Editing Categorical variable (section)

{{More footnotes needed|date=July 2024}}{{Short description|Variable capable of taking on a limited number of possible values}}
In [[statistics]], a '''categorical variable''' (also called '''qualitative variable''') is a [[variable (research)|variable]] that can take on one of a limited, and usually fixed, number of possible values, assigning each individual or other unit of observation to a particular group or [[nominal category]] on the basis of some [[qualitative property]].<ref name="yates">{{cite book | last1 = Yates | first1 = Daniel S. | last2 = Moore | first2 = David S. | last3 = Starnes | first3 = Daren S. | year = 2003 | title = The Practice of Statistics | edition = 2nd | publisher = [[W. H. Freeman and Company|Freeman]] | location = New York | url = http://bcs.whfreeman.com/yates2e/ | isbn = 978-0-7167-4773-4 | access-date = 2014-09-28 | archive-url = https://web.archive.org/web/20050209001108/http://bcs.whfreeman.com/yates2e/ | archive-date = 2005-02-09 | url-status = dead }}</ref> 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 variable|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 observations made of [[qualitative data]] that are summarised as counts or [[cross tabulation]]s, or from observations of [[quantitative data]] grouped 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. [[Ordinal data|Ordinal variables]] have a meaningful ordering, while [[Nominal variable|nominal variables]] have no meaningful ordering.

A categorical variable that can take on exactly two values is termed a ''[[binary variable]]'' or a '''dichotomous variable'''; an important special case is the [[Bernoulli variable]]. Categorical variables with more than two possible values are called '''polytomous variables'''; categorical variables are often assumed to be polytomous unless otherwise specified. [[Discretization]] is treating [[continuous function|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 with one or more quantitative [[dummy variable (statistics)|dummy variables]].