Scale
Chapter 1: Context and Concepts

Maps are miniature representations of part of reality. Scale tells us how miniature they are. Scale is commonly expressed as a ratio, in words, or as a bar graph located somewhere in the map frame. A ratio states the scale as a unit of map distance compared with distance on the ground. This is referred to as the representative fraction (RF). Thus an RF of 1:10,000 means that 1 unit of linear measurement on the map represents 10,000 of those units on the ground. Units are interchangeable; for a 1:10,000 map, 1 inch on the map equals 10,000 inches on the ground, 1 centimeter on the map equals 10,000 centimeters on the ground.

Scale terminology can be confusing. For example, large-scale maps and aerial photographs used by local governments (and quite likely to be used by crime analysts) are often at a scale of 1:2,400. If expressed in inches and feet, this is equivalent to 1 inch equaling 200 feet. Hence users often refer to the maps simply as "200 scale."

Large scale or small scale?

The distinction between large scale and small scale is also a source of confusion, but there is a simple rule to help us understand. Look at the representative fraction. If it is a large fraction, the map scale is large, and vice versa. For example, I open my National Geographic Atlas of the World and flip through it until I come to a map of the world. The scale is expressed in words as follows: "Scale 1:66,300,000 at the Equator." This is extremely small scale, as 1/66,300,000th of something is not much. A few pages farther, I come to a map of the upper midwestern States of the United States. Its scale is expressed as "1:2,278,000"-a fraction 29 times larger than that for the world map. As scales get larger and larger, we move from the realm of "maps" to what we customarily refer to as "plans," such as 1:20, where 1 unit on the map (plan) equals 20 units on the ground or the floor plan. These very large-scale renderings are the domain of the architect or engineer rather than the cartographer.

Scale has implications for the interpretation and meaning of maps. Implicit in the concept of scale is the now-familiar tradeoff between abstraction and detail. Small scale implies more abstraction, large scale less. Evidence from cognitive psychology cited by MacEachren (1995) suggests the importance of progressing from small scale to large scale when presenting maps of different areas, the principle of global-local precedence. In other words, if you were to prepare maps for the entire jurisdiction and also for a small part of it, the best mode of presentation would put the smaller scale map (the entire jurisdiction, perhaps in the form of a satellite image) first. The smaller area (larger scale) would follow this.

 Rules of Thumb for Map Scale Small-scale maps show large areas. Large-scale maps show small areas.

Another implication of scale is that crime data will look different at different scales, such as citywide and beat levels. The same data will appear to be more spread out (less dense) at the scale of the beat and more crowded (more dense) at the citywide scale. But in reality densities (crimes per unit area) are the same on both maps. What has changed is scale.

Scale also has implications for data collection. If maps are to be large scale, detailed data collection is appropriate. But small-scale maps are incapable of representing fine detail, so if the only scale available for a specific purpose is small, collecting data at the micro level is pointless. The detail will be lost on a map incapable of showing it. The converse is also true. Gathering data at the ZIP Code level will be too coarse a scale on a map showing street addresses.