Agriculture Reference
In-Depth Information
Table 10.7
Treatment structure of CRD
Treatment
1
Observations
2
. . .. . .. . .
.
i
.........
.
t
1
y
11
y
21
. . .. . .. . .
..
y
i
1
.........
.
y
t
1
2
y
y
. . .. . .. . .
.
y
i
2
.........
.
y
t
2
12
22
:
:
:
. . .. . .. . .
:
.........
.
:
:
:
:
:
:
:
:
y
2
r
2
:
:
. . .. . .. . .
.
.........
.
:
:
r
i
. . .. . .. . .
.
y
iri
.........
.
:
:
y
:
1
r
1
:
y
tr
t
Total
y
1
0
y
20
. . .. . .. . .
.
y
i
0
.........
..
y
t
0
y
10
y
20
y
i
0
y
t
0
Mean
Table 10.8
ANOVA table for completely randomized design
Sources of variation
d.f.
SS
MS
F
-ratio
Treatment
t
1
TrSS
TrSS
t
TrMS
ErMS
TrMS
¼
1
ErSS
n t
Error
n t
ErSS
ErMS
¼
Total
n
1
TSS
α
Let the level of significance be
. Let the
The analysis for this type of data is the same
as that of one-way classified data discussed in
calculate the following quantities (Table
10.8
):
n ¼
P
i¼
1
r
i
experimen-
tal units be as follows (Table
10.7
):
observations of the total
X
t
X
r
i
X
t
X
r
t
j¼
1
y
ij
¼ G:
Grand total
¼
ð
observation
Þ ¼ y
11
þ y
21
þ y
31
þþy
trt
¼
i¼
1
j
i¼
1
¼
G
2
n
¼
Correction factor
CF
:
X
t
X
r
i
X
t
X
r
t
j¼
1
y
2
2
ð
Þ¼
ð
Þ
¼
ij
:
Total sum of squares TSS
observation
CF
CF
i¼
1
j
i¼
1
2
11
2
21
2
31
2
¼ y
þ y
þ y
þþy
tr
t
CF
:
X
t
X
r
i
j¼
1
y
ij
y
i
0
2
Treatment sum of squares TrSS
ð
Þ ¼
r
i
CF
;
where
y
i
0
¼
i¼
1
¼
sum of the observations for the
i
th treatment
:
2
10
2
20
2
30
2
i
0
2
t
0
¼
y
r
1
þ
y
r
2
þ
y
r
3
þ
y
r
i
þ
y
r
t
CF
:
Error sum of squares by subtraction
ð
Þ ¼
TSS
TrSS
¼
Erss
:
