A receiver operating characteristic curve, or ROC curve, plots the sensitivity of a binary diagnostic test or classifier against its false-positive rate as the
decision threshold varies. If 
is the specificity, then the
false-positive rate is 
.
Thus the horizontal and vertical coordinates of a point on the curve are respectively
and sensitivity.
An ideal test reaches the upper left corner 
.
A test with equal true- and false-positive rates lies on the diagonal. Youden's
J statistic is the greatest vertical distance between the curve and this
diagonal.
