Agriculture Reference
In-Depth Information
Table 10.10
Summary of observations from RBD
Replications/blocks
Treatments
1
2
...
.
j
...
.
r
Total
Mean
1
y
11
y
12
...
.
y
1
j
...
.
y
1
r
y
10
y
10
2
y
y
22
...
.
y
...
.
y
2
r
y
20
y
20
21
2
j
:
:
:
:
:
:
:
:
:
i
y
i
1
y
i
2
...
.
y
ij
...
.
y
ir
y
i
0
y
i
0
:
:
:
:
:
:
:
:
:
t
y
t
1
y
t
2
...
.
y
tj
...
.
y
tr
y
t
0
y
t
0
Total
y
y
02
...
.
y
...
.
y
0
r
y
00
01
0
j
Mean
y
01
y
02
...
.
y
0
j
...
.
y
0
r
Table 10.11
ANOVA table for RBD
Tabulated
F
Tabulated
F
SOV
d.f.
SS
MS
F
-ratio
(0.05)
(0.01)
Treatment
t
1
TrSS
TrSS
t
TrMS
ErMS
TrMS
¼
1
RSS
r
1
RMS
ErMS
Replication
(block)
r
1
RSS
RMS
¼
ErSS
ðt
1
Þðr
1
Þ
Error
(
t
1)
(
r
1)
ErSS
ErMS
¼
Total
rt
1
TSS
Let the observations of these
n ¼ rt
units be
H
0
:ð
1
Þ α
1
¼ α
2
¼¼α
i
¼¼α
t
¼
0
;
as follows (Table
10.10
):
The analysis of this design is the same as that
of two-way classified data with one observation
From the above table, we calculate the follow-
ing quantities (Table
10.11
):
ð
2
Þ β
1
¼ β
2
¼¼β
j
¼¼β
r
¼
0
against the alternative hypotheses
H
1
:ð
1
Þ α
's are not equal,
ð
2
Þ β
's are not equal
:
X
Grand total
¼
y
ij
¼ y
11
þ y
21
þ y
31
þþy
tr
¼ G
i;j
2
rt
¼
¼
G
Correction factor
CF
X
2
2
2
2
2
Total sum of squares TSS
ð
Þ¼
y
ij
CF
¼ y
11
þ y
21
þ y
31
þþy
tr
CF
i;j
P
t
1
y
i
0
2
r
2
10
2
20
2
30
2
i
2
t
¼
y
r
þ
y
r
þ
y
r
þ
y
r
þ
y
i¼
Treatment sum of squares TrSS
ð
Þ¼
CF
r
CF
0
0
P
r
j¼
1
y
0
j
2
2
0
j
2
01
2
02
2
03
y
2
0
r
¼
y
t
þ
y
t
þ
y
t
þ
y
Replication sum of squares RSS
ð
Þ¼
CF
t
þ
t
CF
t
Error sum of squares by subtraction
ð
Þ ¼
TSS
TrSS
RSS
