<s>
In	O
statistics	O
,	O
one-way	B-General_Concept
analysis	I-General_Concept
of	I-General_Concept
variance	I-General_Concept
(	O
abbreviated	O
one-way	B-General_Concept
ANOVA	I-General_Concept
)	O
is	O
a	O
technique	O
that	O
can	O
be	O
used	O
to	O
compare	O
whether	O
two	O
sample	O
's	O
means	O
are	O
significantly	O
different	O
or	O
not	O
(	O
using	O
the	O
F	B-General_Concept
distribution	I-General_Concept
)	O
.	O
</s>
<s>
The	O
ANOVA	B-General_Concept
tests	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
which	O
states	O
that	O
samples	O
in	O
all	O
groups	O
are	O
drawn	O
from	O
populations	O
with	O
the	O
same	O
mean	O
values	O
.	O
</s>
<s>
The	O
ANOVA	B-General_Concept
produces	O
an	O
F-statistic	O
,	O
the	O
ratio	O
of	O
the	O
variance	O
calculated	O
among	O
the	O
means	O
to	O
the	O
variance	O
within	O
the	O
samples	O
.	O
</s>
<s>
Typically	O
,	O
however	O
,	O
the	O
one-way	B-General_Concept
ANOVA	I-General_Concept
is	O
used	O
to	O
test	O
for	O
differences	O
among	O
at	O
least	O
three	O
groups	O
,	O
since	O
the	O
two-group	O
case	O
can	O
be	O
covered	O
by	O
a	O
t-test	B-General_Concept
(	O
Gosset	O
,	O
1908	O
)	O
.	O
</s>
<s>
When	O
there	O
are	O
only	O
two	O
means	O
to	O
compare	O
,	O
the	O
t-test	B-General_Concept
and	O
the	O
F-test	B-General_Concept
are	O
equivalent	O
;	O
the	O
relation	O
between	O
ANOVA	B-General_Concept
and	O
t	O
is	O
given	O
by	O
F	O
=	O
t2	O
.	O
</s>
<s>
An	O
extension	O
of	O
one-way	B-General_Concept
ANOVA	I-General_Concept
is	O
two-way	B-General_Concept
analysis	I-General_Concept
of	I-General_Concept
variance	I-General_Concept
that	O
examines	O
the	O
influence	O
of	O
two	O
different	O
categorical	O
independent	O
variables	O
on	O
one	O
dependent	O
variable	O
.	O
</s>
<s>
The	O
results	O
of	O
a	O
one-way	B-General_Concept
ANOVA	I-General_Concept
can	O
be	O
considered	O
reliable	O
as	O
long	O
as	O
the	O
following	O
assumptions	O
are	O
met	O
:	O
</s>
<s>
If	O
data	O
are	O
ordinal	O
,	O
a	O
non-parametric	O
alternative	O
to	O
this	O
test	O
should	O
be	O
used	O
such	O
as	O
Kruskal	B-General_Concept
–	I-General_Concept
Wallis	I-General_Concept
one-way	I-General_Concept
analysis	I-General_Concept
of	I-General_Concept
variance	I-General_Concept
.	O
</s>
<s>
If	O
the	O
variances	O
are	O
not	O
known	O
to	O
be	O
equal	O
,	O
a	O
generalization	O
of	O
2-sample	O
Welch	B-General_Concept
's	I-General_Concept
t-test	I-General_Concept
can	O
be	O
used	O
.	O
</s>
<s>
ANOVA	B-General_Concept
is	O
a	O
relatively	O
robust	O
procedure	O
with	O
respect	O
to	O
violations	O
of	O
the	O
normality	O
assumption	O
.	O
</s>
<s>
The	O
one-way	B-General_Concept
ANOVA	I-General_Concept
can	O
be	O
generalized	O
to	O
the	O
factorial	O
and	O
multivariate	O
layouts	O
,	O
as	O
well	O
as	O
to	O
the	O
analysis	O
of	O
covariance	O
.	O
</s>
<s>
It	O
is	O
often	O
stated	O
in	O
popular	O
literature	O
that	O
none	O
of	O
these	O
F-tests	B-General_Concept
are	O
robust	O
when	O
there	O
are	O
severe	O
violations	O
of	O
the	O
assumption	O
that	O
each	O
population	O
follows	O
the	O
normal	O
distribution	O
,	O
particularly	O
for	O
small	O
alpha	O
levels	O
and	O
unbalanced	O
layouts	O
.	O
</s>
<s>
Furthermore	O
,	O
it	O
is	O
also	O
claimed	O
that	O
if	O
the	O
underlying	O
assumption	O
of	O
homoscedasticity	B-General_Concept
is	O
violated	O
,	O
the	O
Type	O
I	O
error	O
properties	O
degenerate	O
much	O
more	O
severely	O
.	O
</s>
<s>
He	O
showed	O
that	O
under	O
the	O
usual	O
departures	O
(	O
positive	O
skew	O
,	O
unequal	B-General_Concept
variances	I-General_Concept
)	O
"	O
the	O
F-test	B-General_Concept
is	O
conservative	O
"	O
,	O
and	O
so	O
it	O
is	O
less	O
likely	O
than	O
it	O
should	O
be	O
to	O
find	O
that	O
a	O
variable	O
is	O
significant	B-General_Concept
.	O
</s>
<s>
For	O
more	O
discussion	O
see	O
ANOVA	B-General_Concept
on	I-General_Concept
ranks	I-General_Concept
.	O
</s>
<s>
The	O
core	O
ANOVA	B-General_Concept
analysis	O
consists	O
of	O
a	O
series	O
of	O
calculations	O
.	O
</s>
<s>
A	O
computer	O
typically	O
determines	O
a	O
p-value	B-General_Concept
from	O
F	O
which	O
determines	O
whether	O
treatments	O
produce	O
significantly	O
different	O
results	O
.	O
</s>
<s>
If	O
the	O
result	O
is	O
significant	B-General_Concept
,	O
then	O
the	O
model	O
provisionally	O
has	O
validity	O
.	O
</s>
<s>
The	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
denoted	O
H0	O
,	O
for	O
the	O
overall	O
F-test	B-General_Concept
for	O
this	O
experiment	O
would	O
be	O
that	O
all	O
three	O
levels	O
of	O
the	O
factor	O
produce	O
the	O
same	O
response	O
,	O
on	O
average	O
.	O
</s>
<s>
To	O
calculate	O
the	O
F-ratio	B-General_Concept
:	O
</s>
<s>
Since	O
F	O
=	O
9.3>3.68	O
,	O
the	O
results	O
are	O
significant	B-General_Concept
at	O
the	O
5%	O
significance	B-General_Concept
level	I-General_Concept
.	O
</s>
<s>
One	O
would	O
not	O
accept	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
,	O
concluding	O
that	O
there	O
is	O
strong	O
evidence	O
that	O
the	O
expected	O
values	O
in	O
the	O
three	O
groups	O
differ	O
.	O
</s>
<s>
The	O
p-value	B-General_Concept
for	O
this	O
test	O
is	O
0.002	O
.	O
</s>
<s>
After	O
performing	O
the	O
F-test	B-General_Concept
,	O
it	O
is	O
common	O
to	O
carry	O
out	O
some	O
"	O
post-hoc	O
"	O
analysis	O
of	O
the	O
group	O
means	O
.	O
</s>
<s>
The	O
standard	B-General_Concept
error	I-General_Concept
of	O
each	O
of	O
these	O
differences	O
is	O
.	O
</s>
<s>
Thus	O
the	O
first	O
group	O
is	O
strongly	O
different	O
from	O
the	O
other	O
groups	O
,	O
as	O
the	O
mean	O
difference	O
is	O
more	O
than	O
3	O
times	O
the	O
standard	B-General_Concept
error	I-General_Concept
,	O
so	O
we	O
can	O
be	O
highly	O
confident	O
that	O
the	O
population	O
mean	O
of	O
the	O
first	O
group	O
differs	O
from	O
the	O
population	O
means	O
of	O
the	O
other	O
groups	O
.	O
</s>
<s>
However	O
,	O
there	O
is	O
no	O
evidence	O
that	O
the	O
second	O
and	O
third	O
groups	O
have	O
different	O
population	O
means	O
from	O
each	O
other	O
,	O
as	O
their	O
mean	O
difference	O
of	O
one	O
unit	O
is	O
comparable	O
to	O
the	O
standard	B-General_Concept
error	I-General_Concept
.	O
</s>
<s>
Note	O
F(x,y )	O
denotes	O
an	O
F-distribution	B-General_Concept
cumulative	O
distribution	O
function	O
with	O
x	O
degrees	O
of	O
freedom	O
in	O
the	O
numerator	O
and	O
y	O
degrees	O
of	O
freedom	O
in	O
the	O
denominator	O
.	O
</s>
