Categorical Response Data

Typology of Categorical Data

The most important differentiation of categorical data distinguishes between nominal and ordinal variables. The values of a nominal variable identify categories that do not have a natural rank order. Examples are ethnicity (“Black,” “White,” “Hispanic,” etc.) or marital status (“single,” “married,” “divorced,” “widowed”). Methods using nominal data should not depend on the numerical values assigned to the categories. The categories of ordinal data, in contrast, possess a natural ranking. Examples are social class (“lower,” “middle,” and “upper”), agreement with the statement “Democracies are indecisive” (“strongly agree,” “agree,” “disagree,” and “strongly disagree”), or self-reported political left–right orientation (on a scale from 1 = left to 10 = right). Methods using ordinal data take into account the order of the values, but the exact spacing does not matter. The distinction between nominal and ordinal variables is not always clear. For example, political parties can be ranked on a left–right scale, but the order may be ambiguous for some parties (because they may rank differently on different policies). Moreover, whether a variable is treated as ordinal can depend on the research question.

A further distinction is made between qualitative and quantitative data. Some authors use the former as a synonym for categorical data. However, while nominal data are clearly qualitative, ordinal data are an intermediate type, often treated as quantitative in practice. Moreover, quantitative data can sometimes be treated as categorical. Quantitative data are either continuous or discrete. Continuous variables can take on any real value in a given interval, whereas discrete variables are restricted to a fixed set of distinct values (e.g., integers). Discrete quantitative variables are often considered as categorical when the range of observed values is small. Count data are an example.

Categorical variables can be divided into dichotomous variables that only have two possible outcomes (“yes”/“no”; “male”/“female”) and polytomous variables with more than two categories (“Christian,” “Muslim,” “Hindu,” “Buddhist,” “Jewish,” etc.). A dichotomous variable that is coded 0 and 1 is called an indicator or binary variable. Dichotomous variables are often technically and conceptually easier to handle than polytomous variables.

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