Youden's J statistic

Youden's J statistic (also called Youden's index) is a single statistic that captures the performance of a dichotomous diagnostic test. Informedness is its generalization to the multiclass case and estimates the probability of an informed decision.

with the two right-hand quantities being sensitivity and specificity. Thus the expanded formula is:

${\displaystyle J={true\_positives \over true\_positives+false\_negatives}+{true\_negatives \over true\_negatives+false\_positives}-1}$

The index was suggested by W.J. Youden in 1950 as a way of summarising the performance of a diagnostic test. Its value ranges from -1 to 1, and has a zero value when a diagnostic test gives the same proportion of positive results for groups with and without the disease, i.e the test is useless. A value of 1 indicates that there are no false positives or false negatives, i.e. the test is perfect. The index gives equal weight to false positive and false negative values, so all tests with the same value of the index give the same proportion of total misclassified results.

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