Agriculture Reference
In-Depth Information
Table 10.17
ANOVA for split plot design
SOV
d.f.
MS
MS
F
-ratio
Table value of
F
Replication
r
1
RMS
RMS
RMS/Er.MS I
Main plot factor(A)
m
1
MS(A)
MS(A)
MS(A)/Er.MS I
Error I
(
r
1) (
m
1)
Er.MS(I)
Er.MS I
Subplot factor(B)
(
n
1)
MS(B)
MS(B)
MS(B)/Er.MS II
Interaction (A
B)
(
m
1) (
n
1)
MS(AB)
MS(AB)
MS(AB)/Er.MS II
Error II
m
(
n
1) (
r
1)
Er.MS II
Er.MS II
Total
mnr
1
Table 10.18
Table totals for main plot
replication
a
1
a
2
......
a
j
......
a
m
Total
Mean
R
1
y
y
......
y
......
y
y
y
100
110
120
1
j
0
1
m
0
100
R
2
y
y
......
y
......
y
y
y
200
210
220
2
j
0
2
m
0
200
:
:
:
:
:
:
:
:
R
i
y
i
10
y
i
20
......
y
ij
0
......
y
im
0
y
i
00
y
i
00
:
:
:
:
:
:
:
:
R
r
y
r
10
y
r
20
......
y
rj
0
......
y
rm
0
y
r
00
y
r
00
Total
y
y
......
y
......
y
y
000
y
000
010
020
0
j
0
0
m
0
Mean
y
010
y
020
y
0
j
0
y
0
m
0
P
r
i¼
1
y
1
mn
2
H
1
: γ
's are not all equal,
α
Replication SS
¼
i
00
CF,
's are not all equal,
m
j¼
1
y
1
nr
0
SS(A)
¼
CF, SS Error I
¼
TSS
β
's are not all equal,
υ
j
0
's are not all equal
:
.
5. Work out the sum of squares due to the sub-
plot factor and interaction. For the purpose,
the following table of totals is required to the
formed (Table
10.19
):
Note
: In both tables the totals for main factor
A at different levels will be the same.
ð
Table 10
:
18
Þ
RSS
SS
ð
A
Þ
Let
the
level of
significance be 0.05
(Table
10.17
).
The step-by-step procedure for the computa-
tion of different sums of squares and mean sum
of squares is given as follows:
¼
P
r
i¼
1
m
n
k¼
1
y
ijk
¼
1. Grand total
GT
:
m
X
n
1
r
j¼
1
2
0
TSS
ð
Table 10
:
19
Þ¼
1
y
jk
CF
;
GT
2
2. Correction factor
ð
CF
Þ¼
mnr
:
j¼
1
k¼
3. Total MS
¼
P
r
i¼
1
m
P
n
k¼
1
y
X
n
k¼
1
y
1
mr
2
ijk
CF
:
2
SS B
ðÞ¼
00
k
CF
j¼
1
4. Work out the sum of squares due to the main
plot factor and the replication. For the pur-
pose, the following table of totals is required
to be framed (Table
10.18
):
where
y
ij
0
¼
P
n
SS A
ðÞ¼
TSS
ð
Table 10
:
19
Þ
SS
ð
A
Þ
SS
ð
B
Þ;
SS Error II
ð
Þ
¼
TSS
RSS
SS A
ðÞ
SS Error I
ð
Þ
SS B
ðÞ
SS AB
ð :
k¼
1
y
ijk
Mean sum of squares is calculated by dividing
the sum of squares by the corresponding
degrees of freedom.
P
r
m
¼
1
n
y
2
ij
0
TSS
(Table
10.18
)
CF,
i
j
