Geoscience Reference
In-Depth Information
The estimator of the variance for the duck population is fairly straightforward
because there is only one network sampled where the
y
* is not zero. The joint
inclusion probability using Equation (3.3) for the network of size 7 with itself is
α=α=
0.3056
11
.
1
The joint inclusion probabilities for networks that were not selected do not
need to be calculated because for these,
z
k
= 0. The estimator of the variance
from Equation (3.4) is therefore
α−αα
αα
187
187
·
∑
∑
jk
j
k
(
ˆ
)
**
Va r
τ=
y y
z z
jk
jk
j
=
1
k
=
1
j
k
α−αα
αα
α−αα
αα
*
*
11
11
*
*
12
12
=
yy
zz
+
yy
zz
+
1
1
11
1
2
12
11
12
α αα
αα
*
*
187187
187
187
…
+
yy
zz
187
187
187
187
187
187
α−αα
αα
α−αα
αα
11
11
12
12
=
yy
*
*
zz
+⋅
y
*
0
⋅
z z
+
1
1
11
1
12
11
12
⋅
α αα
αα
*
*
187187
187
187
…
+
yy
0
187
187
187
187
⋅⋅
2
0.3056 0.3056
0.3056
−
2
=
13753
11
2
8
=
4.2978 10
⋅
There are various software packages that can be used for these calculations
(e.g., Morrison et al., 2008).
A considerable amount of literature has been written on how to design an
adaptive cluster sampling method to improve survey efficiency. How efficient
the design will be depends on how clustered the population is; the more clus-
tered the population is, the more efficient adaptive cluster sampling is com-
pared with simple random sampling (Smith et al., 2004, 2011; Brown, 2003).
Efficiency also depends on the survey design, including features such as the
condition used to trigger adaptive selection; the definition of the neighbor-
hood in which adaptive searching takes place (e.g., the surrounding two, four,
or eight neighboring units); the size of the initial sample; and the size of the
sample units. As a general rule, efficient designs will have the final sample
size not excessively larger than the initial sample size and will have small
networks. This can be achieved using large criteria for adapting and small
neighborhood definitions (Brown, 2003). Recent reviews of adaptive cluster
sampling were given by Smith et al
.
(2004) and Turk and Borkowski (2005).
