Examination of the Chayes-Kruskal procedure for testing correlations between proportions |
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Authors: | John O Kork |
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Institution: | (1) Colorado School of Mines, 80401 Golden, Colorado;(2) U.S. Geological Survey, 80225 Denver, Colorado |
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Abstract: | 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. |
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Keywords: | closure correlations geochemistry |
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