Agriculture Reference
In-Depth Information
6.2.1.6 Multistage Sampling
Multistage sampling is the extension of clustering
in more than one stage. Instead of taking blocks/
villages directly as clusters, one may take districts
at the first stage, then blocks/villages from the
selected districts and farmers from the villages,
etc. Thus, districts are the first stage units (fsu)
(or primary stage units (psu)), blocks/villages are
the second stage units, and farmers are the third
stage units or the respondents. A multistage sam-
pling is a two-stage/three-stage, etc., sampling
depending upon the number of stages or clusters.
If one is interested in counting the number of
grains per panicle in a wheat field experiment,
a three-stage sampling with individual hills as
the “fsu” and individual panicles as the “ssu”
and grains in panicle as “tsu” for sampling may
be used.
Multistage sampling is very flexible. The
whole process depends on the expertise of the
supervisor. For two-stage sampling with a popu-
lation divided into
way of tackling the large population. The usual
procedure is to take a large sample of size “
n
0
”
from the population of
N
units to observe the
x
-values of the auxiliary character and to esti-
mate the population parameter (say mean), while
a subsample of size “
n
0
”to
n
” is drawn from “
study the character under consideration.
Let the problem be the selection of a sample
of families with probability proportional to
income. But the problem is that we do not have
any information on the income of the families.
We can take an initial random sample of families
having varied income and collect information on
their incomes; then a subsample is taken from the
initial sample with probability proportional to
the size of income. This will serve as the test
sample for the character under study from a
selected sample on the basis of family income.
Thus, in multiphase sampling, every sample is
obtained from previous sample.
Multiphase sampling should not be confused
with multistage sampling. In multistage sam-
pling, the sampling units at each stage are the
clusters of units of the next stage, and the ulti-
mate observable units are selected in stages,
sampling at each stage being done from each of
the sampling units or clusters selected in the
previous stage.
Multiphase or double sampling is very flexi-
ble and valuable for survey purpose, particularly
where the auxiliary information may not be
available always. But it is tedious, monotonous,
and less accurate.
In many situations, the population mean
N
first stage units and having
M
second stage units in each; the population
N
M
N
i¼
1
Y
i
. If a sample
Y ¼
1
NM
1
N
mean
Y
ij
¼
i
j
of
n
fsu is selected from
N
fsu with SRSWOR
and a sample of
ssu is selected from each
selected fsu with SRSWOR, then an unbiased
estimator for
Y
m
is given by
X
n
i¼
1
y
i
1
n
^
Y
t
¼
with its estimated variance
¼ð
2
b
X
f
1
Þ
s
n
þ
f
1
ð
1
f
2
Þ
nm
of
^
Y
t
V
2
1
s
2
,
an auxiliary character
x
is known. Then the
ratio estimator for
Y
is given by
y
R
¼
y
x
X
, where
where
y
y
and
x
, respectively, based on a sample of size
n
drawn with SRSWOR. It may happen that
X
is not
known and in this case, the ratio of estimation
cannot be used to estimate the population mean
Y
and
x
are sample means of the characters
2
m
n
1
X
n
i¼
1
m
1
y
i
^
Y
t
2
y
i
¼
1
y
ij
;
s
b
¼
and
j¼
1
X
n
m
2
1
nðm
1
Þ
; f
1
¼
n
N
; f
2
¼
m
.
The usual procedure in such a situation is to use
the technique known as two-phase or double sam-
pling. A preliminary random sample without
replacement (SRSWOR) of size
2
2
s
¼
1
y
ij
y
i
M
i¼
1
j¼
6.2.1.7 Multiphase and Double
(Two-Phase) Sampling
Sampling in two or more phases is known as two-
phase or multiphase sampling. This is another
n
0
is taken as
the information on
x
is collected. A subsample
n
0
n
0
and
of size
is drawn (SRSWOR) from
