Geoscience Reference
In-Depth Information
case, then a systematic sample can be treated as effectively a simple random
sample, and the various results given previously for this type of sampling
can all be used.
Another possibility involves the estimation of a sampling variance by rep-
licating a systematic sample. For example, suppose that a 10% sample of a
population is required, where the population units are listed in some order.
Rather than taking every 10th item, starting with one of the items 1 to 10, ran-
domly chosen, it might be possible to take 20 systematic samples, each start-
ing at a different randomly chosen item in the first 200, and sampling every
200th item from that point. The population can then be thought of as con-
sisting of
N
= 200 clusters from which 20 are randomly sampled. Inferences
concerning the population mean and total can be made in the usual manner
for simple random sampling.
If systematic samples are analyzed as if they are simple random samples,
then the sample variance Σ(
y
i
−
y
)
2
/(
n
− 1) will tend to be an overestimate of
the true variance if the population shows a trend and might be an underes-
timate if the population has periodic effects that match or nearly match the
distance between samples. However, if sample points are far enough apart to
be more or less independent, then systematic and random sampling will be
almost equivalent. In most situations, periodicity is unlikely to be a problem.
It would require that, for some reason, the observations at the systematically
determined sample locations tend to be higher or lower than observations
in general.
One alternative to treating a systematic sample as effectively a random
sample involves combining adjacent points into strata, as indicated in
Figure 2.3, which is essentially just a poststratification of the data. The popu-
lation mean and standard error are then estimated using the usual equa-
tions for stratified random sampling. The assumption being made is that the
sample within each of the imposed strata is equivalent to a random sample.
Site Boundary
FIGURE 2.3
Grouping sample points from a systematic sample so that it can be analyzed as a stratified
sample. The sample points • are grouped here into 10 strata, each containing six points.
