Examination of the Chayes-Kruskal procedure for testing correlations between proportions
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The Chayes-Kruskal procedure for testing correlations between proportions uses a linear approximation to the actual closure transformation to provide a null value,p ij , against which an observed closed correlation coefficient,r ij , can be tested. It has been suggested that a significant difference betweenp ij andr ij would indicate a nonzero covariance relationship between theith andjth open variables. In this paper, the linear approximation to the closure transformation is described in terms of a matrix equation. Examination of the solution set of this equation shows that estimation of, or even the identification of, significant nonzero open correlations is essentially impossible even if the number of variables and the sample size are large. The method of solving the matrix equation is described in the appendix.
Key wordsclosure correlations geochemistry
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- Anderson, T. W., 1958, An introduction to multivariate analysis: John Wiley and Sons, Inc., New York, 374 p.Google Scholar
- Chayes, F., 1960, On correlation between variables of constant sum: Jour. Geophys. Research, v. 65, no. 12, p. 4185–4193.Google Scholar
- Chayes, F., 1970, Effect of a single nonzero open covariance on the simple closure test,in Geostatistics: Plenum Press, New York, p. 11–22.Google Scholar
- Chayes, F., 1971, Ratio correlation: The University of Chicago Press, Chicago, 99 p.Google Scholar
- Chayes, F., and Kruskal, W., 1966, An approximate statistical test for correlations between proportions: Jour. Geology, v. 74, no. 5, pt. 2, p. 692–702.Google Scholar
- Graybill, F. A., 1969, Introduction to matrices with applications in statistics: Wadsworth Publishing Co., Belmont, California, 372 p.Google Scholar
- Kendall, M. G., and Stuart, A., 1963, The advanced theory of statistics, v. 1: Charles Griffin and Co., Ltd., London, 433 p.Google Scholar
- Miesch, A. T., 1969, The constant sum problem in geology,in Computer applications in the earth sciences; an international symposium: Plenum Press, New York, p. 161–176.Google Scholar
- Saha, A. K., Bhattacharyya, C., and Lakshmipathy, S., 1974, Some problems in interpreting the correlations between the modal variables in granitic rocks: Jour. Math. Geology, v. 6, no. 3, p. 245–258.Google Scholar
- Wright, T., 1974, Algorithm 475, visible surface plotting program [J6]: Commun. ACM [Assoc. for Computer Machinery], v. 17, no. 3, p. 152–155.Google Scholar