<s>
In	O
statistics	O
,	O
expected	B-General_Concept
mean	I-General_Concept
squares	I-General_Concept
(	O
EMS	O
)	O
are	O
the	O
expected	O
values	O
of	O
certain	O
statistics	O
arising	O
in	O
partitions	O
of	O
sums	O
of	O
squares	O
in	O
the	O
analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
(	O
ANOVA	B-General_Concept
)	O
.	O
</s>
<s>
They	O
can	O
be	O
used	O
for	O
ascertaining	O
which	O
statistic	O
should	O
appear	O
in	O
the	O
denominator	O
in	O
an	O
F-test	B-General_Concept
for	O
testing	O
a	O
null	B-General_Concept
hypothesis	I-General_Concept
that	O
a	O
particular	O
effect	O
is	O
absent	O
.	O
</s>
<s>
When	O
the	O
total	O
corrected	O
sum	O
of	O
squares	O
in	O
an	O
ANOVA	B-General_Concept
is	O
partitioned	O
into	O
several	O
components	O
,	O
each	O
attributed	O
to	O
the	O
effect	O
of	O
a	O
particular	O
predictor	O
variable	O
,	O
each	O
of	O
the	O
sums	O
of	O
squares	O
in	O
that	O
partition	O
is	O
a	O
random	O
variable	O
that	O
has	O
an	O
expected	O
value	O
.	O
</s>
<s>
That	O
expected	O
value	O
divided	O
by	O
the	O
corresponding	O
number	O
of	O
degrees	O
of	O
freedom	O
is	O
the	O
expected	B-General_Concept
mean	I-General_Concept
square	I-General_Concept
for	O
that	O
predictor	O
variable	O
.	O
</s>
<s>
The	O
ANOVA	B-General_Concept
table	O
below	O
partitions	O
the	O
sum	O
of	O
squares	O
(	O
where	O
)	O
:	O
</s>
<s>
A	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
interest	O
is	O
that	O
there	O
is	O
no	O
difference	O
between	O
effects	O
of	O
different	O
treatments	O
—	O
thus	O
no	O
difference	O
among	O
treatment	O
means	O
.	O
</s>
