Agriculture Reference
In-Depth Information
ANOVA table for two-way analysis of
variance with three observations per cell
the difference between any two nitrogen means is
greater than the corresponding critical difference
value 0.252. So we can conclude that nitrogen
doses significantly differ among themselves
with respect to yield of paddy and the nitrogen
dose giving significantly the highest yield
(24.433q/ha) is treatment N
3
.
As far as the response of four varieties of
paddy is concerned, it is found that the difference
between any two variety means is greater than
the critical difference value 0.292. Thus, the
varieties differ significantly among themselves
with respect to yield. Among the varieties, vari-
ety 4 has produced significantly the highest yield,
so this is the best variety.
After identifying the best variety and the best
treatment separately, our task is now to identify
the best nitrogen
SOV
d.f.
SS
MS
F
Variety
3
472.131
157.377
1743.253
Nitrogen
2
395.182
197.591
2188.698
Interaction
(V
4
106.041
17.673
195.767
N)
Error
24
2.167
0.090
Total
26
975.520
Let the level of significance be
α ¼
0.05.
3.40,
F
0.05;3,24
¼
3.01, and
F
0.05;6,24
¼
2.51, that is,
F
cal
> F
tab,
in all the cases, that is, nitrogen,
variety, and nitrogen
The
table
value
of
F
0.05;2,24
¼
variety interaction. So
the tests are significant and we reject the null
hypotheses and conclude that there exists signifi-
cant difference among the effects of doses of
nitrogen, varieties, and their interactions with
respect to the yield of paddy.
Now, we are interested in identifying the best
nitrogen, the best variety, and the nitrogen
variety combination for
yield of paddy from the above information. Let
us construct the following table of average inter-
action values of nitrogen and variety.
Mean table of N
V
variety combination providing the best yield.
To accomplish this task, we calculate the crit-
ical difference (CD)/LSD values for nitrogen,
variety, and interaction separately as follows:
Variety
1
Variety
2
Variety
3
Variety
4
Nitrogen
N1
13.300
17.300
15.533
20.567
N2
14.267
18.467
16.200
25.033
r
2MSE
l v
N3
24.700
22.267
18.600
32.167
CD
0
:
05
ð
Nitrogen
Þ¼
t
0
:
025
;
err
:
d
:
f
:
From the above table, it can be seen that the
difference between any two combinations is
more than the corresponding critical difference
value for nitrogen
r
2
0
:
073
¼
t
0
:
025
;
18
:
3
4
r
2
0
:
090
variety interaction (0.505),
so all the combinations produce significantly dif-
ferent yields of paddy. Among the nitrogen
¼
2
:
064
¼
0
:
252
;
3
4
r
2MSE
r
t
variety combinations, it is noticed that variety
4-nitrogen 3 combination produced the highest
yield; hence, this is the best combination,
followed by V
4
N
2
, which is at par with V1N3.
Thus, from the analysis we draw the following
conclusions:
1. The treatments differ significantly among them-
selves and the best treatment is treatment T
3
.
2. The varieties differ significantly among
themselves and the best variety is V
2
.
3. Treatment T
3
along with variety V
1
, produces
significantly higher yield than any other
combination.
Let us try to know how the above analysis of
variance could be done with MS Excel program
CD
0
:
05
ð
Variety
Þ¼
t
0
:
025
;
err
:
d
:
f
:
r
2
0
:
09
3
3
¼
t
0
:
025
;
18
:
r
2
0
:
09
3
3
¼
2
:
064
¼
0
:
292
;
r
2MSE
r
CD
0
:
05
ð
Tr
:
V
Þ¼
t
0
:
025
;
err
:
d
:
f
:
r
2
0
:
090
¼
t
0
:
025
;
18
:
3
r
2
0
:
090
3
¼
2
:
064
¼
0
:
505
:
Comparing the three nitrogen means provided
in the table of treatment totals, one can find that
