Agriculture Reference
In-Depth Information
Table 7.1 Relative efficiency of the sample mean (MSE/MSE
SRS
) for each design, estimated
using 10,000 replicated samples of the highly clustered population, for different sample sizes,
trend, and homogeneity
No trend
Linear trend
Quadratic trend
Homogeneity
Homogeneity
Homogeneity
Design
n
Low
Med
High
Low
Med
High
Low
Med
High
GRTS
10
1.00
0.98
0.80
0.68
0.66
0.58
0.67
0.67
0.66
CUBE 1
10
1.00
0.98
0.99
0.56
0.55
0.48
0.89
0.88
0.94
CUBE 2
10
1.00
1.00
0.95
0.57
0.56
0.50
0.55
0.55
0.53
DUST 1
10
1.28
1.28
1.09
0.48
0.45
0.35
0.68
0.62
0.58
DUST 2
10
1.24
1.22
0.98
0.46
0.42
0.33
0.58
0.57
0.55
SCPS
10
1.01
0.97
0.78
0.62
0.60
0.50
0.66
0.67
0.66
LPM 1
10
1.01
0.98
0.77
0.59
0.59
0.49
0.65
0.65
0.64
LPM 2
10
1.02
0.97
0.77
0.60
0.58
0.48
0.64
0.65
0.63
GRTS
50
0.99
0.96
0.61
0.54
0.52
0.35
0.59
0.57
0.51
CUBE 1
50
1.00
1.01
0.99
0.51
0.50
0.43
0.89
0.87
0.93
CUBE 2
50
0.99
1.00
0.95
0.52
0.51
0.43
0.49
0.48
0.46
DUST 1
50
2.93
2.76
1.90
0.91
0.83
0.57
1.12
1.04
0.78
DUST 2
50
2.54
2.28
1.48
0.78
0.70
0.44
0.87
0.82
0.57
SCPS
50
0.98
0.93
0.59
0.54
0.50
0.34
0.56
0.54
0.45
LPM 1
50
1.01
0.94
0.59
0.53
0.50
0.32
0.55
0.52
0.44
LPM 2
50
0.99
0.95
0.58
0.53
0.50
0.32
0.55
0.52
0.44
GRTS
100
1.00
0.92
0.56
0.53
0.48
0.30
0.55
0.50
0.41
CUBE 1
100
1.00
1.00
0.98
0.51
0.50
0.42
0.89
0.87
0.93
CUBE 2
100
1.00
0.99
0.93
0.51
0.50
0.42
0.48
0.47
0.45
DUST 1
100
4.00
3.79
2.32
1.27
1.09
0.71
1.45
1.35
0.84
DUST 2
100
3.33
3.01
1.64
1.03
0.87
0.52
1.05
0.98
0.57
SCPS
100
1.01
0.91
0.52
0.52
0.47
0.28
0.53
0.49
0.37
LPM 1
100
1.01
0.90
0.52
0.52
0.46
0.28
0.53
0.48
0.37
LPM 2
100
1.01
0.92
0.51
0.52
0.47
0.28
0.52
0.48
0.37
when the trend was linear. This is the case if the selected units are centered in the
study region and well distributed across it, because they are forced to respect the
variability of the population in the two coordinates. Furthermore, this error reduc-
tion does not appear to change with the sample size, the spatial homogeneity, or the
distribution of the population.
The performance of DUST generally degraded as the sample size increased.
Furthermore, DUST 2 was less efficient. In fact, as expected, the DUST procedure
confirmed that its selection criterion might generate some very unstable and not
robust results. This is the case when the first-order inclusion probabilities are at
least not constant or variable, but not in a planned mode (i.e., when they are defined
in such way to be correlated with y). This circumstance is particularly evident when
the tuning parameter is very far from the unknown homogeneity of the population,
and when the sample size is very high. As a consequence, after some iterations, it is
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