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A measure of association (correlation) in nominal data (contingency tables), using determinants

Colignatus, Thomas (2007): A measure of association (correlation) in nominal data (contingency tables), using determinants.

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Abstract

Nominal data currently lack a correlation coefficient, such as has already defined for real data. A measure is possible using the determinant, with the useful interpretation that the determinant gives the ratio between volumes. With M a m × n contingency table and n ≤ m the suggested measure is r = Sqrt[det[A'A]] with A = Normalized[M]. With M an n1 × n2 × ... × nk contingency matrix, we can construct a matrix of pairwise correlations R so that the overall correlation is f[R]. An option is to use f[R] = Sqrt[1 - det[R]]. However, for both nominal and cardinal data the advisable choice for such a function f is to take the maximal multiple correlation within R.

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