Geoscience Reference
In-Depth Information
TABLE 7.5
Data for Example 7.7
Squared
Standard
Error of
the Mean
(
s
x
2
)
Within-
Stratum
Variance
(
s
2
)
Stratum
Number
(
h
)
Stratum
Size
(
n
h
)
Sample
Size
(
n
h
)
Stratum
Mean
(
X
h
)
Type
Pine
1
1350
30
251
10,860
353.96
Upland hardwoods
2
700
15
164
9680
631.50
Bottom-land hardwoods
3
450
10
110
3020
265.29
Sum
2500
Thus, for stratum 1 (pine type),
10 860
30
,
30
1350
=
s
2
=
1
−
353 96
.
Where the sampling fraction (
n
h
/
N
h
) is small, the fpc can be omitted.
With these data, the population mean is estimated by
NX
N
=
∑
hh
X
st
where
N
= ∑
N
h
.
For this example we have
NX
+
NX
+
NX
(
1350
)(
251
)
+
(
700 164
)(
)
+
(
450 110
)(
)
11
22
34
X
st
=
=
=
201 26
.
N
2500
The formula for the standard error of the stratified mean is cumbersome but not complicated:
2
2
2
1
(
1350
) (
353 96
.
)(
+
700
) (
631 50
.
)(
+
450
)(
295 29
.)
∑
22
=
s
=
Ns
=
12 74
.
x
h
x
st
2
h
2
N
(
2500
)
If the sample size is fairly large, the confidence limits on the mean are given by
95% confidence limits =
99% confid
Xs
±2
st
x
st
ence limits =
X
±2.
s
st
x
st
There is no simple way of compiling the confidence limits for small samples.
7.11.2.1 Sample Allocation
If a sample of
n
units is taken, how many units should be selected in each stratum? Among several
possibilities, the most common procedure is to allocate the sample in proportion to the size of the
stratum; in a stratum having 2/5 of the units of the population, we would take 2/5 of the samples.
In the population discussed in the previous example, the proportional allocation of the 55 sample
units was as follows:
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