Nominal Measure

A nominal measure is part of taxonomy of measurement types for variables developed by psychologist Stanley Smith Stevens in 1946. Other types of measurement include ordinal, interval, and ratio. A nominal variable, sometimes referred to as a categorical variable, is characterized by an exhaustive and mutually exclusive set of categories. Each case in the population to be categorized using the nominal measure must fall into one and only one of the categories. Examples of the more commonly used nominal measures in survey research include gender, race, religious affiliation, and political party.

Unlike other types of measurement, the categories of a variable that is a nominal measure refer to discrete characteristics. No order of magnitude is implied when comparing one category to another. After the relevant attributes of all cases in the population being [Page 511]measured are examined, the cases that share the same criteria are placed into the same category and given the same label, for example, “Female” or “Male.”

Table 1 Example of three types of descriptive statistics appropriate for nominal measures

Numbers can be used as labels, but great care should be used when using the variable in statistical analyses. The number assignment in place of a more descriptive label is completely arbitrary. Because the categories of a nominal variable are without mathematically measurable relationship to each other, there is no measure of standard deviation to apply to such a measure. As a result, the types of statistical analysis that can be used with such variables are limited. The only appropriate measure of central tendency is the mode; the mean or median of such a variable is meaningless.

For each of the categories of a nominal variable, one can calculate a proportion, a percentage, and a ratio. The proportion would be the number of cases having the selected value of the variable divided by the total number of cases resulting in a value of zero (none of the cases), one (all of the cases), or a value in between. The percentage for the same category would simply be the proportion multiplied by 100. The ratio is a measure of two categories of the variable in relation to one another. Ratios are calculated by dividing one category by another category. Table 1 illustrates these three types of descriptive statistics appropriate for nominal measures.

Measures of the strength of the relationship between two nominal variables, often called contingency tests, can be calculated using a chi-square test, which compares the observed counts in each category to the expected values if there were no relationship. The Fisher's Exact test is appropriate when both nominal variables are dichotomous (have only two values). A variety of other nonparametric tests are available that are appropriate for a variety of situations, including empty cells in a cross-tabulation of two nominal variables, sensitivity to extremely large marginal counts, and other factors that can disturb the underlying assumptions of the more commonly used chi-square and Fisher's Exact tests.