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On the analysis of correlation between nominal data and numerical data

Gniazdowski Zenon

Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki

2022

nr 27

57--82

The article investigates the possibility of measuring the strength of a linear corre lation relationship between nominal data and numerical data. Correlation coeffi cients for variables coded with real numbers as well as for variables coded with complex numbers were studied. For variables coded with real numbers, unam biguous measures of real linear correlation were obtained. In the case of complex coding, it has been observed that the obtained complex correlation coefficients change with the permutation of the phases in the complex numbers used to code classes of elements with equal cardinalities. It was found that a necessary condi tion for linear correlation is the possibility of linear ordering of a set with data. Since linear order is not possible in the set of complex numbers, complex correla tion coefficients cannot be used as a measure of linear correlation. In the event of such a situation, a substitute action was suggested that would prevent equal cardi nality of classes of identical elements contained in the set with nominal data. This action would consist in the correction of data, analogous to the correction during preprocessing or cleaning of data containing missing or outlier values.