A statistical comparison between Matthews correlation coefficient (MCC), prevalence threshold, and Fowlkes-Mallows index

Even if assessing binary classifications is a common task in scientific research, no consensus on a single statistic summarizing the confusion matrix has been reached so far. In recent studies, we demonstrated the advantages of the Matthews correlation coefficient (MCC) over other popular rates such as cross-entropy error, F1 score, accuracy, balanced accuracy, bookmaker informedness, diagnostic odds ratio, Brier score, and Cohen's kappa. In this study, we compared the MCC to other two statistics: prevalence threshold (PT), frequently used in obstetrics and gynecology, and Fowlkes-Mallows index, a metric employed in fuzzy logic and drug discovery. Through the investigation of the mutual relations among three metrics and the study of some relevant use cases, we show that, when positive data elements and negative data elements have the same importance, the Matthews correlation coefficient can be more informative than its two competitors, even this time.