<s>
In	O
statistical	O
hypothesis	O
testing	O
,	O
the	O
null	B-General_Concept
distribution	I-General_Concept
is	O
the	O
probability	O
distribution	O
of	O
the	O
test	B-General_Concept
statistic	I-General_Concept
when	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
.	O
</s>
<s>
For	O
example	O
,	O
in	O
an	O
F-test	B-General_Concept
,	O
the	O
null	B-General_Concept
distribution	I-General_Concept
is	O
an	O
F-distribution	B-General_Concept
.	O
</s>
<s>
Null	B-General_Concept
distribution	I-General_Concept
is	O
a	O
tool	O
scientists	O
often	O
use	O
when	O
conducting	O
experiments	O
.	O
</s>
<s>
The	O
null	B-General_Concept
distribution	I-General_Concept
is	O
the	O
distribution	O
of	O
two	O
sets	O
of	O
data	O
under	O
a	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
If	O
the	O
results	O
of	O
the	O
two	O
sets	O
of	O
data	O
are	O
not	O
outside	O
the	O
parameters	O
of	O
the	O
expected	O
results	O
,	O
then	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
said	O
to	O
be	O
true	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
often	O
a	O
part	O
of	O
an	O
experiment	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
tries	O
to	O
show	O
that	O
among	O
two	O
sets	O
of	O
data	O
,	O
there	O
is	O
no	O
statistical	O
difference	O
between	O
the	O
results	O
of	O
doing	O
one	O
thing	O
as	O
opposed	O
to	O
doing	O
a	O
different	O
thing	O
.	O
</s>
<s>
The	O
scientist	O
would	O
use	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
to	O
test	O
the	O
health	O
of	O
the	O
hearts	O
of	O
people	O
who	O
walked	O
two	O
miles	O
a	O
day	O
against	O
the	O
health	O
of	O
the	O
hearts	O
of	O
the	O
people	O
who	O
walked	O
less	O
than	O
two	O
miles	O
a	O
day	O
.	O
</s>
<s>
If	O
there	O
was	O
no	O
difference	O
between	O
their	O
heart	O
rate	O
,	O
then	O
the	O
scientist	O
would	O
be	O
able	O
to	O
say	O
that	O
the	O
test	B-General_Concept
statistics	I-General_Concept
would	O
follow	O
the	O
null	B-General_Concept
distribution	I-General_Concept
.	O
</s>
<s>
In	O
the	O
procedure	O
of	O
hypothesis	O
testing	O
,	O
one	O
needs	O
to	O
form	O
the	O
joint	O
distribution	O
of	O
test	B-General_Concept
statistics	I-General_Concept
to	O
conduct	O
the	O
test	O
and	O
control	O
type	O
I	O
errors	O
.	O
</s>
<s>
However	O
,	O
the	O
true	O
distribution	O
is	O
often	O
unknown	O
and	O
a	O
proper	O
null	B-General_Concept
distribution	I-General_Concept
ought	O
to	O
be	O
used	O
to	O
represent	O
the	O
data	O
.	O
</s>
<s>
For	O
example	O
,	O
one	O
sample	O
and	O
two	O
samples	O
tests	O
of	O
means	O
can	O
use	O
t	O
statistics	O
which	O
have	O
Gaussian	O
null	B-General_Concept
distribution	I-General_Concept
,	O
while	O
F	B-General_Concept
statistics	I-General_Concept
,	O
testing	O
k	O
groups	O
of	O
population	O
means	O
,	O
which	O
have	O
Gaussian	O
quadratic	O
form	O
the	O
null	B-General_Concept
distribution	I-General_Concept
.	O
</s>
<s>
The	O
null	B-General_Concept
distribution	I-General_Concept
is	O
defined	O
as	O
the	O
asymptotic	O
distributions	O
of	O
null	O
quantile-transformed	O
test	B-General_Concept
statistics	I-General_Concept
,	O
based	O
on	O
marginal	O
null	B-General_Concept
distribution	I-General_Concept
.	O
</s>
<s>
During	O
practice	O
,	O
the	O
test	B-General_Concept
statistics	I-General_Concept
of	O
the	O
null	B-General_Concept
distribution	I-General_Concept
is	O
often	O
unknown	O
,	O
since	O
it	O
relies	O
on	O
the	O
unknown	O
data	O
generating	O
distribution	O
.	O
</s>
<s>
Resampling	O
procedures	O
,	O
such	O
as	O
non-parametric	O
or	O
model-based	O
bootstrap	B-Application
,	O
can	O
provide	O
consistent	O
estimators	O
for	O
the	O
null	B-General_Concept
distributions	I-General_Concept
.	O
</s>
<s>
Improper	O
choice	O
of	O
the	O
null	B-General_Concept
distribution	I-General_Concept
poses	O
significant	O
influence	O
on	O
type	O
I	O
error	O
and	O
power	B-General_Concept
properties	O
in	O
the	O
testing	O
process	O
.	O
</s>
<s>
Another	O
approach	O
to	O
obtain	O
the	O
test	B-General_Concept
statistics	I-General_Concept
null	B-General_Concept
distribution	I-General_Concept
is	O
to	O
use	O
the	O
data	O
of	O
generating	O
null	B-General_Concept
distribution	I-General_Concept
estimation	O
.	O
</s>
<s>
The	O
null	B-General_Concept
distribution	I-General_Concept
plays	O
a	O
crucial	O
role	O
in	O
large	O
scale	O
testing	O
.	O
</s>
<s>
Large	O
sample	O
size	O
allows	O
us	O
to	O
implement	O
a	O
more	O
realistic	O
empirical	O
null	B-General_Concept
distribution	I-General_Concept
.	O
</s>
<s>
Under	O
a	O
Bayesian	O
framework	O
,	O
the	O
large-scale	O
studies	O
allow	O
the	O
null	B-General_Concept
distribution	I-General_Concept
to	O
be	O
put	O
into	O
a	O
probabilistic	O
context	O
with	O
its	O
non-null	O
counterparts	O
.	O
</s>
<s>
When	O
sample	O
size	O
n	O
is	O
large	O
,	O
like	O
over	O
10	O
,	O
000	O
,	O
the	O
empirical	O
nulls	O
utilize	O
a	O
study	O
's	O
own	O
data	O
to	O
estimate	O
an	O
appropriate	O
null	B-General_Concept
distribution	I-General_Concept
.	O
</s>
<s>
The	O
important	O
assumption	O
is	O
that	O
due	O
to	O
the	O
large	O
proportion	O
of	O
null	O
cases	O
(	O
>	O
0.9	O
)	O
,	O
the	O
data	O
can	O
show	O
the	O
null	B-General_Concept
distribution	I-General_Concept
itself	O
.	O
</s>
<s>
In	O
addition	O
,	O
the	O
correlation	O
across	O
sampling	O
units	O
and	O
unobserved	O
covariates	O
may	O
lead	O
to	O
wrong	O
theoretical	O
null	B-General_Concept
distribution	I-General_Concept
.	O
</s>
<s>
Permutation	O
methods	O
are	O
frequently	O
used	O
in	O
multiple	O
testing	O
to	O
obtain	O
an	O
empirical	O
null	B-General_Concept
distribution	I-General_Concept
generated	O
from	O
data	O
.	O
</s>
