Geoscience Reference
In-Depth Information
10.2 Design Characteristics
This section contains short and informal discussions about a few design
characteristics that are important for practitioners. The section defines sci-
entific surveys, gives a few examples of nonscientific surveys, and discusses
the difference between research and monitoring studies.
10.2.1 Scientific Designs
A working and practical definition of scientific designs involves probability
samples, which in turn depend on the definition of inclusion probabilities.
Thus, inclusion probabilities (specifically, the first-order inclusion probabili-
ties) are defined first, followed by probability samples, followed by the prac-
tical definition of scientific design.
The first-order inclusion probability (or sometimes just inclusion probabil-
ity) is simply the probability of including any particular site in the sample.
Technically, inclusion probabilities are strictly greater than 0 and less than
or equal to 1. Inclusion probabilities can either be constant across sites or
vary site to site. When inclusion probabilities vary, they commonly depend
on strata membership or geographic location or are proportional to an exter-
nal continuous valued variable associated with the site (such as elevation,
annual rainfall, distance from the coast, etc.).
To make this definition concrete, consider the following example: Consider
a study area partitioned into 100 quadrats (squares) and assume a researcher
wishes to draw a simple random sample of 3 quadrats from these 100. A total of
100 99 98
321
××
××
100
3
=
=
161,700
possible samples exists, and any particular quadrat is present in
99 98
21
4,851
×
×
99
2
=
=
of them. The probability of including a quadrat is therefore 4,851/161,700 = 0.03,
as expected. If, instead of a simple random sample, the researcher ordered the
list of quadrats by location, flipped a coin for each quadrat, and included the
first three associated with heads, the inclusion probability of any particular
quadrat would depend on its place in the list and the geometric distribution.
A working definition of a probability sample is a sample drawn in a way
that the first-order inclusion probability of all sites can be known exactly.
This definition admits those samples for which the first-order inclusion
probabilities are not immediately known but could be calculated for all sites
