Agriculture Reference
In-Depth Information
10.4.1 Data Transformation
be drawn on the basis of transformed mean
values and on the basis of calculations made
through transformed data. However, while
presenting the mean table, it will be appropriate
to recalculate the means by taking the antilog of
the transformed data. In practice, the treatment
means are calculated from the original data
because of simplicity of calculations, but statis-
tically the procedure of converting transformed
mean to original form is more appropriate.
If there is a mismatch in the two procedures,
then the procedure of converting the transformed
mean with the help of the antilog is preferred
over the other procedure.
Among the different types of transformation
generally used to make the data corrected for
analysis of variance,
logarithmic transformation,
square
root
transformation,
and
angular
transformation
are widely used.
10.4.1.1 Logarithmic Transformation
The number of plant insects, number of egg
mass per unit area, number of larvae per unit
area, etc., are typical examples wherein variance
is proportional to the mean and logarithmic trans-
formation can be used effectively. The procedure
is to take simply the logarithm of each and
every observation and carry out the analysis of
variance following the usual procedure with the
transformed data. However, if in the data set
small values (less than 10) are recorded, then
instead of taking log(
Example 10.4.
The following data give the
number of fruit set after the application of eight
different hormonal treatments in jackfruit. Use
suitable transformation and analyze the data
using the suitable model.
x
), it will be better to take
log(
x
+ 1). The final results or inference should
Hormone
Replication 1
Replication 2
Replication 3
Replication 4
H1
2
9
8
2
H2
4
5
6
3
H3
5
7
12
6
H4
3
11
8
13
H5
19
26
15
22
H6
24
34
24
27
H7
3
1
1
5
H8
15
11
13
15
Solution. Because this experiment is related
with count data, violation of the assumption of
ANOVA is suspected and the analysis of the data
is required to be made on the basis of the
transformed data. The appropriate transforma-
tion would be logarithmic transformation.
The following table presents the transformed
data. It may be noted that as some of the
observations are below 10, we apply log(
X
+1)
transformation instead of log(
X
).
Hormone
H1
H2
H3
H4
H5
H6
H7
H8
Replication 1
0.4771
0.6990
0.7782
0.6021
1.3010
1.3979
0.6021
1.2041
Replication 2
1.0000
0.7782
0.9031
1.0792
1.4314
1.5441
0.3010
1.0792
Replication 3
0.9542
0.8451
1.1139
0.9542
1.2041
1.3979
0.3010
1.1461
Replication 4
0.4771
0.6021
0.8451
1.1461
1.3617
1.4472
0.7782
1.2041
Average
0.7271
0.7311
0.9101
0.9454
1.3246
1.4468
0.4956
1.1584
