An intuitive general rank-based correlation coefficient

Correlation analysis is an effective mechanism for studying patterns in data and making predictions. Many interesting discoveries have been made by formulating correlations in seemingly unrelated data. We propose an algorithm to quantify the theory of correlations and to give an intuitive, more accurate correlation coefficient. We propose a predictive metric to calculate correlations between paired values, known as the general rank-based correlation coefficient. It fulfills the five basic criteria of a predictive metric: independence from sample size, value between -1 and 1, measuring the degree of monotonicity, insensitivity to outliers, and intuitive demonstration. Furthermore, the metric has been validated by performing experiments using a real-time dataset and random number simulations. Mathematical derivations of the proposed equations have also been provided. We have compared it to Spearman's rank correlation coefficient. The comparison results show that the proposed metric fares better than the existing metric on all the predictive metric criteria.