Agriculture Reference
In-Depth Information
This allocation is also known as
Neyman
random out of all the clusters. Clusters need not
necessarily be natural aggregates; these may
be virtual or hypothetical or artificial also, like
grids in the map. The best size of cluster depends
on the cost of collecting information from the
clusters and the resulting variance. The objective
is to reduce both the cost and variance, and for
that we can have a pilot survey also, if felt
necessary.
Cluster sampling is useful where listing of
population units is not available; for example,
in a crop survey, the list of plots may not be
available, but the list of villages may be avail-
able. Here, villages will be treated as clusters
similarly. In animal husbandry, the list of cattle
may not be available, but the list of rearers
may be available. In such case, rearers will be
considered as clusters.
A population of
allocation
.
Stratified random sampling gives more repre-
sentative sample, that is, more accuracy in
sampling and efficient estimation of population
parameters. However, it is more costly than sim-
ple random sampling and involves complicated
analysis and estimation procedure.
6.2.1.4 Systematic Sampling
In this method of sampling, only the first unit is
selected with the help of a random number, and
the rest of the units of the sample get selected
automatically according to some predesigned
pattern. Suppose there are 500 population units
numbered from 1 to 500 in some order and we
want to draw a sample size of 50, We have
500
10, where 50 is the sample size
and 10 is an integer; let a random number less
than or equal to “10” be selected and every 10th
unit thereafter; such a procedure is termed
¼
50
NM
units is divided into
N
M
Y
ij
be the value
clusters having
units each. Let
of the character
th observation
corresponding to
i
th cluster (
i ¼
1, 2, 3,
...
,
N
and
y
under study for
j
linear
systematic
sampling
. f
N 6¼ nk
, where
Y
j ¼
1, 2, 3,
...
,
M
). The population mean
N ¼
population size,
n ¼
sample size, and
k ¼
is defined as
k
an integer, and every
th unit is included in a
circular manner till the whole list is exhausted,
it will be called
X
X
N
N
M
.
Systematic sampling is used in various surveys
like in census work, forest surveys, milk yield
surveys, and fisheries.
circular systematic sampling
1
NM
1
N
Y ¼
Y
i
;
Y
ij
¼
i
j
i¼
1
Y
i
where
n
clusters is drawn with SRSWOR, and all the
units in the selected clusters are surveyed. An
unbiased estimator of the population mean
is the
i
th cluster mean. A sample of
6.2.1.5 Cluster Sampling
When the population is very wide or big, say for
countrywide survey, it may not be feasible to
take sample units directly from the population
itself. Moreover, this type of sampling is used
when the population size is very large, and strat-
ification is also not feasible to the best possible
way because of nonavailability of full informa-
tion on each and every element of the population.
Resource constraint is also a major factor. In
such cases, auxiliary/secondary information like
block list, village list, and subdivision lists is
used in probability sampling. In cluster sampling,
the whole population is divided into a number of
clusters, each consisting of several sampling
units. Cluster size may definitely vary from clus-
ter to cluster. Then some clusters are selected at
Y
is
given by
X
n
1
n
^
Y
c
¼
1
y
i
;
i¼
and its estimated variance is
¼
N n
N
2
b
s
^
Y
c
V
n
;
M
j¼
1
y
ij
¼
where
y
i
¼
1
M
mean for the
i
th selected
2
n
1
P
n
i¼
1
y
i
^
Y
c
2
1
cluster and
s
b
¼
