Optimal Scaling Level and Measurement Level
This can be a very confusing concept when you first use Categories procedures. When specifying the level, you specify not the level at which variables are measured but the level at which they are scaled. The idea is that the variables to be quantified may have nonlinear relations regardless of how they are measured.
For Categories purposes, there are three basic levels of measurement:
- The nominal level implies that a variable's values represent unordered categories. Examples of variables that might be nominal are region, zip code area, religious affiliation, and multiple choice categories.
- The ordinal level implies that a variable's values represent ordered categories. Examples include attitude scales representing degree of satisfaction or confidence and preference rating scores.
- The numerical level implies that a variable's values represent ordered categories with a meaningful metric so that distance comparisons between categories are appropriate. Examples include age in years and income in thousands of dollars.
For example, suppose that the variables region, job, and age are coded as shown in the following table.
| Region code | Region value | Job code | Job value | Age |
|---|---|---|---|---|
| 1 | North | 1 | intern | 20 |
| 2 | South | 2 | sales rep | 22 |
| 3 | East | 3 | manager | 25 |
| 4 | West | 27 |
The values shown represent the categories of each variable. Region would be a nominal variable. There are four categories of region, with no intrinsic ordering. Values 1 through 4 simply represent the four categories; the coding scheme is completely arbitrary. Job, on the other hand, could be assumed to be an ordinal variable. The original categories form a progression from intern to manager. Larger codes represent a job higher on the corporate ladder. However, only the order information is known--nothing can be said about the distance between adjacent categories. In contrast, age could be assumed to be a numerical variable. In the case of age, the distances between the values are intrinsically meaningful. The distance between 20 and 22 is the same as the distance between 25 and 27, while the distance between 22 and 25 is greater than either of these.