I am interested in determining the classification accuracy of an outcome (binary DV - whether a participant has capacity or not to make a legal decision) based on a continuous variable (score on a cognitive test, i.e., Mini-Mental Status Examination (scores 0-30)).

Logistic regression in SPSS automatically selects a 'cut-point' of 0.5. This can be customised to different values. The default is 0.5; I am interested in knowing how SPSS achieves the cut-point (i.e., is this the median score on the IV, or a goodness-of-fit test?).

I have plotted a ROC curve, and am aware of trading sensitivity with specificity, but cannot see, in my data, where the 0.5 corresponds to on this graph.

Thanking you in advance for your consideration.