Abstract
A method of estimating the product moment correlation from the polychoric series is developed. This method is shown to be a generalization of the method which uses the tetrachoric series to obtain the tetrachoric correlation. Although this new method involves more computational labor, it is shown to be superior to older methods for data grouped into a small number of classes.
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Bernstein, S. Sur l'extension du théorème limite du calcul des probabilités aux sommes de quantités dépendantes.Math. Annalen, 1926,97, 1–59.
Irwin, J. O. On the distribution of a weighted estimate of variance and on analysis of variance in certain cases of unequal weighting.J. roy. statist. Soc., 1942,105, 115–118.
Lancaster, H. O. The derivation and partition ofx 2 in certain discrete distributions.Biometrika, 1949,36, 117–129.
Lancaster, H. O. The structure of bivariate distributions.Ann. math. Statist., 1958,29, 719–736.
Mehler, F. G. Uber die Entwicklung einer Funktion von beliebig vielen Variablen nach Laplaceschen Funktionen höherer Ordnung.J. f. Mathematik, 1866,66, 161–176.
Pearson, K. On a criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling.Phil. Mag., 1900a,50, 157–175.
Pearson, K. Mathematical contribution to the theory of evolution VII: On the correlation of characters not quantitatively measurable.Philos. Trans. roy. Soc. London, 1900b,195A, 1–47.
Pearson, K. Mathematical contribution to the theory of evolution XIII: On the theory of contingency and its relation to association and normal correlation.Drapers Company Research Memoirs, Biometric Series No. 1, 1904.
Pearson, K. On the measurement of the influence of “broad categories” on correlation.Biometrika, 1913,9, 116–139.
Pearson, K. and Heron, D. On theories of association.Biometrika, 1913,9, 159–315.
Pearson, K. and Lee, A. On the laws of inheritance in man.Biometrika, 1903,2, 357–462.
Pearson, K. and Pearson, E. S. On polychoric coefficients of correlation.Biometrika, 1922,14, 127–156.
Ritchie-Scott, A. The correlation coefficient of a polychoric table.Biometrika, 1918,12, 93–133
Szegö, G.Orthogonal polynomials. Colloquium Publ. No. 23, Amer. Math. Soc., 1959.
Tschuprow, A. A.Grundbegriffe und Grundproblem der Korrelationtheorie. Leipzig: Teubner, 1925. Translated asPrinciples of the Mathematical Theory of Correlation. London: Hodge, 1939.
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Lancaster, H.O., Hamdan, M.A. Estimation of the correlation coefficient in contingency tables with possibly nonmetrical characters. Psychometrika 29, 383–391 (1964). https://doi.org/10.1007/BF02289604
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DOI: https://doi.org/10.1007/BF02289604