Geoscience Reference
In-Depth Information
Stratum
Relative Size (
n
h
/
n
)
Sample Allocation
1
0.54
29.7 or 30
2
0.28
15.4 or 15
3
0.18
9.9 or 10
Sums
1.00
55
Some other possibilities are equal allocation, allocation proportional to estimated value, and
optimum allocation. In optimum allocation, an attempt is made to get the smallest standard error
possible for a sample of
n
units. This is done by sampling more heavily in the state having a larger
variation. The equation for optimum allocation is
Ns
Ns
hh
hh
n
=
n
h
∑
Optimum allocation obviously requires estimates of the within-stratum variances—information
that may be difficult to obtain. A refinement of optimum allocation is to take sampling cost differ-
ences into account and allocate the sample so as to get the most information per dollar. If the cost
per sampling unit in stratum
h
is
c
h
, the equation is
Ns
c
Ns
c
hh
h
n
=
n
h
∑
hh
h
7.11.2.2 Sample Size
To estimate the size of sample to take for a specified error at a given level of confidence, it is first
necessary to decide on the method of allocation. Ordinarily, proportional allocation is the simplest
and perhaps the best choice. With proportional allocation, the size of sample needed to be within
±
E
units of the true value at the 0.05 probability level can be approximated by
(
)
∑
2
NNs
NE
hh
n
=
22
∑
2
+
Ns
hh
4
For the 0.01 probability level, use 6.76 in place of 4.
■
EX AMPLE 7. 8
Problem:
Assume that prior to sampling a 500-acre forest we decided to estimate the mean volume
per acre to within ±100 cubic feet per acre unless a 1-in-20 chance occurs in sampling. As we plan
to sample with 0.2-acre plots, the error specification should be put on a 0.2-acre basis. Therefore,
E
= 20. From previous sampling, the stratum variances for 0.2-acre volumes are estimated to be
2
2
2
s
=
8000
s
=
10 000
,
s
=
5000
1
2
3
Therefore,
[
]
2500
(
1350
)(
8000
)
+
(
700 10 000
)(,
)(
+
450
)(
5000
)
n
=
=
77 7, or 78
.
2
2
(
2500
) ()
20
[
]
+
(
1350
)(
8000
)
+
(
700 10 000
)(,
))(
+
450
)(
5000
)
4
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