J = (true_positives x true_negatives - false_positives x false_negatives) / (positives x negatives)

where positives and negatives are the number of real positive and real negative samples.

Its value ranges from 0 through 1 (inclusive)


This is simply a result of assuming that the test/classifier performs better than with its answers swapped. As it is said in the original paper (Youden, 1950):

1. The possible range of values for the 
index is from zero to one inclusive. (It is 
expected that the test will show a greater 
proportion of positive results for the diseased 
group than for the control.) 

But theoretically Youden's J statistic can be negative and whether the test/classifier needs class-swapping that's another issue I would say.

Why is this assumption assumed by default? For me it is not so obvious.


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