Fig. 4

Plots of \(\text {MCC}_{\text {TNR},\text {TPR}}(p)\) for different values of \(\text {TNR}\) and \(\text {TPR}\) with \(\text {TNR}+\text {TPR} > 1\). The behaviour of MCC as a function of the prevalence p depends on the particular pair \((\text {TNR},\text {TPR})\); the curve tends to be more symmetric when values of \(\text {TNR}\) and \(\text {TPR}\) are similar, and MCC values are high when \(\text {TNR}\) and \(\text {TPR}\) are high. In the current plot we show three examples: one symmetric with low \(\text {TNR}\) and \(\text {TPR}\) values (red line), and two asymmetric curves, the former where both rates are high (black) and the latter where one one rate is high (blue). Due to the symmetry in the \(\text {MCC}_{\text {TNR},\text {TPR}}(p)\) equation, we can restrict the display to the case \(\text {TNR}+\text {TPR} > 1\). Finally, the non-linearity of the same equation prevents from predicting more precise features of the MCC behaviour in terms of \(p,\text {TNR},\text {TPR}\)