Agriculture Reference
In-Depth Information
Let us examine the analysis of the above
problem without transforming the data using MS
Excel and following the steps discussed above.
ANOVA with original data
Summary
Count
Sum
Average
Variance
H1
4
21
5.2500
14.2500
H2
4
18
4.5000
1.6667
H3
4
30
7.5000
9.6667
H4
4
35
8.7500
18.9167
H5
4
82
20.5000
21.6667
H6
4
109
27.2500
22.2500
H7
4
10
2.5000
3.6667
H8
4
54
13.5000
3.6667
Replication 1
8
75
9.3750
74.5536
Replication 2
8
104
13.0000
125.4286
Replication 3
8
87
10.8750
47.5536
Replication 4
8
93
11.6250
85.6964
ANOVA
Source of variation
SS
d.f.
MS
F
P
value
F
crit
Hormone
2100.21875
7
300.0313
27.1105
0.0000
2.4876
Replication
54.84375
3
18.2813
1.6519
0.2078
3.0725
Error
232.40625
21
11.0670
Total
2387.46875
31
The LSD value at 5% level of significance
with original data is given by
10.4.1.2 Square Root Transformation
For count data consisting of small whole
numbers and percentage data where the data
ranges either between 0 and 30% or between 70
and to 100%, that is, the data in which the vari-
ance tends to be proportional to the mean, the
square root transformation is used. Data obtained
from counting rare events like the number of
death per unit time, the number of infested leaf
per plant, the number of call received in a tele-
phone exchange, or the percentage of infestation
(disease or pest) in a plot (either 0-30% or
70-100%) are examples where square root trans-
formation can be useful before taking up analysis
of variance to draw a meaningful conclusion or
inference. If most of the values in a data set are
small
r
2ErMS
r
LSD
ð
0
:
05
Þ
¼
t
0
:
025
;
21
r
2
11
:
067
¼
2
:
08
¼
4
:
893
:
4
By arranging the treatment means in
descending order, we find that hormone 6 is the
best treatment, recording the highest number of
fruit set per plant, and all other hormonal effects
are statistically different with it.
Thus, the con-
clusion on the basis of original data clearly
differs from that of transformed data
.
10) coupled with the presence of
0 values, instead of using
(
<
Hormone
Original average
p
transformation, it
H6
27.25
p
.Thenanalysisof
variance to be conducted with the transformed
data and the mean table should be made from
the transformed data instead of taking the mean
from the original data because of the facts stated
earlier.
ðx þ
H5
20.5
is better to use
0
:
5
Þ
H8
13.5
H4
8.75
H3
7.5
H1
5.25
H2
4.5
