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

Thomas Colignatus ()

MPRA Paper from University Library of Munich, Germany

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.

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 (search for similar items in EconPapers)
JEL-codes: C10 (search for similar items in EconPapers)
Date: 2007-03-20, Revised 2007-04-10
New Economics Papers: this item is included in nep-ecm
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/2662/1/MPRA_paper_2662.pdf original version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:2662

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().