<s>
In	O
statistics	O
,	O
Tukey	B-General_Concept
's	I-General_Concept
test	I-General_Concept
of	I-General_Concept
additivity	I-General_Concept
,	O
named	O
for	O
John	O
Tukey	O
,	O
is	O
an	O
approach	O
used	O
in	O
two-way	O
ANOVA	B-General_Concept
(	O
regression	O
analysis	O
involving	O
two	O
qualitative	O
factors	O
)	O
to	O
assess	O
whether	O
the	O
factor	O
variables	O
(	O
categorical	O
variables	O
)	O
are	O
additively	O
related	O
to	O
the	O
expected	O
value	O
of	O
the	O
response	O
variable	O
.	O
</s>
<s>
The	O
test	B-General_Concept
statistic	I-General_Concept
proposed	O
by	O
Tukey	O
has	O
one	O
degree	O
of	O
freedom	O
under	O
the	O
null	O
hypothesis	O
,	O
hence	O
this	O
is	O
often	O
called	O
"	O
Tukey	O
's	O
one-degree-of-freedom	O
test.	O
"	O
</s>
<s>
The	O
most	O
common	O
setting	O
for	O
Tukey	B-General_Concept
's	I-General_Concept
test	I-General_Concept
of	I-General_Concept
additivity	I-General_Concept
is	O
a	O
two-way	O
factorial	O
analysis	B-General_Concept
of	I-General_Concept
variance	I-General_Concept
(	O
ANOVA	B-General_Concept
)	O
with	O
one	O
observation	O
per	O
cell	O
.	O
</s>
<s>
Under	O
the	O
null	O
hypothesis	O
,	O
the	O
test	B-General_Concept
statistic	I-General_Concept
has	O
an	O
F	B-General_Concept
distribution	I-General_Concept
with	O
1	O
,	O
q	O
degrees	O
of	O
freedom	O
,	O
where	O
q	O
=	O
mn( m+n	O
)	O
is	O
the	O
degrees	O
of	O
freedom	O
for	O
estimating	O
the	O
error	O
variance	O
.	O
</s>
