For one of my binary classification models, I have observed this (Simpson's Rule-esque) paradox. The AUC on the test set as a whole is 0.8.
Gender is one of the model's features. So I decided to produce a "bias" report, for which I calculated AUCs for each of the Male and Female subgroups. But I noticed that each of these AUCs is around 0.7. How is this possible, given that the overall test AUC is 0.8? (In my dataset, every data point belongs to either the Male or the Female subgroup.) I don't expect the overall AUC to simply be a (weighted) linear combination of AUCs for the individual strata.
I'm hoping to get both a technical/mathematical answer and a high-level explanation. Please let me know if any further information is needed (if you think I should plot the overall, Male, and Female ROC curves, for instance). Thank you!