<s>
In	O
statistics	O
,	O
the	O
multinomial	B-General_Concept
test	I-General_Concept
is	O
the	O
test	O
of	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
that	O
the	O
parameters	O
of	O
a	O
multinomial	O
distribution	O
equal	O
specified	O
values	O
;	O
it	O
is	O
used	O
for	O
categorical	O
data	O
.	O
</s>
<s>
These	O
are	O
the	O
parameter	O
values	O
under	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
The	O
significance	O
probability	O
for	O
the	O
test	O
is	O
the	O
probability	O
of	O
occurrence	O
of	O
the	O
data	O
set	O
observed	O
,	O
or	O
of	O
a	O
data	O
set	O
less	O
likely	O
than	O
that	O
observed	O
,	O
if	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
.	O
</s>
<s>
In	O
practice	O
this	O
becomes	O
computationally	O
onerous	O
as	O
and	O
increase	O
so	O
it	O
is	O
probably	O
only	O
worth	O
using	O
exact	B-General_Concept
tests	I-General_Concept
for	O
small	O
samples	O
.	O
</s>
<s>
One	O
of	O
these	O
approximations	O
is	O
the	O
likelihood	B-General_Concept
ratio	I-General_Concept
.	O
</s>
<s>
If	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
,	O
then	O
as	O
increases	O
,	O
the	O
distribution	O
of	O
converges	O
to	O
that	O
of	O
chi-squared	O
with	O
degrees	O
of	O
freedom	O
.	O
</s>
<s>
In	O
the	O
special	O
case	O
where	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
that	O
all	O
the	O
values	O
are	O
equal	O
to	O
(	O
i.e.	O
</s>
<s>
where	O
is	O
the	O
expected	O
number	O
of	O
cases	O
in	O
category	O
under	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
This	O
statistic	O
also	O
converges	O
to	O
a	O
chi-squared	O
distribution	O
with	O
degrees	O
of	O
freedom	O
when	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
true	O
but	O
does	O
so	O
from	O
below	O
,	O
as	O
it	O
were	O
,	O
rather	O
than	O
from	O
above	O
as	O
does	O
,	O
so	O
may	O
be	O
preferable	O
to	O
the	O
uncorrected	O
version	O
of	O
for	O
small	O
samples	O
.	O
</s>
