As a means of summarizing the potential relationship between two (or more) random categorical variables X and Y , a number of measures of association have been proposed over the years. A historical review of such measures and new proposals have been presented in a series of papers by Goodman and Kruskal (1979) [see also Kendall and Stuart (1979), Ch. 33 and Liebetrau (1983)]. Such summary measures depend on whether X and Y are nominal or ordinal as well as on whether X and Y are to be treated symmetrically or asymmetrically. In the symmetric case, X and Y are treated equivalently and no causal relationship is assumed to exist between them. In the asymmetric case, a causal relationship between X and Y is considered to exist so that one variable is treated as the explanatory variable (X) and the other variable treated as the response variable (Y ).
The focus here will be on the case when both X and Yare nominal categorical variables, i.e., no natural ordering exists for the variables....
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References and Further Reading
Agresti A (2002) Categorical data analysis, 2nd edn. Wiley, Hoboken, NJ
Bishop YMM, Fienberg SE, Holland PW(1975) Discrete multivariate analysis. MIT, Cambridge, MA
Cramér H (1946) Mathematical methods for statistics. Princeton University Press, Princeton, NJ
Goodman LA, Kruskal WH (1979) Measures of association for cross-classifications. Springer, New York
Kendall M, Stuart A (1979) The advanced theory of statistics, vol.2, 4th edn. Charles Griffin, London
Kvålseth TO (1987) Entropy and correlation: some comments. IEEE Transactions on Systems, Man, and Cybernetics, SMC-17, 517–519
Liebetrau AM (1983) Measures of Association. Beverly Hills, CA: Sage Publications.
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Kvålseth, T.O. (2011). Association Measures for Nominal Categorical Variables. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_122
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