<s>
In	O
statistics	O
,	O
the	O
multivariate	B-General_Concept
Behrens	I-General_Concept
–	I-General_Concept
Fisher	I-General_Concept
problem	I-General_Concept
is	O
the	O
problem	O
of	O
testing	O
for	O
the	O
equality	O
of	O
means	O
from	O
two	O
multivariate	O
normal	O
distributions	O
when	O
the	O
covariance	O
matrices	O
are	O
unknown	O
and	O
possibly	O
not	O
equal	O
.	O
</s>
<s>
Since	O
this	O
is	O
a	O
generalization	O
of	O
the	O
univariate	O
Behrens-Fisher	B-Algorithm
problem	I-Algorithm
,	O
it	O
inherits	O
all	O
of	O
the	O
difficulties	O
that	O
arise	O
in	O
the	O
univariate	O
problem	O
.	O
</s>
<s>
The	O
multivariate	B-General_Concept
Behrens	I-General_Concept
–	I-General_Concept
Fisher	I-General_Concept
problem	I-General_Concept
is	O
to	O
test	O
the	O
null	O
hypothesis	O
that	O
the	O
means	O
are	O
equal	O
versus	O
the	O
alternative	O
of	O
non-equality	O
:	O
</s>
<s>
In	O
the	O
case	O
where	O
the	O
dispersion	O
matrices	O
are	O
equal	O
,	O
the	O
distribution	O
of	O
the	O
statistic	O
is	O
known	O
to	O
be	O
an	O
F	B-General_Concept
distribution	I-General_Concept
under	O
the	O
null	O
and	O
a	O
noncentral	O
F-distribution	B-General_Concept
under	O
the	O
alternative	O
.	O
</s>
<s>
Use	O
generalized	B-General_Concept
p-values	I-General_Concept
based	O
on	O
generalized	B-General_Concept
test	I-General_Concept
variables	I-General_Concept
.	O
</s>
