How this calculator works
The rate relationship can also recover sensitivity or specificity when the result remains between zero and one. Youden J adds sensitivity and specificity and subtracts one. It is the vertical separation between a threshold point and the chance diagonal on an ROC curve. Equal importance is assigned to both classes. A value of one indicates perfect separation at that threshold, zero matches the chance diagonal, and negative values indicate reversed separation. This index does not incorporate prevalence, predictive values or the consequences of false results. Maximising it on the same data can overstate future performance.
Formula
J = sensitivity + specificity - 1 = TPR - FPR. Balanced accuracy = (J + 1)/2.
Worked example
Sensitivity 80% and specificity 90% give J = 0.7 and balanced accuracy 85%. With 50% sensitivity and 50% specificity, J = 0.
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Frequently asked questions
Does a larger J always imply a better decision threshold?
It gives equal weight to sensitivity and specificity. A real decision may attach different costs to false positives and false negatives.
Does prevalence enter the formula?
No. Sensitivity and specificity condition on the true class. Predictive values and expected consequences also depend on prevalence.
Can J be negative?
Yes. Values range from -1 to 1. A negative result suggests the classifier points in the opposite direction at that threshold.