<s>
In	O
statistics	O
,	O
a	O
generalized	B-General_Concept
p-value	I-General_Concept
is	O
an	O
extended	O
version	O
of	O
the	O
classical	O
p-value	B-General_Concept
,	O
which	O
except	O
in	O
a	O
limited	O
number	O
of	O
applications	O
,	O
provides	O
only	O
approximate	O
solutions	O
.	O
</s>
<s>
Conventional	O
statistical	O
methods	O
do	O
not	O
provide	O
exact	O
solutions	O
to	O
many	O
statistical	O
problems	O
,	O
such	O
as	O
those	O
arising	O
in	O
mixed	B-General_Concept
models	I-General_Concept
and	O
MANOVA	B-General_Concept
,	O
especially	O
when	O
the	O
problem	O
involves	O
a	O
number	O
of	O
nuisance	O
parameters	O
.	O
</s>
<s>
Use	O
of	O
approximate	O
and	O
asymptotic	O
methods	O
may	O
lead	O
to	O
misleading	O
conclusions	O
or	O
may	O
fail	O
to	O
detect	O
truly	O
significant	B-General_Concept
results	O
from	O
experiments	O
.	O
</s>
<s>
Tests	O
based	O
on	O
generalized	B-General_Concept
p-values	I-General_Concept
are	O
exact	O
statistical	O
methods	O
in	O
that	O
they	O
are	O
based	O
on	O
exact	O
probability	O
statements	O
.	O
</s>
<s>
While	O
conventional	O
statistical	O
methods	O
do	O
not	O
provide	O
exact	O
solutions	O
to	O
such	O
problems	O
as	O
testing	O
variance	B-General_Concept
components	I-General_Concept
or	O
ANOVA	B-General_Concept
under	O
unequal	O
variances	O
,	O
exact	O
tests	O
for	O
such	O
problems	O
can	O
be	O
obtained	O
based	O
on	O
generalized	B-General_Concept
p-values	I-General_Concept
.	O
</s>
<s>
In	O
order	O
to	O
overcome	O
the	O
shortcomings	O
of	O
the	O
classical	O
p-values	B-General_Concept
,	O
Tsui	O
and	O
Weerahandi	O
extended	O
the	O
classical	O
definition	O
so	O
that	O
one	O
can	O
obtain	O
exact	O
solutions	O
for	O
such	O
problems	O
as	O
the	O
Behrens	O
–	O
Fisher	O
problem	O
and	O
testing	O
variance	B-General_Concept
components	I-General_Concept
.	O
</s>
<s>
To	O
describe	O
the	O
idea	O
of	O
generalized	B-General_Concept
p-values	I-General_Concept
in	O
a	O
simple	O
example	O
,	O
consider	O
a	O
situation	O
of	O
sampling	O
from	O
a	O
normal	O
population	O
with	O
the	O
mean	O
,	O
and	O
the	O
variance	O
.	O
</s>
<s>
Therefore	O
,	O
a	O
test	O
of	O
a	O
hypothesis	O
with	O
a	O
one-sided	O
alternative	O
such	O
as	O
can	O
be	O
based	O
on	O
the	O
generalized	B-General_Concept
p-value	I-General_Concept
,	O
a	O
quantity	O
that	O
can	O
be	O
easily	O
evaluated	O
via	O
Monte	O
Carlo	O
simulation	O
or	O
using	O
the	O
non-central	O
t-distribution	O
.	O
</s>
