discriminabilityyn

Discriminabilityyn is a proposed statistical measure intended to quantify how well two classes or conditions can be distinguished in a dataset under a given model, with explicit normalization for noise and prevalence. It is related to established concepts such as discriminability, Youden’s index, and signal detection metrics, but introduces a normalization factor denoted by n to enable cross-dataset comparisons when noise levels differ. The term is not widely standardized and may be defined differently in various studies.

The term discriminabilityyn is a coinage used to describe a generic, noise-adjusted notion of discriminability in binary classification tasks. It is applicable across domains such as medical imaging, cognitive experiments, and sensor data analysis, wherever researchers seek to compare discrimination performance while accounting for dataset-specific noise.

Calculation and interpretation commonly involve a threshold-based classifier. A typical formulation is D_disyn = max_theta (TPR(theta) − FPR(theta)) / n, where TPR and FPR are true and false positive rates at threshold theta, and n is a positive normalization constant reflecting measurement noise or uncertainty. Alternative implementations may use related, n-normalized metrics such as a normalized area under the ROC curve or a weighted Youden’s index. In practice, D_disyn is estimated from a held-out evaluation set to avoid optimistic bias, and higher values indicate stronger discriminability with consistent comparison conditions when n is fixed.

Relation to other metrics and limitations: it shares goals with ROC AUC, Youden’s J, and d-prime but differs by its explicit normalization for noise. Limitations include sensitivity to the choice of n, thresholding strategy, and dataset representativeness. Researchers should report the chosen n and estimation method when presenting discriminabilityyn scores. See also discriminability, ROC AUC, Youden’s index, and d’ (signal detection theory).