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.

Item Type: | MPRA Paper |
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Institution: | Thomas Cool Consultancy & Econometrics |

Original Title: | A measure of association (correlation) in nominal data (contingency tables), using determinants |

Language: | English |

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 |

Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C10 - General |

Item ID: | 2662 |

Depositing User: | Thomas Colignatus |

Date Deposited: | 10 Apr 2007 |

Last Modified: | 27 Sep 2019 13:59 |

References: | Colignatus is the name of Thomas Cool in science. Becker, L.A. (1999), “Measures of Effect Size (Strength of Association)”, http://web.uccs.edu/lbecker/SPSS/glm_effectsize.htm, Retrieved from source Cool, Th. (1999, 2001), “The Economics Pack, Applications for Mathematica”, http://www.dataweb.nl/~cool, ISBN 90-804774-1-9, JEL-99-0820 Colignatus, Th. (2006), “On the sample distribution of the adjusted coefficient of determination (R2Adj) in OLS”, http://library.wolfram.com/infocenter/MathSource/6269/ Colignatus, Th. (2007a), “A logic of exceptions”, http://www.dataweb.nl/~cool, ISBN 978-90-804774-4-5 Colignatus, Th. (2007b), “Voting theory for democracy”, 2nd edition, http://www.dataweb.nl/~cool, ISBN 978-90-804774-5-2 Garson, D. (2007), “Nominal Association: Phi, Contingency Coefficient, Tschuprow's T, Cramer's V, Lambda, Uncertainty Coefficient”, http://www2.chass.ncsu.edu/garson/pa765/assocnominal.htm, Retrieved from source Johnston J. (1972), “Econometric methods”, McGraw-Hill Kleinbaum, D.G., K.M. Sullivan and N.D. Barker (2003), “ActivEpi Companion texbook”, Springer Losh, S.C. (2004), “Guide 5: Bivariate Associations and Correlation Coefficient Properties”, http://edf5400-01.fa04.fsu.edu/Guide5.html, Retrieved from Source Mood, A.M. and F.A. Graybill (1963), “Introduction to the theory of statistics”, McGraw-Hill Pearl, J. (2000), “Causality. Models, reasoning and inference”, Cambridge Simon, R. (2007), “Lecture Notes and Exercises 2006/07”, http://www.maths.lse.ac.uk/Courses/MA201/, Retrieved from source Takayama A. (1974), “Mathematical economics”, The Dryden Press Theil H. (1971), “Principles of econometrics”, North-Holland UCLA ATS (2007), “SAS Textbook Examples. Econometric Analysis, Fourth Edition by Greene. Chapter 16: Simultaneous Equations Models”, http://www.ats.ucla.edu/stat/SAS/examples/greene/chapter16.htm, Retrieved from source (Other) websites http://en.wikipedia.org/wiki/Contingency_table http://post.queensu.ca:8080/SASDoc/getDoc/en/procstat.hlp/corr_sect26.htm http://en.wikipedia.org/wiki/Fisher%27s_exact_test |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/2662 |