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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.
There are many equivalent definitions of a category. [1] One commonly used definition is as follows. A category C consists of a class ob(C) of objects, a class mor(C) of morphisms or arrows, a domain or source class function dom: mor(C) → ob(C), a codomain or target class function cod: mor(C) → ob(C),
This is a list of statistical procedures which can be used for the analysis of categorical data, also known as data on the nominal scale and as categorical variables.
Ordinal measurements have imprecise differences between consecutive values, but have a meaningful order to those values, and permit any order-preserving transformation. Interval measurements have meaningful distances between measurements defined, but the zero value is arbitrary (as in the case with longitude and temperature measurements in ...
A theory is κ-categorical (or categorical in κ) if it has exactly one model of cardinality κ up to isomorphism. Morley's categoricity theorem is a theorem of Michael D. Morley stating that if a first-order theory in a countable language is categorical in some uncountable cardinality, then it is categorical in all uncountable cardinalities.
Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. [1] Psychologist Stanley Smith Stevens developed the best-known classification with four levels, or scales, of measurement: nominal, ordinal, interval, and ratio.
Category theory was originally introduced for the need of homological algebra, and widely extended for the need of modern algebraic geometry (scheme theory). Category theory may be viewed as an extension of universal algebra , as the latter studies algebraic structures , and the former applies to any kind of mathematical structure and studies ...
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.