10.6Two-Way Analysis of Variance with Interaction 469
TABLE 10.4
Two-way ANOVA with l Observations per Cell: N
=
nm
(l
−
1)
Source of Degrees ofVariation Freedom Sum of Squares
F-Statistic
Level
α
Test
p-Value if
F
=
v
Row
m
−
1
SS
=r
ln
∑
m i=
( 1
Xi
−..
X...
(^2) )
Fr
SS
/(r
m
−
- SS
/e
N
Reject
H
r 0
P{
Fm
−1,
N
v}
if
Fr
Fm
−1,
N
,α
Column
n
−
1
SS
=e
lm
∑
n j=
( 1
X.
j.
−
X...
(^2) )
Fc
SS
/(c
n
−
SS
/Ne
Reject
H
c 0
P{
Fn
−1,
N
v}
if
Fc
Fn
−1,
N
,α
Interaction (
n−
1)(
m
−
SS
int
∑l
n j=
1
Fint
SS
int
/(n
−
1)(
m
−
SS
/e
N
Reject
H
int 0
P{
F(
n−
1)(
m−
1),
N
v}
×
∑
m i=
( 1
Xij
−.
Xi
−..
X.
j.
- X...
(^2) )
if
Fint
F(
n−
1)(
m−
1),
N
,α
Error
NSS
=e
∑
l k=
∑ 1
n j=
1
×
∑
m i=
( 1
Xijk
−
Xij
(^2) ).