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 experimenters 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)?
  • 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 ...

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