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

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  • Colignatus, Thomas

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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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 2662.

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Date of creation: 20 Mar 2007
Date of revision: 10 Apr 2007
Handle: RePEc:pra:mprapa:2662

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Keywords: association; correlation; contingency table; volume ratio; determinant; nonparametric methods; nominal data; nominal scale; categorical data; Fisher’s exact test; odds ratio; tetrachoric correlation coefficient; phi; Cramer’s V; Pearson; contingency coefficient; uncertainty coefficient; Theil’s U; eta; meta-analysis; Simpson’s paradox; causality; statistical independence;

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Cited by:
  1. Colignatus, Thomas, 2007. "Correlation and regression in contingency tables. A measure of association or correlation in nominal data (contingency tables), using determinants," MPRA Paper 3394, University Library of Munich, Germany, revised 07 Jun 2007.
  2. Colignatus, Thomas, 2007. "A comparison of nominal regression and logistic regression for contingency tables, including the 2 × 2 × 2 case in causality," MPRA Paper 3615, University Library of Munich, Germany, revised 19 Jun 2007.
  3. Colignatus, Thomas, 2007. "The 2 x 2 x 2 case in causality, of an effect, a cause and a confounder. A cross-over’s guide to the 2 x 2 x 2 contingency table," MPRA Paper 3351, University Library of Munich, Germany, revised 14 May 2007.

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