Explainable Correlation of Categorical Data and Bar Charts

We propose a method of calculating the correlation between frequency distributions defined on a finite set of categories. The method is based on the general approach to constructing an invertible correlation function on a set with involutive operation. This correlation function is constructed using a suitable similarity (or dissimilarity) function defined on such a set. For constructing a correlation function on the set of frequency distributions, we use the recently introduced involutive negation of probability distributions and a suitable dissimilarity function between them. Surprisingly, the obtained correlation function coincides with the Pearson correlation coefficient. The proposed approach is illustrated in an example of calculating the correlation between categories of a categorical variable corresponding to strings of a contingency table. The traditional graphical interpretation of the Pearson correlation by linear regression gives an explanation of obtained correlations.