Geoscience Reference
In-Depth Information
these are briefly mentioned. For further details on these methods, see Manly
(2009, Chapter 2). The following chapters also describe some other strategies.
With cluster sampling, groups of sample units that are close in some sense
are randomly sampled together and then all measured. The idea is that this
will reduce the cost of sampling each unit so that more units can be mea-
sured than would be possible if they were all sampled individually. This
advantage is offset to some extent by the tendency of sample units that are
close together to have similar measurements. Therefore, in general, a cluster
sample of
n
units will give estimates that are less precise than a simple ran-
dom sample of
n
units. Nevertheless, cluster sampling may give better value
than the sampling of individual units in terms of what is obtained for a fixed
total sampling effort.
With multistage sampling, the sample units are regarded as falling within
a hierarchic structure. Random sampling is then conducted at the various
levels within this structure. For example, suppose that there is interest in
estimating the mean of some water quality variable in the lakes in a large
area, such as a whole country. The country might then be divided into pri-
mary sampling units consisting of states or provinces, each primary unit
might then consist of a number of counties, and each county might contain a
certain number of lakes. A three-stage sample of lakes could then be obtained
by first randomly selecting several primary sampling units, next randomly
selecting one or more counties (second-stage units) within each sampled
primary unit, and finally randomly selecting one or more lakes (third-stage
units) from each sampled county. This type of sampling plan might be use-
ful when a hierarchic structure already exists or when it is simply convenient
to sample at two or more levels.
The technique of composite sampling is valuable when the cost of select-
ing and acquiring sample units is much less than the cost of analyzing them.
What this involves is mixing several samples from approximately the same
location and then analyzing the composite samples. For example, sets of four
samples might be mixed so that the number of analyses is only one-quarter
of the number of samples. This should have little effect on the estimated
mean providing that samples are mixed sufficiently so that the observation
from a composite sample is close to the mean for the samples that it contains.
However, there is a loss of information about extreme values for individual
sample units because of dilution effects. If there is a need to identify indi-
vidual samples with extreme values, then methods are available to achieve
this without the need to analyze every sample.
Ranked set sampling is another method that can be used to reduce the
cost of analysis in surveys. The technique was originally developed for the
estimation of the biomass of vegetation (McIntyre, 1952), but the potential
uses are much wider. It relies on the existence of an inexpensive method of
assessing the relative magnitude of a small set of observations to supplement
expensive accurate measurements.
