Agriculture Reference
In-Depth Information
then analysis of variance is to be taken up with
(
10.10 Missing Plot Technique
1) replication for the corresponding treat-
ment and total (
r
n
1) number of observations
In many of the experiments, it is found that the
information from an experimental unit is missing
because of some reasons or otherwise. Responses
from a particular experimental unit may be lost.
Crops of a particular experimental unit may be
destroyed, animals under a particular treatment
may die because of some reason, fruits/flowers
from a particular experimental unit may be
stolen, errors on the part of the data recorder
during recording time, etc., may result in missing
data.
instead of
observation for the whole experi-
ment. But the effect of missing observations on
the surrounding experimental units should be
noted carefully.
n
10.10.1 Missing Plot Technique in RBD
Let the following table provide the observations
of an RBD with a missing observation
y
ij
In this connection, the difference between
the missing observation and the zero observation
should be clearly understood
(Table
10.13
):
With reference to the above table, the obser-
vation
. For example, if
because of an insecticide treatment, the number
of insects count per plant is zero or if because of a
treatment in studying the pest control measure
the yield of any experimental units is zero, then
these should be entered zero, not to be treated as
missing values. If the information from the whole
experiments is to be discarded because of one or
two missing values, it will be a great loss of time,
resources, and other factors. In order to avoid and
overcome the situations, missing plot technique
has been developed. Missing observation can,
however, be estimated following the least square
technique, and application of analysis of variance
with some modification can be used for practical
purposes to provide reasonably correct result.
In CRD, the above technique is of little use
because of the fact that in CRD, analysis of
variance is possible with variable number of
replications for different treatments. Thus, if
one observation from a treatment is missing,
y
ij
¼ y
(say) is estimated by minimizing error sum of
squares, and the corresponding estimate would be
y
ij
is missing. This missing value
0
i
0
þ ry
0
0
j
y
0
00
ty
y ¼
ðr
1
Þðt
1
Þ
where
y
0
i
0
is the total of known observations in the
i
th
treatment
0
0
y
is the total of known observations in
j
th
j
replication (block)
0
00
is the total of all known observations
Once the estimated value for the missing
observation is worked out, the usual analysis of
variance is taken up with the estimated value
of the missing observation. The treatment sum
of squares is corrected by subtracting the upward
bias
y
Table 10.13
Observations from RBD with one missing value
Replications (blocks)
...
.
j
...
.
r
Treatments
1
2
Total
1
y
y
...
.
y
1
j
...
.
y
y
11
12
1
r
10
2
y
21
y
22
...
.
y
2
j
...
.
y
2
r
y
20
:
:
:
:
:
:
:
:
y
0
i
0
i
y
i
1
y
i
2
...
.
-
...
.
y
ir
:
:
:
:
:
:
:
:
t
y
t1
y
t2
...
.
y
tj
...
.
y
tr
y
t
0
y
0
0
j
y
0
00
Total
y
01
y
02
...
.
...
.
y
0
r
