Nominal scale

Variables at a nominal scale of measurement are, typically, those such as gender, political affiliation, color, etc. The values of these variables are qualitative, simple "labels", with no real quantitative difference between them. Thus, it is not possible to say that a particular value is better or greater than other, only different. Equally, it is not reasonable to organize those values hierarchically according to importance.

For example, political affiliation may be an interesting variable to use to predict political support in a particular state. However, it is not reasonable to say that "republicans" are better than "democrats" and these better than "independents" in their political affiliation. Color may be an interesting variable to use to predict certain emotional states. However, it is not reasonable to say that "red" is a better color than "blue" or "green" a better color than "yellow".

The values of variables at the nominal scale may be coded as a number (eg red = 1, blue = 2, yellow = 3…), yet such number is still a convenient "label" not a real quantitative claim.

We may use the concept of "nominal variable" (or "nominal-level variable", "categorical variable" or "qualitative variable") to refer to those variables which use a nominal scale of measurement. This is "handy" although not fully correct. That is, the quality of being "nominal" refers to the scale not to the variable. That is, it may sometimes be possible to transform the values of "quantitative" variables into a nominal scale, and, although less likely, to transform the values of a qualitative variable into a quantitative scale.

For example, we may transform a quantitative variable (age) into a qualitative one (clusters of people according to age) to assess, for example, the relationship between age clusters and salary. A cluster may not necessarily group people in a quantitative manner but, even if the clusters organized themselves in such a manner that they could be considered as values of a quantitative variable, we may still be interested in their nominal value only.
Alternatively, available research may have established that red is "better" than blue and blue "better" than yellow in eliciting a particular emotional state. This may provide us with the opportunity to use statistics as for an interval scale of measurement (instead of a nominal one) if we wanted to research the topic further, for example.

# Properties

• Nominal variables vary qualitatively, not quantitatively. Thus, no value per se is better or worse than any other value.
• The values of nominal variables cannot be organized hierarchically in regards to importance (independently of whether the value is expressed as a "label" or as a number. Thus, extra care is needed when incorporating (numerical) nominal variables into statistical analyses.
• The most appropriate statistic for describing nominal variables are frequencies.
• If required, the most appropriate "average" for nominal variables is the mode.
• Nominal variables can be easily converted into "dummy" quantitative variables by treating each of their values as independent variables with only two values. When the nominal variable has only two values, statistical analyses can typically be done as normal, but you need to remember that whatever values the variable has are not real values but labels. In these cases, the variable acts as a "dummy" variable, and can be used with correlation tests and other statistics

For example, political affiliation can be made into three "dummy" variables, as follows: "republican" (values "0 = yes" and "1 = no"), "democrat" (values "0 = yes" and "1 = no"), and "independent" (values "0 = yes" and "1 = no"). Of course, there are nominal variables, such as gender, which already have two values only and, thus, do not need further transformation.
Once a nominal variable acts as a "dummy" variable, it can be used with most statistical analysis, although interpretation of results need to be done with care. For example, the arithmetic mean of gender would inform which value (man or woman) is more frequent in a dataset. This is, actually, another way of "finding" the mode of the variable, and the result should be reported as such mode (not as a mean). You can also correlate gender with a quantitative variable (eg salary). The result of the correlation can be easily interpreted as the relationship between both variables. Again the interpretation of the correlation needs to be qualitative in nature and, thus, it is dependent on which labels have being used to represent men or women.

# Want to know more?

Wikipedia - Level of measurement
You can learn a bit more about levels of measurement in Wikipedia.