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.
