In order to understand the usefulness of quantitative analysis, we have to be familiar with the kinds of information that a variable may possess. At the NOMINAL level, a variable has no numeric qualities at all. The values of a nominal variable are simply labels. Religious affiliation, for example, is a nominal variable with values such as Protestant, Catholic, Jewish, or none. These are labels that describe kinds of religious organizations.
What other nominal variables can you think of?
The values of nominal variables are unordered. For this reason, they may be presented in any order. No mathematical operations (such as adding or multiplying) are valid for nominal variables. They are, for this reason, of rather limited usefulness in quantitative analysis.
In ORDINAL variables, the values are ordered along some continuum; they represent rank. For example, the variable church attendance might have the values weekly, monthly, a few times a year, or never. These values are ordered from more frequent to less frequent attendance. We know that someone who says they attend weekly attends more frequently than someone who says a few times a year.
What we don't know with ordinal data, however, is the amount of difference between the values. In this example, we don't know how much more often a person who attends weekly attends than some one who attends a few times a year.
Ordinal variables, then, have order information, but no magnitude information. Ordinal variables have more numerical qualities than nominal variables, but we cannot treat the values as if they were numbers. Some mathematical operations are valid with ordinal data, but some are not.
What ordinal variables come to mind?
Only INTERVAL level variables are fully numeric. The values of interval level variables are real numbers, with both order and magnitude information. Examples of interval variables include age, household income (in dollars), occupational prestige scores, number of foreign films seen last year, and so forth. Because mathematical operations are meaningful with interval level data, they are generally the most useful kind of data for quantitative analysis.
Some researchers distinguish between interval and RATIO variables. The latter are fully numeric and contain a real zero point. A value of zero, then would indicate the absence of the quality being measured. In the case of interval variables, the value of zero is simply an arbitrary starting point for the scale.