A Note on Approximating Correlations from Odds Ratios
- 1 February 1988
- journal article
- research article
- Published by SAGE Publications in Sociological Methods & Research
- Vol. 16 (3) , 407-424
- https://doi.org/10.1177/0049124188016003003
Abstract
An approximate relationship between the odds ratio and the tetrachoric correlation for 2×2 contingency tables is presented. The approximation is simple in form and demonstrates a close linkage between these two important measures of association. This relationship can be used to reconcile (at least in part) the two ostensibly different ways to study association or partial association. The approximation is related to Yule's Q and can also be motivated by recent results on association models. The approximation is used to relate the parameters of the common factor model and the 2-class latent structure model applied to dichotomous items.Keywords
This publication has 15 references indexed in Scilit:
- Some Useful Extensions of the Usual Correspondence Analysis Approach and the Usual Log-Linear Models Approach in the Analysis of Contingency TablesInternational Statistical Review, 1986
- The Analysis of Cross-Classified Data Having Ordered and/or Unordered Categories: Association Models, Correlation Models, and Asymmetry Models for Contingency Tables With or Without Missing EntriesThe Annals of Statistics, 1985
- Latent Structure Analysis of a Set of Multidimensional Contingency TablesJournal of the American Statistical Association, 1984
- Approximating the Tetrachoric Correlation CoefficientPublished by JSTOR ,1983
- Association models and the bivariate normal for contingency tables with ordered categoriesBiometrika, 1981
- Simple Models for the Analysis of Association in Cross-Classifications Having Ordered CategoriesJournal of the American Statistical Association, 1979
- Calculation of the Tetrachoric Correlation CoefficientPsychometrika, 1979
- Algorithm AS 116: The Tetrachoric Correlation and its Asymptotic Standard ErrorJournal of the Royal Statistical Society Series C: Applied Statistics, 1977
- Some Properties of the Range in Samples from Tukey's Symmetric Lambda DistributionsJournal of the American Statistical Association, 1971
- The Measure of Association in a 2 × 2 TableJournal of the Royal Statistical Society. Series A (General), 1963