Categorical Variables

A categorical variable is one that takes on values in a set of categories, as opposed to a continuous variable, which takes on a range of values along a continuum. The simplest examples of categorical variables are binary variables with only two possible responses, for instance “yes” and “no.” Categorical variables are most common in the social, biological, and behavioral sciences, although they can be found in almost any area of application. For example, the variable of marital status can be described as “single,” “married,” “divorced,” or “widowed”: four categories. The variable sex can be described as “male” or “female”: two categories. Education level can be classified as “grammar school only,” “some high school,” “completed high school,” “some university,” “completed university,” or “advanced or professional degree.”

When the categories ascribed to the variable are labels only, with no intrinsic ordering, then the variable is nominal. For example, it is generally meaningless to say that an individual who is divorced has higher or lower marital status than an individual who is widowed. Hence marital status is a nominal categorical variable. On the other hand, when the categories are naturally ordered, as with education level, socioeconomic status, or evaluation on a scale ranging from strongly disagree to strongly agree, then the variable is an ordinal categorical variable. In this case, qualitative comparisons of individuals in different categories are meaningful. It is sensible to state that a person who has completed university has attained a higher level of education than a person who has completed only high school.

Categorical variables can be used as either the explanatory or the response variable in a statistical analysis. When the response is a categorical variable, appropriate analyses may include generalized linear models (for dichotomous or polytomous responses, with suitable link functions), log linear models, chi-square goodness-of-fit analysis, and the like, depending on the nature of the explanatory variables and the sampling mechanism. Categorical variables also fill a useful role as explanatory variables in standard regression, analysis of variance, and analysis of covariance models, as well as in generalized linear models. When the data are cross-classified according to several categorical variables (that is, when they come in the form of a table of counts), analyses for contingency tables, including log linear models, are appropriate. It is important to heed the distinction between nominal and ordinal variables in data analysis. When there are ordinal variables in a data set, the ordering needs to be entered explicitly into the model; this is usually achieved by incorporating constraints on parameters, which makes the analysis more complex.

In sum, categorical variables arise in a wide variety of scientific contexts. They require specialized statistical techniques, and these have been developed both theoretically and in terms of practical implementation.