Agriculture Reference
In-Depth Information
Table 10.15
Table of A
B treatment totals over the replications
b
1
b
2
.........
b
j
......
.
b
n
Total
P
r
k¼
P
r
k¼
P
r
k¼
P
r
k¼
a
1
y
100
1
y
11
k
1
y
12
k
1
y
1
jk
1
y
1
nk
P
r
k¼
1
y
21
k
P
r
k¼
1
y
22
k
P
r
k¼
1
y
2
jk
P
r
k¼
1
y
2
nk
y
200
a
2
.
.
.
..................
:
:
:
::::::::::::::::::::::
:
:
:
::::::::::::::::::::::
P
r
k¼
P
r
k¼
P
r
k¼
P
r
k¼
a
i
y
i
00
1
y
i
1
k
1
y
i
2
k
1
y
2
jk
1
y
2
nk
:
:
:
:
:
:
:
:
:
:
P
r
k¼
P
r
k¼
P
r
k¼
P
r
k¼
a
m
y
m
00
1
y
m
1
k
1
y
m
2
k
1
y
mjk
1
y
mnk
y
y
y
y
0
y
Total
010
020
0j0
n
0
000
Table 10.16
Analysis of variance table for FRBD with two factorsThe structure of analysis of variance table is as
follows:
SOV
d.f.
SS
MS
F
r
1
RMS
¼
RSS/(
r
1)
Replication
RSS
RMS/ErMS
Factor A
m
1
ASS
AMS
¼
ASS/(
m
1)
AMS/ErMS
Factor B
n
1
BSS
BMS
¼
BSS/(
n
1)
BMS/ErMS
Interaction (A
B)
(
m
1)(
n
1)
ABSS
ABMS
¼
ABSS/(
m
1)(
n
1)
ABMS/ErMS
Error
(
r
1)(
mn
1)
ErSS
ErMS
¼
ErSS/(
r
1)(
mn
1)
mnr
1
Total
TSS
r
ErMS
r
due to factor A are not all equal to zero. Similarly
H
02
,
LSD AB
ðÞ¼
t
α=
2
;
err
:
d
:
f
:
H
03
,and
H
04
are rejected if the calculated
F
0.05
with
corresponding d.f. If the main effects and/or the
interaction effects are significant, then we calculate
the critical difference (CD)/least significant differ-
ence (LSD):
F >
value
of
table
value
of
Note
factorial experiment can also be
conducted in a basic CRD or LSD if situation
permits.
:The
m n
Example 10.15.
The following table gives the
yield (q/ha) of rice from an experiment conducted
with four doses of nitrogen under three spacing
treatments using RBD with three replications.
Find out the best dose of nitrogen, spacing, and
interaction of these two factors to yield maximum.
r
2ErMS
r n
LSD A
ðÞ¼
t
α=
2
;
err
:
d
:
f
r
2ErMS
r m
ðÞ¼
t
α=
2
;
err
:
d
:
f
LSD B
R1
R2
R3
Nitrogen
S1
S2
S3
S1
S2
S3
S1
S2
S3
N1
13.50
16.00
15.20
14.00
16.00
15.00
14.50
15.50
14.80
N2
14.80
16.50
15.80
15.20
16.80
15.20
16.00
16.20
15.50
N3
14.00
15.20
14.80
13.80
15.50
14.30
13.50
14.80
14.50
N4
13.70
15.80
15.00
14.50
15.70
14.80
15.00
15.20
14.70
