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The article investigates the possibility of measuring the strength of alinear correlation relationship between nominal data and numerical data.Correlation coefficients for variables coded with real numbers as well as forvariables coded with complex numbers were studied. For variables coded withreal numbers, unambiguous measures of real linear correlation were obtained. Inthe case of complex coding, it has been observed that the obtained complexcorrelation coefficients change with the permutation of the phases in thecomplex numbers used to code classes of elements with equal cardinalities. Itwas found that a necessary condition for linear correlation is the possibilityof linear ordering of a set with data. Since linear order is not possible inthe set of complex numbers, complex correlation coefficients cannot be used asa measure of linear correlation. In the event of such a situation, a substituteaction was suggested that would prevent equal cardinality of classes ofidentical elements contained in the set with nominal data. This action wouldconsist in the correction of data, analogous to the correction duringpreprocessing or cleaning of data containing missing or outlier values.

On the Analysis of Correlation Between Nominal Data and Numerical Data