Analysis of GIS Data by Simple Examination - Introducing Geographic Information Systems with ArcGIS - page 361

Putting Values into Classes
Another way of reducing a large group of numbers to a more manageable size is to put similar values
into classes or categories. For example, we might have the data on real estate parcel sizes. We could
put each parcel into one of several categories: (1) greater than 10 acres, (2) 10 acres to 5 acres, (3) 5 acres
to 1 acre, and less than 1 acre. In the Step-by-Step section of this chapter, you will do an exercise on
classification of values.

Measurement Scales
When you see a number, its context determines how you interpret that number and how you may use
it in computation and comparison. A number that represents some description or measurement of
something in the real world will fall into one of four categories:

Nominal—A nominal data set is just a set of names, except the names take the form of numbers. If
in a teaching laboratory you randomly assign numbers to test tubes (say, to prevent student experi-
menters from knowing what is in them), you are forming a set of nominal data. There is no numeric
relationship between the numbers. Each is merely a name. The only operators you may use on the
numbers are equal (=) and not-equal (< >). For example, suppose the soil type found in area A is
stored as x and the soil type found in area B is stored as y, you can ask: “Does x = y ?” (assuming x
and y are integers or text strings)?

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Ordinal—The numbers in an ordinal data set indicate an order among the entities they represent.
Perhaps 1, 2, and 3 indicate first-born, second-born, and third-born children. You know that, in a
given family, a child numbered 1 was born before a child numbered 3. But you don't know how
many months or years before. In addition to using the equal and not-equal operators on ordinal data,
you may use less than (<), less than or equal (<=), greater than or equal (>=), and greater than (>).
For example, house numbers on a given side of a street in the United States are generally in order.
Suppose house numbers increased along the right side of a north-south road as you proceeded
south. You could determine which of two houses was the southmost house by asking: is house num-
ber of X greater than house number of Y?

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Interval—An interval data set consists of numbers that come from a measurement scale where a unit
amount is established and values along the scale are linear multiples of that amount. Examples are
the common, nonscientific temperature scales: Celsius and Fahrenheit. With interval data, you may
use all the operators described previously and also the arithmetic operators addition (plus, +) and
subtraction (minus, -) as well. For example, if it were 20ºF in the morning and it became 60ºF in the
afternoon, you may say that it had become 40ºF warmer (60 - 20) = 40.

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You have to be very careful when using multiplication and division operators on interval data. For
example, you may not say, given the preceding numbers, that it became three times as warm in the
afternoon. The reason is that a set of interval data does not necessarily have a meaningful zero point
from which to measure. 5 For example, if the morning temperature were negative 20ºF and the after-
noon positive 20ºF, the difference would still be 40ºF, but you can see the difficulty in saying that one

5 The zero in the Fahrenheit scale was originally determined by the temperature of a mixture of ice and salt. Check the
Internet for the bizarre determination of 100 in that scale. The zero in a Celsius (centigrade—changed in 1948 to honor
the inventor of the Celsius thermometer, Anders Celsius) scale is arbitrarily defined to be the freezing point of water
and 100 is its boiling point.