Categorical variable in the context of Bar chart

In mathematics and statistics, a quantitative variable may be continuous or discrete. If it can take on two real values and all the values between them, the variable is continuous in that interval. If it can take on a value such that there is a non-infinitesimal gap on each side of it containing no values that the variable can take on, then it is discrete around that value. In some contexts, a variable can be discrete in some ranges of the number line and continuous in others. In statistics, continuous and discrete variables are distinct statistical data types which are described with different probability distributions.

A nominal category (also nominal variable or nominal group) is a collection of objects or ideas grouped according to a particular qualitative property. Nominal categories do not have a natural order, which means that statistical analyses of these variables will always produce the same results, regardless of the order in which the data is presented.

A variable used to associate each data point in a set of observations, or in a particular instance, to a certain qualitative category is a categorical variable. Categorical variables have two types of scales, ordinal and nominal. The first type of categorical scale is dependent on natural ordering, levels that are defined by a sense of quality. Variables with this ordering convention are known as ordinal variables. In comparison, variables with unordered scales are nominal variables.

Pattern recognition is the task of assigning a class to an observation based on patterns extracted from data. While similar, pattern recognition (PR) is not to be confused with pattern machines (PM) which may possess PR capabilities but their primary function is to distinguish and create emergent patterns. PR has applications in statistical data analysis, signal processing, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning. Pattern recognition has its origins in statistics and engineering; some modern approaches to pattern recognition include the use of machine learning, due to the increased availability of big data and a new abundance of processing power.

Pattern recognition systems are commonly trained from labeled "training" data. When no labeled data are available, other algorithms can be used to discover previously unknown patterns. KDD and data mining have a larger focus on unsupervised methods and stronger connection to business use. Pattern recognition focuses more on the signal and also takes acquisition and signal processing into consideration. It originated in engineering, and the term is popular in the context of computer vision: a leading computer vision conference is named Conference on Computer Vision and Pattern Recognition.

Quantitative genetics is the study of quantitative traits, which are phenotypes that vary continuously—such as height or mass—as opposed to phenotypes and gene-products that are discretely identifiable—such as eye-colour, or the presence of a particular biochemical.

Both of these branches of genetics use the frequencies of different alleles of a gene in breeding populations (gamodemes), and combine them with concepts from simple Mendelian inheritance to analyze inheritance patterns across generations and descendant lines. While population genetics can focus on particular genes and their subsequent metabolic products, quantitative genetics focuses more on the outward phenotypes, and makes only summaries of the underlying genetics.

Linear discriminant analysis (LDA), normal discriminant analysis (NDA), canonical variates analysis (CVA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes or separates two or more classes of objects or events. The resulting combination may be used as a linear classifier, or, more commonly, for dimensionality reduction before later classification.

LDA is closely related to analysis of variance (ANOVA) and regression analysis, which also attempt to express one dependent variable as a linear combination of other features or measurements. However, ANOVA uses categorical independent variables and a continuous dependent variable, whereas discriminant analysis has continuous independent variables and a categorical dependent variable (i.e. the class label). Logistic regression and probit regression are more similar to LDA than ANOVA is, as they also explain a categorical variable by the values of continuous independent variables. These other methods are preferable in applications where it is not reasonable to assume that the independent variables are normally distributed, which is a fundamental assumption of the LDA method.

In computer programming, an enumerated type (also called enumeration, enum, or factor in the R programming language, a condition-name in the COBOL programming language, a status variable in the JOVIAL programming language, an ordinal in the PL/I programming language, and a categorical variable in statistics) is a data type consisting of a set of named values called elements, members, enumeral, or enumerators of the type. The enumerator names are usually identifiers that behave as constants in the language. An enumerated type can be seen as a degenerate tagged union of unit type. A variable that has been declared as having an enumerated type can be assigned any of the enumerators as a value. In other words, an enumerated type has values that are different from each other, and that can be compared and assigned, but are not generally specified by the programmer as having any particular concrete representation in the computer's memory; compilers and interpreters can represent them arbitrarily.
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In probability theory and statistics, a categorical distribution (also called a generalized Bernoulli distribution, multinoulli distribution) is a discrete probability distribution that describes the possible results of a random variable that can take on one of K possible categories, with the probability of each category separately specified. There is no innate underlying ordering of these outcomes, but numerical labels are often attached for convenience in describing the distribution, (e.g. 1 to K). The K-dimensional categorical distribution is the most general distribution over a K-way event; any other discrete distribution over a size-K sample space is a special case. The parameters specifying the probabilities of each possible outcome are constrained only by the fact that each must be in the range 0 to 1, and all must sum to 1.

The categorical distribution is the generalization of the Bernoulli distribution for a categorical random variable, i.e. for a discrete variable with more than two possible outcomes, such as the roll of a die. On the other hand, the categorical distribution is a special case of the multinomial distribution, in that it gives the probabilities of potential outcomes of a single drawing rather than multiple drawings.

In statistics, data can have any of various types. Statistical data types include categorical (e.g. country), directional (angles or directions, e.g. wind measurements), count (a whole number of events), or real intervals (e.g. measures of temperature).

The data type is a fundamental concept in statistics and controls what sorts of probability distributions can logically be used to describe the variable, the permissible operations on the variable, the type of regression analysis used to predict the variable, etc. The concept of data type is similar to the concept of level of measurement, but more specific. For example, count data requires a different distribution (e.g. a Poisson distribution or binomial distribution) than non-negative real-valued data require, but both fall under the same level of measurement (a ratio scale).

A test method is a method for a test in science or engineering, such as a physical test, chemical test, or statistical test. It is a specified procedure that produces a test result. To ensure accurate and relevant results, a test method should be "explicit, unambiguous, and experimentally feasible.", as well as effective and reproducible.

A test is an observation or experiment that determines one or more characteristics of a given sample, product, process, or service, with the purpose of comparing the test result to expected or desired results. The results can be qualitative (yes/no), quantitative (a measured value), or categorical and can be derived from personal observation or the output of a precision measuring instrument.

A color code is a system for encoding and representing non-color information with colors to facilitate communication. This information tends to be categorical (representing unordered/qualitative categories) though may also be sequential (representing an ordered/quantitative variable).

In probability theory and statistics, the conditional probability distribution is a probability distribution that describes the probability of an outcome given the occurrence of a particular event. Given two jointly distributed random variables ${\displaystyle X}$ and ${\displaystyle Y}$, the conditional probability distribution of ${\displaystyle Y}$ given ${\displaystyle X}$ is the probability distribution of ${\displaystyle Y}$ when ${\displaystyle X}$ is known to be a particular value; in some cases the conditional probabilities may be expressed as functions containing the unspecified value ${\displaystyle x}$ of ${\displaystyle X}$ as a parameter. When both ${\displaystyle X}$ and ${\displaystyle Y}$ are categorical variables, a conditional probability table is typically used to represent the conditional probability. The conditional distribution contrasts with the marginal distribution of a random variable, which is its distribution without reference to the value of the other variable.

If the conditional distribution of ${\displaystyle Y}$ given ${\displaystyle X}$ is a continuous distribution, then its probability density function is known as the conditional density function. The properties of a conditional distribution, such as the moments, are often referred to by corresponding names such as the conditional mean and conditional variance.