Spatial Thinking in Planning Practice: An Introduction to GIS

10 Ordinal datasets establish rank order. In the race, the order they !nished (i.e. 1st, 2nd, and 3rd place) are mea- sured on an ordinal scale (second column in Figure 2.5). While order is known, how much better one runner is than the other is not. "e ranks ‘high’, ‘medium’, and ‘low’ are also ordinal. So while we know the rank order, we do not know the interval. Usually both numeric and character ordinal data are coded with characters because ordinal data cannot be added, subtracted, multiplied, or divided in a meaningful way. "e middle value, the “median”, in a string of ordinal values, however, is a good substitute for a mean (average) value. Examples of ordinal data o$en seen on reference maps include political boundaries that are classi!ed hierarchi- cally (national, state, county, etc.) and transportation routes (primary highway, secondary highway, light-duty road, unimproved road). Ordinal data measured by the Census Bureau include how well individuals speak En- glish (very well, well, not well, not at all), and level of educational attainment (high school graduate, some college no degree, etc.). Social surveys of preferences and perceptions are also usually scaled ordinally. Individual observations measured at the ordinal level are not numerical, thus should not be added, subtracted, multiplied, or divided. For example, suppose two 600-acre grid cells within your county are being evaluated as potential sites for a hazardous waste dump. Say the two areas are evaluated on three suitability criteria, each ranked on a 0 to 3 ordinal scale, such that 0 = completely unsuitable, 1 = marginally unsuitable, 2 = marginally suitable, and 3 = suitable. Now say Area A is ranked 0, 3, and 3 on the three criteria, while Area B is ranked 2, 2, and 2. If the Siting Commission was to simply add the three criteria, the two areas would seem equally suitable (0 + 3 + 3 = 6 = 2 + 2 + 2), even though a ranking of 0 on one criteria ought to disqualify Area A. "e Interval scale, like we will discuss with ratio data, pertains only to numbers; there is no use of character data. With interval data the di#erence—the “interval”—between numbers is meaningful. Interval data, unlike ratio data, however, do not have a starting point at a true zero. "us, while interval numbers can be added and subtracted, division and multiplication do not make mathematical sense. In the marathon race, the time of the day each runner !nished is measured on an interval scale. If the runners !nished at 10:10 a.m., 10:20 a.m. and 10:25 a.m., then the !rst runner !nished 10 minutes before the second runner and the di#erence between the !rst two runners is twice that of the di#erence between the second and third place runners (see third column 3 Figure 2.5). "e runner !nishing at 10:10 a.m., however, did not !nish twice as fast as the runner !nishing at 20:20 (8:20 p.m.) did. A good non-race example is temperature. It makes sense to say that 20° C is 10° warmer than 10° C. Celsius temperatures (like Fahrenheit) are measured as interval data, but 20° C is not twice as warm as 10° C because 0° C is not the lack of temperature, it is an arbitrary point that conveys when water freezes. Re- turning to phone numbers, it does not make sense to say that 968-0244 is 62195 more than 961-8049, so they are not interval values. Ratio is similar to interval. "e di#erence is that ratio values have an absolute or natural zero point. In our race, the !rst place runner !nished in a time of 2 hours and 30 minutes, the second place runner in a time of 2 hours and 40 minutes, and the 450th place runner took 10 hours. "e 450th place !nisher took over !ve times longer than the !rst place runner did. With ratio data, it makes sense to say that a 100 lb woman weighs half as much as a 200 lb man, so weight in pounds is ratio. "e zero point of weight is absolute. Addition, subtraction, multipli- cation, and division of ratio values make statistical sense. "e main reason that it’s important to recognize levels of measurement is that di#erent analytical operations are possible with data at di#erent levels of measurement (Chrisman 2002). Some of the most common operations include: % Group: Categories of nominal and ordinal data can be grouped into fewer categories. For instance, group- ing can be used to reduce the number of land use/land cover classes from, for instance, four (residential, commercial, industrial, parks) to one (urban). Chapter 1: De!ning a Geographic Information System