<s>
In	O
statistics	O
,	O
the	O
strictly	B-General_Concept
standardized	I-General_Concept
mean	I-General_Concept
difference	I-General_Concept
(	O
SSMD	B-General_Concept
)	O
is	O
a	O
measure	O
of	O
effect	B-Application
size	I-Application
.	O
</s>
<s>
It	O
is	O
the	O
mean	O
divided	O
by	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
a	O
difference	O
between	O
two	O
random	O
values	O
each	O
from	O
one	O
of	O
two	O
groups	O
.	O
</s>
<s>
in	O
high-throughput	O
screening	O
(	O
HTS	O
)	O
and	O
has	O
become	O
a	O
statistical	O
parameter	O
measuring	O
effect	B-Application
sizes	I-Application
for	O
the	O
comparison	O
of	O
any	O
two	O
groups	O
with	O
random	O
values	O
.	O
</s>
<s>
Signal-to-noise	O
ratio	O
(	O
S/N	O
)	O
,	O
signal-to-background	O
ratio	O
(	O
S/B	O
)	O
,	O
and	O
the	O
Z-factor	B-General_Concept
have	O
been	O
adopted	O
to	O
evaluate	O
the	O
quality	O
of	O
HTS	O
assays	O
through	O
the	O
comparison	O
of	O
two	O
investigated	O
types	O
of	O
wells	O
.	O
</s>
<s>
proposed	O
the	O
Z-factor	B-General_Concept
.	O
</s>
<s>
The	O
advantage	O
of	O
the	O
Z-factor	B-General_Concept
over	O
the	O
S/N	O
and	O
S/B	O
is	O
that	O
it	O
takes	O
into	O
account	O
the	O
variabilities	O
in	O
both	O
compared	O
groups	O
.	O
</s>
<s>
As	O
a	O
result	O
,	O
the	O
Z-factor	B-General_Concept
has	O
been	O
broadly	O
used	O
as	O
a	O
QC	O
metric	O
in	O
HTS	O
assays	O
.	O
</s>
<s>
The	O
absolute	O
sign	O
in	O
the	O
Z-factor	B-General_Concept
makes	O
it	O
inconvenient	O
to	O
derive	O
its	O
statistical	O
inference	O
mathematically	O
.	O
</s>
<s>
proposed	O
SSMD	B-General_Concept
to	O
evaluate	O
the	O
differentiation	O
between	O
a	O
positive	O
control	O
and	O
a	O
negative	O
control	O
in	O
HTS	O
assays	O
.	O
</s>
<s>
SSMD	B-General_Concept
has	O
a	O
probabilistic	O
basis	O
due	O
to	O
its	O
strong	O
link	O
with	O
d+	O
-probability	O
(	O
i.e.	O
,	O
the	O
probability	O
that	O
the	O
difference	O
between	O
two	O
groups	O
is	O
positive	O
)	O
.	O
</s>
<s>
Supported	O
on	O
its	O
probabilistic	O
basis	O
,	O
SSMD	B-General_Concept
has	O
been	O
used	O
for	O
both	O
quality	O
control	O
and	O
hit	O
selection	O
in	O
high-throughput	O
screening	O
.	O
</s>
<s>
As	O
a	O
statistical	O
parameter	O
,	O
SSMD	B-General_Concept
(	O
denoted	O
as	O
)	O
is	O
defined	O
as	O
the	O
ratio	O
of	O
mean	O
to	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
the	O
difference	O
of	O
two	O
random	O
values	O
respectively	O
from	O
two	O
groups	O
.	O
</s>
<s>
In	O
the	O
situation	O
where	O
the	O
two	O
groups	O
are	O
correlated	O
,	O
a	O
commonly	O
used	O
strategy	O
to	O
avoid	O
the	O
calculation	O
of	O
is	O
first	O
to	O
obtain	O
paired	O
observations	O
from	O
the	O
two	O
groups	O
and	O
then	O
to	O
estimate	O
SSMD	B-General_Concept
based	O
on	O
the	O
paired	O
observations	O
.	O
</s>
<s>
derived	O
the	O
maximum-likelihood	O
estimate	O
(	O
MLE	O
)	O
and	O
method-of-moment	O
(	O
MM	O
)	O
estimate	O
of	O
SSMD	B-General_Concept
.	O
</s>
<s>
(	O
UMVUE	O
)	O
of	O
SSMD	B-General_Concept
is	O
,	O
</s>
<s>
SSMD	B-General_Concept
looks	O
similar	O
to	O
t-statistic	O
and	O
Cohen	O
's	O
d	O
,	O
but	O
they	O
are	O
different	O
with	O
one	O
another	O
as	O
illustrated	O
in	O
.	O
</s>
<s>
SSMD	B-General_Concept
is	O
the	O
ratio	O
of	O
mean	O
to	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
the	O
difference	O
between	O
two	O
groups	O
.	O
</s>
<s>
When	O
the	O
data	O
is	O
preprocessed	O
using	O
log-transformation	O
as	O
we	O
normally	O
do	O
in	O
HTS	O
experiments	O
,	O
SSMD	B-General_Concept
is	O
the	O
mean	O
of	O
log	O
fold	O
change	O
divided	O
by	O
the	O
standard	B-General_Concept
deviation	I-General_Concept
of	O
log	O
fold	O
change	O
with	O
respect	O
to	O
a	O
negative	O
reference	O
.	O
</s>
<s>
SSMD	B-General_Concept
directly	O
measures	O
the	O
magnitude	O
of	O
difference	O
between	O
two	O
groups	O
.	O
</s>
<s>
Therefore	O
,	O
SSMD	B-General_Concept
can	O
be	O
used	O
for	O
both	O
quality	O
control	O
and	O
hit	O
selection	O
in	O
HTS	O
experiments	O
.	O
</s>
<s>
where	O
are	O
the	O
medians	O
and	O
median	B-General_Concept
absolute	I-General_Concept
deviations	I-General_Concept
in	O
the	O
positive	O
and	O
negative	O
controls	O
,	O
respectively	O
.	O
</s>
<s>
The	O
Z-factor	B-General_Concept
based	O
QC	O
criterion	O
is	O
popularly	O
used	O
in	O
HTS	O
assays	O
.	O
</s>
<s>
Applying	O
the	O
same	O
Z-factor-based	O
QC	O
criteria	O
to	O
both	O
controls	O
leads	O
to	O
inconsistent	O
results	O
as	O
illustrated	O
in	O
the	O
literatures	O
.	O
</s>
<s>
The	O
SSMD-based	O
QC	O
criteria	O
listed	O
in	O
the	O
following	O
table	O
take	O
into	O
account	O
the	O
effect	B-Application
size	I-Application
of	O
a	O
positive	O
control	O
in	O
an	O
HTS	O
assay	O
where	O
the	O
positive	O
control	O
(	O
such	O
as	O
an	O
inhibition	O
control	O
)	O
theoretically	O
has	O
values	O
less	O
than	O
the	O
negative	O
reference	O
.	O
</s>
<s>
In	O
application	O
,	O
if	O
the	O
effect	B-Application
size	I-Application
of	O
a	O
positive	O
control	O
is	O
known	O
biologically	O
,	O
adopt	O
the	O
corresponding	O
criterion	O
based	O
on	O
this	O
table	O
.	O
</s>
<s>
Similar	O
SSMD-based	O
QC	O
criteria	O
can	O
be	O
constructed	O
for	O
an	O
HTS	O
assay	O
where	O
the	O
positive	O
control	O
(	O
such	O
as	O
an	O
activation	O
control	O
)	O
theoretically	O
has	O
values	O
greater	O
than	O
the	O
negative	O
reference	O
.	O
</s>
<s>
More	O
details	O
about	O
how	O
to	O
apply	O
SSMD-based	O
QC	O
criteria	O
in	O
HTS	O
experiments	O
can	O
be	O
found	O
in	O
a	O
book	O
.	O
</s>
<s>
SSMD	B-General_Concept
can	O
not	O
only	O
rank	O
the	O
size	O
of	O
effects	O
but	O
also	O
classify	O
effects	O
as	O
shown	O
in	O
the	O
following	O
table	O
based	O
on	O
the	O
population	O
value	O
(	O
)	O
of	O
SSMD	B-General_Concept
.	O
</s>
<s>
The	O
estimation	O
of	O
SSMD	B-General_Concept
for	O
screens	O
without	O
replicates	O
differs	O
from	O
that	O
for	O
screens	O
with	O
replicates	O
.	O
</s>
<s>
In	O
many	O
cases	O
,	O
scientists	O
may	O
use	O
both	O
SSMD	B-General_Concept
and	O
average	O
fold	O
change	O
for	O
hit	O
selection	O
in	O
HTS	O
experiments	O
.	O
</s>
