<s>
The	O
sensitivity	B-Algorithm
index	I-Algorithm
or	O
discriminability	B-Algorithm
index	I-Algorithm
or	O
detectability	B-Algorithm
index	I-Algorithm
is	O
a	O
dimensionless	O
statistic	O
used	O
in	O
signal	O
detection	O
theory	O
.	O
</s>
<s>
The	O
discriminability	B-Algorithm
index	I-Algorithm
is	O
the	O
separation	O
between	O
the	O
means	O
of	O
two	O
distributions	O
(	O
typically	O
the	O
signal	O
and	O
the	O
noise	O
distributions	O
)	O
,	O
in	O
units	O
of	O
the	O
standard	O
deviation	O
.	O
</s>
<s>
This	O
is	O
the	O
maximum	O
(	O
Bayes-optimal	O
)	O
discriminability	B-Algorithm
index	I-Algorithm
for	O
two	O
distributions	O
,	O
based	O
on	O
the	O
amount	O
of	O
their	O
overlap	O
,	O
i.e.	O
</s>
<s>
can	O
also	O
be	O
computed	O
from	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
of	O
a	O
yes/no	O
task	O
between	O
two	O
univariate	O
normal	O
distributions	O
with	O
a	O
single	O
shifting	O
criterion	O
.	O
</s>
<s>
It	O
can	O
also	O
be	O
computed	O
from	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
of	O
any	O
two	O
distributions	O
(	O
in	O
any	O
number	O
of	O
variables	O
)	O
with	O
a	O
shifting	O
likelihood-ratio	O
,	O
by	O
locating	O
the	O
point	O
on	O
the	O
ROC	B-Algorithm
curve	I-Algorithm
that	O
is	O
farthest	O
from	O
the	O
diagonal	O
.	O
</s>
<s>
sub-optimal	O
)	O
discriminability	B-Algorithm
index	I-Algorithm
that	O
has	O
a	O
closed-form	O
is	O
to	O
take	O
the	O
average	O
of	O
the	O
variances	O
,	O
i.e.	O
</s>
<s>
It	O
is	O
times	O
the	O
-score	O
of	O
the	O
area	O
under	O
the	O
receiver	B-Algorithm
operating	I-Algorithm
characteristic	I-Algorithm
curve	I-Algorithm
(	O
AUC	O
)	O
of	O
a	O
single-criterion	O
observer	O
.	O
</s>
