Agriculture Reference
In-Depth Information
Arranging the treatment means in ascending
order, we find that insecticide 1 is the best insec-
ticide treatment, recording the lowest number of
insects per 20 insects, and insecticides 2 and 4
are at par with insecticide 1. On the other hand,
insecticide 6 has retained insect weeds per 20
insects. But with transformed data I1, I2, and I3
are at par.
percentage data into angles measured in degrees,
that is, to transform 0-100% data into 0-90
angles. The actual procedure is to convert the
percentage data into proportions and transform
it into sin
1
p
, where
is the percentage data
measured in proportions. Ready-made tables are
available for different percentage values with
their corresponding transformed values. How-
ever, in MS Excel with the following functional
form, a percentage data can be directly converted
to arcsine transformed data.
ΒΌ
p
Insecticide Average
I1 3.0000
I2 3.5000
I4 4.0000
I3 5.7500
I5 8.0000
I6 10.5000
10.4.1.3 Angular Transformation
Data on proportions/percentages arising out of
count data require angular transformation or the
arcsine transformation. It may be noted emphati-
cally that the percentage data (e.g., percentage of
carbohydrate, protein, and sugar; percentage of
marks; and percentage of infections) which are
not arising out of count data
n
degrees (asin(sqrt(
p
/100))), where
p
is the
percentage value.
Analysis of variance is taken up on the
transformed data and inferences are made
accordingly with the transformed means. How-
ever, to get original means retransformation of
transformed means is preferred over the means
from original data because of the fact stated
earlier.
Example 10.6.
The following table gives the
germination percentage of eight varieties of
wheat in a field trial with three replications.
Analyze the data to find out the best variety
w.r.t. germination.
should
not be put under arcsine transformation. More-
over, all the percentage data arising out of count
data need not be subjected to arcsine transforma-
tion before analysis of variance:
(a) For percentage data ranging either between
0 and 30% or 70 and 100% but not both, the
square root transformation should be used.
(b) For percentage data ranging between 30 and
70%, no transformation is required.
(c) Percentage data which overlaps the above
two situations should only be put under arc-
sine transformation.
Thus, a data set having 0 to more than 30%,
less than 70-100%, and 0-100% should be put
under arcsine transformation.
The values of 0% should be substituted by
100
Replication
3
Replication
1
Replication
2
Variety
V1
62
55
48
V2
28
23
32
V3
70
75
72
V4
85
86
88
V5
92
90
95
V6
18
15
17
V7
20
16
18
V8
68
65
66
Solution. From the given information it is clear
that (a) the data can be analyzed per the analysis
of two-way classified data and (b) the data relates
to percentage data arising out of count data and
the percentage ranges from 15 to 95%. Thus,
there is a chance of heterogeneous variance.
So we opt for arcsine transformation before
taking up the analysis of variance.
1
4
n
1
4
n
and the values of 100% by 100
is
the number of counts on which percentages are
worked out before transformation of data follow-
ing arcsine rule of transformation. The essence
of arcsine transformation is to convert
, where
n
the
