Agriculture Reference
In-Depth Information
Table 10.6
Output of two-way classified data with
ml
(
>
1) observations per cell using MS Excel
Anova: two-factor with replication
Summary
Variety 1
Variety 2
Variety 3
Variety 4
Total
N
Count
3
3
3
3
12
Sum
39.900
51.900
46.600
61.700
200.100
Average
13.300
17.300
15.533
20.567
16.675
Variance
0.070
0.070
0.003
0.043
7.733
N
Count
3
3
3
3
12
Sum
42.800
55.400
48.600
75.100
221.900
Average
14.267
18.467
16.200
25.033
18.492
Variance
0.093
0.203
0.010
0.303
18.083
N
Count
3
3
3
3
12
Sum
74.100
66.800
55.800
96.500
293.200
Average
24.700
22.267
18.600
32.167
24.433
Variance
0.130
0.063
0.010
0.083
26.942
Total
Count
9
9
9
9
Sum
156.800
174.100
151.000
233.300
Average
17.422
19.344
16.778
25.922
Variance
30.042
5.143
1.957
25.782
ANOVA
Source of variation
SS
d.f.
MS
F
P
value
F
crit
Sample(nitrogen)
395.182
2
197.591
2188.698
0.000
3.403
Columns (variety)
472.131
3
157.377
1743.253
0.000
3.009
Interaction (V
N)
106.041
6
17.673
195.767
0.000
2.508
Within
2.167
24
0.090
Total
975.520
35
The ultimate output will be as
follows
10.4 Violation of Assumptions
in ANOVA
(Table
10.6
):
Step 4: Get the result as given above. Here
samples are the nitrogen, and columns are the
varieties.
Step 5: From the above table we see that both the
factors and their interaction effects are signifi-
cant at
Analysis of variance works under the assumption
that the effects (treatments and the environmental)
are additive in nature and experimental errors are
i.i.d.
2
); failures to meet these assumptions
adversely affect both the sensitivity of
N
(0,
σ
0.05. So we need to calculate the CD/
LSD values to identify the pair of nitrogen means
and pair of variety means which are significantly
different from each other and also to identify the
best type and the best combination of nitrogen
and variety to produce the highest yield.
Corresponding CD values are calculated per
formulae given above.
p ¼
F
-and
t
-tests and the level of significance. Thus, the
data which are found to be drastically deviated
from one or more of the assumptions are required
to be corrected before taking up the analysis of
variance. Data transformation is by far the most
widely used procedure for data violating the
assumptions of analysis of variance.
