Youden's 
statistic, also called the Youden index, summarizes the performance of a binary diagnostic
test. It is defined by
 |
Here sensitivity is the probability of a positive result when the condition is present, and specificity
is the probability of a negative result when the condition is absent. The statistic
ranges from 
to 1; a perfect test has 
, while a test with equal true- and false-positive rates
has 
.
For a test based on a continuous score, maximizing 
over possible thresholds gives the point on the receiver
operating characteristic curve having the greatest vertical distance above the
diagonal.
