Ordinal data is a categorical, statistical data type where the variables have natural, ordered categories and the distances between the categories are not known. These data exist on an ordinal scale, one of four levels of measurement described by S. S. Stevens in 1946. The ordinal scale is distinguished from the nominal scale by having a ranking. It also differs from the interval scale and ratio scale by not having category widths that represent equal increments of the underlying attribute.
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Ordinal data in the context of Categorical data
In statistics, a categorical variable (also called qualitative variable) is a 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. 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 observations made of qualitative data that are summarised as counts or cross tabulations, 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 variables have a meaningful ordering, while nominal variables have no meaningful ordering.
Ordinal data in the context of Nominal category
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.
Ordinal data in the context of Statistical classification
When classification is performed by a computer, statistical methods are normally used to develop the algorithm.
Often, the individual observations are analyzed into a set of quantifiable properties, known variously as explanatory variables or features. These properties may variously be categorical (e.g. "A", "B", "AB" or "O", for blood type), ordinal (e.g. "large", "medium" or "small"), integer-valued (e.g. the number of occurrences of a particular word in an email) or real-valued (e.g. a measurement of blood pressure). Other classifiers work by comparing observations to previous observations by means of a similarity or distance function.