Correlation Coefficients For More Than One Scale Type

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Abstract
The problem of correlating variables from different scale types is discussed. A general correlation coefficient, based on symmetrization theory, is derived. This coefficient is invariant over permitted transformations of the variables for their respective (possibly nonequivalent) scale types. Such a general coefficient is called an E-correlation family. One such family (based on the product-moment correlation coefficient and a nominal scale correlation coefficient), is given for the set composed of interval, ordinal and nominal scales. Finally the individual comparison problem over variables on different scale types is discussed and a solution is proposed.

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