Attribute has become the preferred term for any recorded characteristic or property of a place (see Table 1‑2 for a more formal definition). A place’s name is an obvious example of an attribute, but a vast array of other options has proven useful for various purposes. Some are measured, including elevation, temperature, or rainfall. Others are the result of classification, including soil type, land-use or land cover type, or rock type. Government agencies provide a host of attributes in the form of statistics, for places ranging in size from countries all the way down to neighbourhoods and streets. The characteristics that people assign rightly or mistakenly to places, such as “expensive”, “exciting”, “smelly”, or “dangerous” are also examples of attributes. Attributes can be more than simple values or terms, and today it is possible to construct information systems that contain entire collections of images as attributes of hotels, or recordings of birdsong as attributes of natural areas. But while these are certainly feasible, they are beyond the bounds of most techniques of spatial analysis.

Many terms have been adopted to describe attributes. From the perspective of spatial analysis the most useful divides attributes as follows:

·         Nominal. An attribute is nominal if it successfully distinguishes between locations, but without any implied ranking or potential for arithmetic. For example, a telephone number can be a useful attribute of a place, but the number itself generally has no numeric meaning. It would make no sense to add or divide telephone numbers, and there is no sense in which the number 9680244 is more or better than the number 8938049. Likewise, assigning arbitrary numerical values to classes of land type, e.g. 1=arable, 2=woodland, 3=marsh, 4=other is simply a convenient form of naming (the values are nominal)

·         Ordinal. An attribute is ordinal if it implies a ranking, in the sense that Class 1 may be better than Class 2, but as with nominal attributes no arithmetic operations make sense, and there is no implication that Class 3 is worse than Class 2 by the precise amount by which Class 2 is worse than Class 1. An example of an ordinal scale might be preferred locations for residences — an individual may prefer some areas of a city to others, but such differences between areas may be barely noticeable or quite profound

·         Interval. The remaining three types of attributes are all quantitative, representing various types of measurements. Attributes are interval if differences make sense, as they do for example with measurements of temperature on the Celsius or Fahrenheit scales, or for measurements of elevation above sea level

·         Ratio. Attributes are ratio if it makes sense to divide one measurement by another. For example, it makes sense to say that one person weighs twice as much as another person, but it makes no sense to say that a temperature of 20 Celsius is twice as warm as a temperature of 10 Celsius, because while weight has an absolute zero Celsius temperature does not (but on an absolute scale of temperature, such as the Kelvin scale, 200 degrees can indeed be said to be twice as warm as 100 degrees). It follows that negative values cannot exist on a ratio scale

·         Cyclic. Finally, it is not uncommon to encounter measurements of attributes that represent directions or cyclic phenomena, and to encounter the awkward property that two distinct points on the scale can be equal — for example, 0 and 360 degrees are equal. Directional data are cyclic, as are calendar dates. Arithmetic operations are problematic with cyclic data, and special techniques are needed, such as the techniques used to overcome the Y2K problem, when the year after (19)99 was (20)00. For example, it makes no sense to average 1° and 359° to get 180°, since the average of two directions close to north clearly is not south. Mardia and Jupp (1999) provide a comprehensive review of the analysis of directional or cyclic data

While this terminology of measurement types is standard, spatial analysts find that another distinction is particularly important. This is the distinction between attributes that are termed spatially intensive and spatially extensive. Spatially extensive attributes include total population, measures of a place’s area or perimeter length, and total income — they are true only of the place as a whole. Spatially intensive attributes include population density, average income, and percent unemployed, and if the place is homogeneous they will be true of any part of the place as well as of the whole. For many purposes it is necessary to keep spatially intensive and spatially extensive attributes apart, because they respond very differently when places are merged or split, and when many types of spatial analysis are conducted.