About one approach to calculating the rank correlation. Part I

Abstract

When calculating the rank correlation, the same situation arises as in some other subject areas: researchers have the opinion that new possible constructions in this subject area are either impossible (everything has already been done), or are not needed. In the article, we try to show that further theoretical developments are possible, which can lead to quite interesting practical results. We propose our own version of calculating the rank correlation coefficient, which (in its simplest form) can be considered “located between” the Kendall and Spearman coefficients. More specifically, we use not only the conditions for the coincidence of the results of predicates that determine the order of the elements of the corresponding pairs (as in calculating the Kendall coefficient), and not only a generalization of the general version of calculating the pair correlation in the case of rank (as in calculating the Spearman coefficient), but both of these techniques together. We use the obtained formulas to calculate different variants of rank correlation coefficients in several different subject areas, and try to justify by reasoning that the criterion we propose is quite successful. We also propose options for generalizing our criterion, and we believe that these possible generalizations do not coincide with the generalizations given in classical monographs (but they do not contradict them, but complement them).