<s>
Exact	B-General_Concept
statistics	I-General_Concept
,	O
such	O
as	O
that	O
described	O
in	O
exact	B-General_Concept
test	I-General_Concept
,	O
is	O
a	O
branch	O
of	O
statistics	O
that	O
was	O
developed	O
to	O
provide	O
more	O
accurate	O
results	O
pertaining	O
to	O
statistical	O
testing	O
and	O
interval	O
estimation	O
by	O
eliminating	O
procedures	O
based	O
on	O
asymptotic	O
and	O
approximate	O
statistical	O
methods	O
.	O
</s>
<s>
Exact	O
statistical	O
methods	O
help	O
avoid	O
some	O
of	O
the	O
unreasonable	O
assumptions	O
of	O
traditional	O
statistical	O
methods	O
,	O
such	O
as	O
the	O
assumption	O
of	O
equal	O
variances	O
in	O
classical	O
ANOVA	B-General_Concept
.	O
</s>
<s>
They	O
also	O
allow	O
exact	B-General_Concept
inference	I-General_Concept
on	O
variance	B-General_Concept
components	I-General_Concept
of	O
mixed	B-General_Concept
models	I-General_Concept
.	O
</s>
<s>
When	O
exact	O
p-values	B-General_Concept
and	O
confidence	O
intervals	O
are	O
computed	O
under	O
a	O
certain	O
distribution	O
,	O
such	O
as	O
the	O
normal	O
distribution	O
,	O
then	O
the	O
underlying	O
methods	O
are	O
referred	O
to	O
as	O
exact	O
parametric	O
methods	O
.	O
</s>
<s>
For	O
advanced	O
methods	O
such	O
as	O
higher-way	O
ANOVA	B-General_Concept
regression	O
analysis	O
,	O
and	O
mixed	B-General_Concept
models	I-General_Concept
,	O
only	O
exact	O
parametric	O
methods	O
are	O
available	O
.	O
</s>
<s>
In	O
such	O
situations	O
,	O
the	O
asymptotic	O
p-values	B-General_Concept
may	O
differ	O
substantially	O
from	O
the	O
exact	O
p-values	B-General_Concept
.	O
</s>
<s>
All	O
classical	O
statistical	O
procedures	O
are	O
constructed	O
using	O
statistics	O
which	O
depend	O
only	O
on	O
observable	O
random	O
vectors	O
,	O
whereas	O
generalized	O
estimators	O
,	O
tests	O
,	O
and	O
confidence	O
intervals	O
used	O
in	O
exact	B-General_Concept
statistics	I-General_Concept
take	O
advantage	O
of	O
the	O
observable	O
random	O
vectors	O
and	O
the	O
observed	O
values	O
both	O
,	O
as	O
in	O
the	O
Bayesian	O
approach	O
but	O
without	O
having	O
to	O
treat	O
constant	O
parameters	O
as	O
random	O
variables	O
.	O
</s>
<s>
Exact	B-General_Concept
inferences	I-General_Concept
on	O
based	O
on	O
probabilities	O
and	O
expected	O
values	O
of	O
are	O
possible	O
because	O
its	O
distribution	O
and	O
the	O
observed	O
value	O
are	O
both	O
free	O
of	O
nuisance	O
parameters	O
.	O
</s>
<s>
Classical	O
statistical	O
methods	O
do	O
not	O
provide	O
exact	B-General_Concept
tests	I-General_Concept
to	O
many	O
statistical	O
problems	O
such	O
as	O
testing	O
Variance	B-General_Concept
Components	I-General_Concept
and	O
ANOVA	B-General_Concept
under	O
unequal	O
variances	O
.	O
</s>
<s>
To	O
rectify	O
this	O
situation	O
,	O
the	O
generalized	B-General_Concept
p-values	I-General_Concept
are	O
defined	O
as	O
an	O
extension	O
of	O
the	O
classical	O
p-values	B-General_Concept
so	O
that	O
one	O
can	O
perform	O
tests	O
based	O
on	O
exact	O
probability	O
statements	O
valid	O
for	O
any	O
sample	O
size	O
.	O
</s>
