversion factors that allow exchange between the two scales.

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