Comparison of
Ranked Set Sampling to Alternative Sample Designs and
Investigation of its Usefulness in Environmental Monitoring
Loveday L. Conquest
Ranked set
sampling (RSS) is a two-phase sampling procedure
involving initial ranking of each of m samples of size m
(often via a relatively cheap or fast method of
measurement), followed by observing (often using a more
accurate and more expensive method of measurement) the
first order statistic from the first sample, the second
order statistic from the second sample, and so on, until
the mth order statistic from the mth sample yields a
secondary sample of size m from the initial m^2 data
points. Two examples are as follows:
1.
Assessing sediment contamination can involve measuring
the amount of a toxic substance in samples of sediment.
Suppose there is a cheap way to get a rough estimate of
the amount of contaminant present in a batch of
sediment, along with a more expensive way which yields a
more accurate estimate. We cannot afford to do too many
of these expensive measurements, so it is important to
obtain as representative a sample of the population as
possible.
2. Much of stream and wetland
monitoring involves measuring the amount of area present
that can be attributed to different habitat types, such
as pools and riffles in a stream, or types of different
vegetative cover in a wetland. Currently, measurement of
habitat unit or vegetative cover area is done largely by
visual examination (which is quick and has many
problems) and occasionally by more precise measurement
(more labor intensive and thus more costly).
In
both of the above examples, RSS could potentially yield
more representative samples. By making use of the
cheaper measurement method, the initial ranking (of m
samples of size m) could be accomplished at a lower cost
per unit, thus saving the more expensive and more
accurate measurement method for the second stage of
sampling, when only m units are measured. It is also
possible to run additional cycles of m ranked sets to
yield m more measured units per cycle.
Previous
research on RSS has evaluated its utility compared to
simple random sampling (SRS) designs and has
demonstrated its superiority over SRS. We will examine
alternative sample designs that are used in other fields
to see under what conditions RSS is an appropriate
procedure. The dual phase nature of ranked set sampling
raises many interesting statistical questions. For
example, more extensive stratification in phase 1 might
help, particularly if first-phase sample points were
ranked relative to the assumed distribution of the
entire data set (using chosen "cup points" based on
prior knowledge). Another issue concerns the effect of
ranking errors. Assessing effects of errors in ranking
could increase the usefulness of RSS for environmental
managers. We also plan to apply RSS to actual sets of
data concerning habitat measurements for streams and
estuarine areas in Washington and Oregon. For more
information go to A
Comparison of Methods for Estimating Stream Habitat
Area.
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