Categorical variable

In statistics, a categorical variable is a variable that can take on one of a limited, and usually fixed, number of possible values, thus assigning each individual to a particular group or "category."  In computer science and some branches of mathematics, categorical variables are referred to as enumerations or enumerated types. Commonly (though not in this article), each of the possible values of a categorical variable is referred to as a level. The probability distribution associated with a random categorical variable is called a categorical distribution.

Categorical data is the statistical data type consisting of categorical variables or of data that has been converted into that form, for example as grouped data. More specifically, categorical data may derive from either or both of observations made of qualitative data, where the observations are summarised as counts or cross tabulations, or of quantitative data, where observations might be directly observed counts of events happening or might be counts of values that occur within given intervals. Often, purely categorical data are summarised in the form of a contingency table. However, particularly when considering data analysis, it is common to use the term "categorical data" to apply to data sets that, while containing some categorical variables, may also contain non-categorical variables.

A categorical variable that can take on exactly two values is termed a binary variable or dichotomous variable; an important special case is the Bernoulli variable. Categorical variables with more than two possible values are called polytomous variables; variables are often assumed to be polytomous unless otherwise specified. Discretization is treating continuous data as if it were categorical. Dichotomization is treating continuous data or polytomous variables as if they were binary variables. Regression analysis often treats category membership as a quantitative dummy variable.

Examples of categorical variables

Examples of values that might be represented in a categorical variable:

• The blood type of a person: A, B, AB or O.
• The state that a resident of the United States lives in.
• The political party that a voter in a European country might vote for: Christian Democrat, Social Democrat, Green Party, etc.
• The type of a rock: igneous, sedimentary or metamorphic.
• The identity of a particular word (e.g., in a language model): One of V possible choices, for a vocabulary of size V.

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