<s>
Analysis	B-General_Concept
of	I-General_Concept
covariance	I-General_Concept
(	O
ANCOVA	B-General_Concept
)	O
is	O
a	O
general	O
linear	O
model	O
which	O
blends	O
ANOVA	B-General_Concept
and	O
regression	O
.	O
</s>
<s>
ANCOVA	B-General_Concept
evaluates	O
whether	O
the	O
means	O
of	O
a	O
dependent	O
variable	O
(	O
DV	O
)	O
are	O
equal	O
across	O
levels	O
of	O
a	O
categorical	O
independent	O
variable	O
(	O
IV	O
)	O
often	O
called	O
a	O
treatment	O
,	O
while	O
statistically	O
controlling	O
for	O
the	O
effects	O
of	O
other	O
continuous	O
variables	O
that	O
are	O
not	O
of	O
primary	O
interest	O
,	O
known	O
as	O
covariates	O
(	O
CV	O
)	O
or	O
nuisance	O
variables	O
.	O
</s>
<s>
Mathematically	O
,	O
ANCOVA	B-General_Concept
decomposes	O
the	O
variance	O
in	O
the	O
DV	O
into	O
variance	O
explained	O
by	O
the	O
CV(s )	O
,	O
variance	O
explained	O
by	O
the	O
categorical	O
IV	O
,	O
and	O
residual	O
variance	O
.	O
</s>
<s>
Intuitively	O
,	O
ANCOVA	B-General_Concept
can	O
be	O
thought	O
of	O
as	O
'	O
adjusting	O
 '	O
the	O
DV	O
by	O
the	O
group	O
means	O
of	O
the	O
CV(s )	O
.	O
</s>
<s>
The	O
ANCOVA	B-General_Concept
model	O
assumes	O
a	O
linear	O
relationship	O
between	O
the	O
response	O
(	O
DV	O
)	O
and	O
covariate	O
(	O
CV	O
)	O
:	O
</s>
<s>
ANCOVA	B-General_Concept
can	O
be	O
used	O
to	O
increase	O
statistical	B-General_Concept
power	I-General_Concept
(	O
the	O
probability	O
a	O
significant	B-General_Concept
difference	I-General_Concept
is	O
found	O
between	O
groups	O
when	O
one	O
exists	O
)	O
by	O
reducing	O
the	O
within-group	O
error	O
variance	O
.	O
</s>
<s>
In	O
order	O
to	O
understand	O
this	O
,	O
it	O
is	O
necessary	O
to	O
understand	O
the	O
test	O
used	O
to	O
evaluate	O
differences	O
between	O
groups	O
,	O
the	O
F-test	B-General_Concept
.	O
</s>
<s>
The	O
F-test	B-General_Concept
is	O
computed	O
by	O
dividing	O
the	O
explained	O
variance	O
between	O
groups	O
(	O
e.g.	O
,	O
medical	O
recovery	O
differences	O
)	O
by	O
the	O
unexplained	O
variance	O
within	O
the	O
groups	O
.	O
</s>
<s>
If	O
this	O
value	O
is	O
larger	O
than	O
a	O
critical	O
value	O
,	O
we	O
conclude	O
that	O
there	O
is	O
a	O
significant	B-General_Concept
difference	I-General_Concept
between	O
groups	O
.	O
</s>
<s>
Another	O
use	O
of	O
ANCOVA	B-General_Concept
is	O
to	O
adjust	O
for	O
preexisting	O
differences	O
in	O
nonequivalent	O
(	O
intact	O
)	O
groups	O
.	O
</s>
<s>
There	O
are	O
several	O
key	O
assumptions	O
that	O
underlie	O
the	O
use	O
of	O
ANCOVA	B-General_Concept
and	O
affect	O
interpretation	O
of	O
the	O
results	O
.	O
</s>
<s>
The	O
fifth	O
issue	O
,	O
concerning	O
the	O
homogeneity	O
of	O
different	O
treatment	O
regression	O
slopes	O
is	O
particularly	O
important	O
in	O
evaluating	O
the	O
appropriateness	O
of	O
ANCOVA	B-General_Concept
model	O
.	O
</s>
<s>
Tested	O
by	O
Levene	B-General_Concept
's	I-General_Concept
test	I-General_Concept
of	O
equality	O
of	O
error	O
variances	O
.	O
</s>
<s>
To	O
see	O
if	O
the	O
CV	O
significantly	O
interacts	O
with	O
the	O
IV	O
,	O
run	O
an	O
ANCOVA	B-General_Concept
model	O
including	O
both	O
the	O
IV	O
and	O
the	O
CVxIV	O
interaction	O
term	O
.	O
</s>
<s>
If	O
the	O
CVxIV	O
interaction	O
is	O
significant	O
,	O
ANCOVA	B-General_Concept
should	O
not	O
be	O
performed	O
.	O
</s>
<s>
If	O
the	O
CV×IV	O
interaction	O
is	O
not	O
significant	O
,	O
rerun	O
the	O
ANCOVA	B-General_Concept
without	O
the	O
CV×IV	O
interaction	O
term	O
.	O
</s>
<s>
If	O
there	O
was	O
a	O
significant	O
main	B-General_Concept
effect	I-General_Concept
,	O
it	O
means	O
that	O
there	O
is	O
a	O
significant	B-General_Concept
difference	I-General_Concept
between	O
the	O
levels	O
of	O
one	O
IV	O
,	O
ignoring	O
all	O
other	O
factors	O
.	O
</s>
<s>
To	O
find	O
exactly	O
which	O
levels	O
are	O
significantly	O
different	O
from	O
one	O
another	O
,	O
one	O
can	O
use	O
the	O
same	O
follow-up	O
tests	O
as	O
for	O
the	O
ANOVA	B-General_Concept
.	O
</s>
<s>
One	O
can	O
investigate	O
the	O
simple	O
main	B-General_Concept
effects	I-General_Concept
using	O
the	O
same	O
methods	O
as	O
in	O
a	O
factorial	B-General_Concept
ANOVA	I-General_Concept
.	O
</s>
<s>
While	O
the	O
inclusion	O
of	O
a	O
covariate	O
into	O
an	O
ANOVA	B-General_Concept
generally	O
increases	O
statistical	B-General_Concept
power	I-General_Concept
by	O
accounting	O
for	O
some	O
of	O
the	O
variance	O
in	O
the	O
dependent	O
variable	O
and	O
thus	O
increasing	O
the	O
ratio	O
of	O
variance	O
explained	O
by	O
the	O
independent	O
variables	O
,	O
adding	O
a	O
covariate	O
into	O
ANOVA	B-General_Concept
also	O
reduces	O
the	O
degrees	O
of	O
freedom	O
.	O
</s>
