Youden's J statistic

Youden's J statistic (also called Youden's index) is a single statistic that captures the performance of a diagnostic test.

Definition

J = Sensitivity + Specificity − 1

with the two right-hand quantities being sensitivity and specificity. It is also known as deltap' [1] and generalizes from the dichotomous to the multiclass case as Informedness.[2]

An unrelated but more commonly used combination of basic statistics is the F-score, being the harmonic mean of recall and precision where recall = sensitivity = true positive rate, but specificity and precision are separate terms. The use of a single index is "not generally to be recommended",[3] but Informedness or Youden's index is the probability of an informed decision (as opposed to a random guess), and unlike F-score takes into account all cells of the contingency table and is thus a better choice in general. Youden's index like Cohen's Kappa is a chance corrected measure and is better interpretable across different problems and populations than easily biased measures like recall and precision, accuracy or F-score.[2]

Matthews correlation coefficient is the geometric mean of the regression coefficient of the problem and its dual, where the component regression coefficients of the Matthews correlation coefficient are Markedness (deltap) and Informedness (deltap'). Youden's index (dichotomous Informedness) also has a connection to Receiver Operating Characteristic analysis as the height above the chance line, and it is also equivalent to the Area under the Curve subtended by a single operating point.[2]

References

1. ^ Perruchet, P.; Peereman, R. (2004). "The exploitation of distributional information in syllable processing". J. Neurolinguistics 17: 97−119.
2. ^ a b c Powers, David M W (2007/2011). "Evaluation: From Precision, Recall and F-Score to ROC, Informedness, Markedness & Correlation". Journal of Machine Learning Technologies 2 (1): 37–63.
3. ^ Everitt B.S. (2002) The Cambridge Dictionary of Statistics. CUP ISBN 0-521-81099-X
• Youden W. J., "Index for rating diagnostic tests.", Cancer 1950; 3: 32-35