Agriculture Reference
In-Depth Information
Analysis of Variance for Leaf Yield
The appropriate statistical model for RBD
will be
Total sum of squares
¼
TSS
X
X
10
3
j¼
1
y
ij
2
¼
CF
i¼
1
89
2
57
2
¼
158
:
þ
164
:
y
ij
¼ μ þ g
i
þ b
j
þ e
ij
21
2
þþ
:
175
where
y
ij
¼
CF
¼
24747
:
19
j
response corresponding to the
th replica-
th genotype
μ ¼
general effect
g
i
¼
tion of the
i
Replication sum of squares
X
3
j¼
1
y
1
t
additional effect due to the
i
th genotype
2
¼
¼
0
j
RSS
CF
b
j
¼
additional effect due to the
j
th replication
e
ij
¼
error associated with
j
th replication of the
1
10
59
2
45
2
36
2
¼
1846
:
þ
1839
:
þ
1855
:
i
th genotype
¼
:
CF
12
75
α ¼
:
Let the level of significance be
0
05.
Let us make the following table:
Treatment sum of squares
X
10
i¼
1
y
1
r
Leaf yield/plant(
Y
)
2
i
0
¼
TrSS
¼
CF
Genotype
R1
R2
R3
Total
G1
158.89
164.57
152.54
476.00
1
3
476
2
28
2
99
2
¼
þ
577
:
þþ
527
:
G2
192.59
193.24
191.45
577.28
G3
195.18
190.24
201.45
586.87
CF
¼
24515
:
98
G4
211.11
209.12
213.45
633.68
G5
202.22
200.12
204.52
606.86
Error sum of squares
¼
TSS
RSS
TrSS
G6
205.56
207.42
203.28
616.26
¼
¼
218.46
With the help of the above quantities, we now
make the following ANOVA table for leaf yield
per plant:
24747.19
12.75
24515.98
G7
217.78
215.65
219.45
652.88
G8
170.00
165.25
175.59
510.84
G9
117.93
116.39
118.42
352.74
G10
175.33
177.45
175.21
527.99
Total
1846.59
1839.45
1855.36
5541.4
ANOVA table for yield/plant (
y
)
SOV
d.f.
S.S
M.S
F
-ratio
From the above table, the following quantities
are calculated:
REP
2
12.75
6.38
0.53
GEN.
9
24515.98
2724.00
224.44
EROR
18
218.459
12.14
X
X
10
3
Total 29 24747.19
Similarly, following the same procedures, we
can also perform the analysis of variance for other
characters and make the following ANOVA tables:
Grand total
¼ G ¼
1
y
ij
i¼
1
j¼
¼
57
þþ
158
:
89
þ
164
:
175
:
21
¼
5541
:
4
ANOVA table for total shoot length (
x
1
)
SOV
d.f.
S.S
M.S
F
-ratio
2
r t
¼
4
2
¼
G
5541
:
REP
2
379.00
189.50
1.22
Correction factor
¼
CF
3
10
GEN.
9
499621.8
55513.54
356.98
EROR
18
2799.156
155.51
¼
1
;
023
;
570
Total
29
502800
