Читать книгу Applied Univariate, Bivariate, and Multivariate Statistics - Daniel J. Denis - Страница 37

Measurement at the nominal scale is hardly considered real measurement, because it is simply the process of grouping objects or subjects into classes. Each class is usually represented by a number, letter, name, etc. Other than naming these categories, no other properties are assumed or inferred, such as distance between objects or magnitude.

A classic example of measurement at the nominal level is that of hockey jersey numbers. That the number “99” is greater than the number “22” on the shirts of two hockey players does not imply anything about magnitude (though Wayne Gretzky did in this case wear “99” and was perhaps the best hockey player ever). The numbers 99 and 22 are simply “classes,” they are symbols used to identify (or name) one class as different or distinct from the other. The fact that we use a rational system such as the real numbers to identify these different classes of “99” versus “22” does not imply anything about order or magnitude at the level of substantive measurement. Yes, to the mathematician, 99 is indeed numerically greater than 22. That is, an order property is implied in the numbers. However, to the scientist, nothing of order or magnitude needs to be implied when working with a nominal scale.

To briefly elaborate on this point, the concept of using numbers to represent classes makes for an ideal example of the distinction between mathematical measurement versus scientific measurement. In the mathematical measurement of the distance on the real line (e.g., the “length” between two real numbers), order is a necessary implication and differentiates any two numbers on the line. In scientific measurement, though we may still use the “objects” (i.e., the numbers) of pure mathematics, whether there exist order and magnitude in our empirical objects of study is for us to decide as scientists with the aid of our measurement tools. It is not solely a mathematical or “abstract” consideration.

As an example, consider the following objects:

* $ # %

Though we can say, at minimum, that nominal level measurement has been achieved (the objects have different symbols, that is, different names), we cannot say anything more about either the distance or magnitude between the objects, unless we decide to impose an order relation on the above objects. For instance, if we decide, based on our rules of measurement, that $ is greater than *, then not only have we measurement at the nominal level, we also have measurement at the ordinal level.