Agriculture Reference
In-Depth Information
α
i
¼
additional effect due to the
i
th level of
X
X
X
X
2
3
4
3
irrigation,
P
α
i
¼
0
β
j
¼
Grand total GT
ðÞ¼
1
y
ijkl
¼
1331
:
4
i¼
1
j¼
1
k¼
1
l¼
additional effect due to the
j
th level of
phosphate,
P
β
j
¼
0
GT
2
4
2
1331
:
γ
k
¼
additional effect due to the
k
th level of
Correction factor CF
ðÞ¼
3
¼
nitrogen,
P
γ
k
¼
2
:
3
:
4
:
72
0
¼
24619
:
805
αð
ij
¼
interaction effect of the
i
th level of irri-
X
X
X
X
2
3
4
3
l¼
1
y
gation and the
j
th level of phosphate,
2
P
αð
ij
¼
P
j
TSS
¼
ijkl
CF
¼
461
:
767
αð
ij
¼
0
i¼
1
j¼
1
k¼
1
i
X
3
l¼
1
y
1
m:n:p
αð
ik
¼
interaction effect of the
i
th level of
2
RSS
¼
000
l
CF
irrigation and the
k
th level of nitrogen,
P
αð
ik
¼
P
k
αð
ik
¼
0
446
:
6
2
þ
442
:
2
2
þ
442
:
2
2
¼
24619
:
805
i
24
βð
jk
¼
interaction effect of the
j
th level of
¼
:
:
0
500
l
phosphate and the
th level of nitrogen,
P
βð
jk
¼
P
k
βð
jk
¼
0;
From the above table first let us form the
following tables and from the table get the fol-
lowing quantities:
j
αβð
ijk
¼
interaction effect of the
i
th level of
irrigation,
the
j
th level of phosphate, and
th level of nitrogen,
P
i
the
k
αβð
ijk
¼
Table of totals for irrigation
nitrogen
P
αβð
ijk
¼
P
k
αβð
ijk
¼
0
j
Irrigation
I1
δ
l
¼
additional effect due to the
l
th replication,
P
δ
l
¼
Nitrogen
I2
Total
Average
0
N0
156.800
177.000
333.800
18.544
e
ijkl
¼
error component associated with the
l
th
N1
153.650
172.600
326.250
18.125
i
replicate due to the
th level of irrigation and
N2
168.700
185.900
354.600
19.700
the
j
th level of phosphate and the
k
th level of
N3
145.900
170.800
316.700
17.594
2
)
nitrogen and
e
ijkl
~ i.i.d.
N
(0,
σ
Total
625.050
706.300
Hypothesis to Be Tested
Average
17.363
19.619
H
0
: α
1
¼ α
2
¼
;
β
1
¼ β
2
¼ β
3
¼
0
Table of totals for irrigation
phosphate
;
γ
1
¼ γ
2
¼ γ
3
¼ γ
4
¼
0
0
;
Irrigation
I1
Phosphate
I2
Total
Average
δ
1
¼ δ
2
¼ δ
3
¼
0
;
P1
238.350
265.500
503.850
20.994
P2
195.000
218.500
413.500
17.229
All interaction effects
¼
0 against
P3
191.700
222.300
414.000
17.250
Total
625.050
706.300
H
1
:
All
α
's are not equal,
Average
17.363
19.619
All
β
's are not equal,
All
γ
's are not equal,
X
2
i¼
1
y
1
n:p:r
2
SS
ð
Irrigation
Þ¼
iooo
CF
δ
;
All
's are not equal
05
2
3
2
625
:
þ
706
:
All interaction effects are not equal.
Let the level of significance be 0.05.
From the given data table, let us calculate the
following quantities:
¼
3
:
4
:
3
24619
:
805
¼
91
:
688
