Agriculture Reference
In-Depth Information
information on
y
is measured. The ratio estimator
respectively,
b
being the sample regression
for
Y
coefficient of
y
2
on
y
1
based on matched part of
based on double sampling is given by
y
1
h
¼
P
s
y
1
i
s
1
,
W
being a constant, and
n
;
y
hm
¼
y
Rd
¼
y
P
s
1
yhi=m; ðh ¼
x
x
0
;
;
Þ
1
2
The alternatives to the above scheme are the
schemes based on (1)
where
x
and
y
are subsample means of
x
and
y
,
respectively, and
x
0
is the sample mean in the first
sample. It is noted that
(i.e.,
retaining the sample of the first occasion to the
second occasion completely) or (2)
complete matching
y
Rd
is biased and the
complete
V y
R
ðÞ
estimator of
to the first-order approxima-
replacement
(i.e., drawing a single independent
sample at the second occasion and
ta
king the
sample mean as the estimator of
tion is given by
Y
2
in both
cases). The partial matching procedure is better
than the other two procedures; for all practical
purposes, one should retain 25-30% units at the
second occasion for the gain in the efficiency.
s
1
n
0
1
N
1
n
1
n
0
V y
R
ðÞ¼
2
y
þ
2
y
þ R
2
Rs
yx
2
2
s
s
x
1
X
n
where
R ¼
y
1
n
x
; s
yx
¼
i¼
1
y
i
y
ð
Þ x
i
x
ð
Þ
6.2.1.9 Inverse Sampling
Inverse sampling is generally used for the esti-
mation of a rare population and is a method of
sampling in which the drawing of a sample unit
continues until certain specified conditions
dependent on the results of those drawings have
been fulfilled, for example, until a given number
of individuals of specified type have emerged.
For example, if we want to draw a sample of
population affected by pox disease in which at
least “
6.2.1.8 Sampling in Two Occasions
In agriculture, plant characters are commonly
measured at different growth stages of the crop.
For example, tiller number in rice may be
measured at 30, 60, 90, and 120 days after trans-
planting or at the tillering, flowering, and harve-
sting stages. If suchmeasurements are made on the
same plants at all stages of observation, the
resulting data may be biased because plants that
are subjected to frequent handling may behave
differently from others. In this situation, if sam-
pling on successive occasions is done according to
a specific rule, with partial replacement of sam-
pling units, it is known as
rotation sampling
.
On the first occasion, a SRSWOR sample “
” has been affected by “chicken pox,”
while doing so, we do not know about the exact
size of the sample because unless and otherwise
we have “
k
” number of persons affected by
chicken pox, the drawing will continue and the
sample size will go on increasing. Thus, though
costly and time and labor- consuming, this sam-
pling gives due weightage to rare elements in the
population.
Let
k
s
”
of size “
”
units; on the second occasion, a SRSWOR sam-
ple “
n
” is selected from a population of “
N
denote the proportion of units in the
population possessing the rare attribute under
study. Therefore, NP number of units in the
population will possess the rare attributes. To
estimate
P
s
1
”of“
m
” units from “
s
” and a SRSWOR
sample “
s
2
”of“
u
”(
¼ n m
) units from the
(
N n
) units in the population not included in
“
” are selected. The estimate for the population
mean
Y
2
on the second occasion is given by
^
Y
2
¼ Wy
2
n
þð
s
, units are drawn one by one with
SRSWOR. Sampling is discontinued as soon as
the number of units in the sample possessing the
rare attribute (a predetermined number,
P
WÞy
0
2
m
1
y
2
n
¼
P
s
2
m
)is
y
2
i
u
y
0
2
m
¼ y
2
m
b y
1
m
where
and
ð
reached. Let us denote by
the number of units
required to be drawn in the sample to obtain m
units possessing the rare attribute. An unbiased
estimator of
n
are the simple mean for
Y
2
based on the
replaced (unmatched) portion and the regression
estimator for
y
1
n
Þ
Y
2
based on the matched portion,
P
is given by
