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Ordinal data is a categorical, statistical data type where the variables have natural, ordered categories and the distances between the categories are not known. [1]: 2 These data exist on an ordinal scale, one of four levels of measurement described by S. S. Stevens in 1946.
The ordinal scale places events in order, but there is no attempt to make the intervals of the scale equal in terms of some rule. Rank orders represent ordinal scales and are frequently used in research relating to qualitative phenomena. A student's rank in his graduation class involves the use of an ordinal scale.
Scaling of data: One of the properties of the tests is the scale of the data, which can be interval-based, ordinal or nominal. [3] Nominal scale is also known as categorical. [6] Interval scale is also known as numerical. [6] When categorical data has only two possibilities, it is called binary or dichotomous. [1]
Ordinal regression turns up often in the social sciences, for example in the modeling of human levels of preference (on a scale from, say, 1–5 for "very poor" through "excellent"), as well as in information retrieval. In machine learning, ordinal regression may also be called ranking learning. [3] [a]
In the analysis of multivariate observations designed to assess subjects with respect to an attribute, a Guttman scale (named after Louis Guttman) is a single (unidimensional) ordinal scale for the assessment of the attribute, from which the original observations may be reproduced. The discovery of a Guttman scale in data depends on their ...
An example is a preference ranking. Some data are measured at the interval level. Numbers indicate the magnitude of difference between items, but there is no absolute zero point. Examples are attitude scales and opinion scales. Some data are measured at the ratio level. Numbers indicate magnitude of difference and there is a fixed zero point.
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).
In statistics, ranking is the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted.. For example, if the numerical data 3.4, 5.1, 2.6, 7.3 are observed, the ranks of these data items would be 2, 3, 1 and 4 respectively.