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10.4.2.1 Systematic Sampling in Two Dimensions
Systematic samples, also called grid samples, are special cases of cluster sam-
pling for which each cluster is spread over the entire study area (i.e., secondary
units are not contiguous) and only one cluster is sampled. Systematic samples
derive their name from the fact that sample sites are systematically placed.
That is, after an initial random start, systematic samples choose secondary
units in the same relative location within groups or blocks of units. The size
and shape of each block are the design's step size (or grid spacing) and define
the number of secondary sites chosen. In general, systematic samples do not
yield a fixed number of sites per draw. That is, the clusters do not all contain
the same number of sites unless the study area size is evenly divisible by the
sample size (in all directions). Although varying sample size can pose prob-
lems logistically, it is known that varying cluster sizes do not pose any statis-
tical problems (Särndal et al . , 1992). This section discusses two-dimensional
systematic samples. One-dimensional systematic samples are possible and
should be implemented as GRS as discussed in the next section.
A systematic sample of a rectangular geographic region is shown in
Figure 10.5. This has dashed lines to show boundaries of blocks of second-
ary units from which a single unit is selected. The width and height of these
blocks are the horizontal and vertical step sizes. The width and height of
blocks are determined by the sample size and the width and height of the
FIGURE 10.5
Example of a 6 × 6 systematic sample with random start. Dashed lines indicate blocks of sec-
ondary units (sites) from which a single unit is selected. The set of sites in the same relative
position in each block constitutes a cluster.
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