Level of Measurement

Nominal

Nominal variables are variables for which there is no relationship between the numeric values of the variable and characteristics those numbers represent. For example, one might have a variable “region,” which takes on the numeric values 1, 2, 3, and 4, where 1 represents “North,” 2 represents “South,” 3 represents “East,” and 4 represents “West.” Region is a nominal variable because there is no mathematical relationship between the number 1 and the region North, or the number 2 and the region South, and so forth.

For nominal variables, researchers cannot compute statistics like the mean, variance, or median because they will have no intuitive meaning; the mode of the distribution can be computed, however. Nominal variables also cannot be used in associational analyses like covariance or correlation and cannot be used in regressions. To use nominal variables in associational analyses, the nominal variable must be separated into [Page 422]a series of binary variables. Only nonparametric statistical tests can be used with nominal variables.

Binary

Binary or “dummy” variables are a special type of nominal variable that can take on exactly two mutually exclusive values. For instance, one might have a variable that indicates whether or not someone is registered to vote, which would take on the value 1 if the person is registered and 0 if the person is not registered. The values are mutually exclusive because someone cannot be both registered and not registered, and there are no other possibilities. Like with nominal variables, there is no mathematical relationship between the number 1 and being registered to vote, but unlike nominal variables, binary variables can be used in associational analyses. Technically, only nonparametric statistical tests should be used with nominal variables, but the social science literature is filled with examples where researchers have used parametric tests.

Ordinal

Ordinal variables are variables for which the values of the variable can be rank ordered. For instance, a researcher might ask someone their opinion about how the president is doing his job, where 1 = strongly approve, 2 = somewhat approve, 3 = somewhat disapprove, and 4 = strongly disapprove. In this case, the values for job approval can be ranked, and researchers can make comparisons between values, for example, saying that someone who gives a job approval value of 1 approves of the president more than someone who gives a job approval value of 3.

However, a researcher cannot make exact mathematical comparisons between values of the variable; for example, it cannot be assumed that a respondent who gives a job approval of 4 disapproves of the president twice as much as someone else who gives a job approval of 2. Researchers can, however, compare values using “greater than” or “less than” terminology and logic.

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