Geoscience Reference
In-Depth Information
drawn because all areas are equally represented from a statistical point of
view regardless of sample site locations.
10.4.1.2 Two-Stage Sampling
Two-stage designs (Cochran, 1977, Chapter 11; Scheaffer et al
.
, 1979, Chapter 9;
Särndal et al
.
, 1992, Chapter 4; Lohr, 2010, Chapter 6) contain two nested levels
of sampling. Two-stage sampling is implemented when sites can be naturally
grouped into large collections and it is relatively easy to select the large col-
lections. The large collections of sample sites are called primary sample units
and are defined to exist at level 1 of the study. When geographic areas are
sampled, the primary units are usually large polygons such as watersheds,
sections, counties, states, and the like. In general, primary units could be any
structure containing multiple sites or sample units. Under this design, pri-
mary units are selected using one of the basic spatial designs, such as simple
random sampling, systematic sampling, GRS, or BAS.
Once primary sample units are defined and selected via some design, the
actual locations for sample sites are selected from within the chosen primary
units. In this setting, sample sites are called secondary sample units and
are said to exist at level 2 of the study. Secondary units are selected from
each primary unit using one of the basic spatial samples, for instance simple
random, systematic, GRS, or BAS. It is not necessary for the sampling design
or sample size to be consistent across primary units but usually it is. An
example two-stage sample appears in Figure 10.2.
It is possible to implement a design with three or more levels when sam-
ple units naturally nest within one another. For example, when sampling
the entire Unites States, it may make sense to select states, then townships
within states, then sections within townships, then sites within townships.
Two-stage designs with less than a census of primary units at level 1 are
relatively rare in ecological studies. More commonly, every primary unit at
stage 1 is selected, and all sampling is done at stage 2. In this case, the design
is said to be stratified (see next section). However, if there are many large pri-
mary units, selecting a spatially balanced sample of primary units followed
by a spatially balanced sample of secondary units may be a good design for
either research or monitoring purposes.
10.4.1.3 Stratified Sampling
Stratified designs, as covered in Chapter 2, are special cases of two-stage
designs that occur when all primary units are selected and a sample of sec-
ondary units is drawn from each. When all primary units are sampled, the
primary units are renamed strata. Collectively, the strata partition the study
area into mutually exclusive sets of secondary units (sites). An example strat-
ified sample appears in Figure 10.3. Like two-stage sampling, sample size
and even design can vary between strata.
