The Benefits of the Matthews Correlation Coefficient (MCC) over the Diagnostic Odds Ratio (DOR) in Binary Classification Assessment

To assess the quality of a binary classification, researchers often take advantage of a four-entry contingency table called confusion matrix, containing true positives, true negatives, false positives, and false negatives. To recap the four values of a confusion matrix in a unique score, researchers and statisticians have developed several rates and metrics. In the past, several scientific studies already showed why the Matthews correlation coefficient (MCC) is more informative and trustworthy than confusion-entropy error, accuracy, F1 score, bookmaker informedness, markedness, and balanced accuracy. In this study, we compare the MCC with the diagnostic odds ratio (DOR), a statistical rate employed sometimes in biomedical sciences. After examining the properties of the MCC and of the DOR, we describe the relationships between them, by also taking advantage of an innovative geometrical plot called confusion tetrahedron, presented here for the first time. We then report some use cases where the MCC and the DOR produce discordant outcomes, and explain why the Matthews correlation coefficient is more informative and reliable between the two. Our results can have a strong impact in computer science and statistics, because they clearly explain why the trustworthiness of the information provided by the Matthews correlation coefficient is higher than the one generated by the diagnostic odds ratio.