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If the same categories are used for two nominal scale variables, this information should be used in similarity measures between those variables. Two such similarity measures, one proposed by Goodman & Kruskal and one (kappa) by Cohen, are examined. Two alternative coefficients, called C and S are further proposed. They are found to be generalizations of the G index and the phi coefficient respectively. Both of them seem to have many desirable characteristics, e.g., they are both E-coefficients. They may also be used as measures of similarity between persons classifying into categories defined beforehand.
Janson et al. (Sun,) studied this question.