Geoscience Reference
In-Depth Information
into nonoverlapping strata, and an independent simple random sample is
selected from each of these strata.
Often, there is nothing to lose by using this more complicated type of
sampling, but there are some potential gains. First, if the individuals within
strata are rather more similar than individuals in general, then the estimate
of the overall population mean will have a smaller standard error than can
be obtained with the same simple random sample size. Second, there may be
value in having separate estimates of population parameters for the differ-
ent strata. Third, stratification makes it possible to sample different parts of
a population in different ways, which may make some cost savings possible.
On the other hand, a stratified sampling design has problems when there
are errors in allocating sample units to the strata. This may occur, for exam-
ple, if the allocation is made using a map that is not completely accurate.
Then, when sample units are visited in the field, it may be found that some
are not in the expected strata. If these units are reclassified into the correct
strata, then this means that all population units within the new stratum no
longer have the same probability of being sampled. Hence, the sampling
design is changed, with the possibility of introduction of some estimation
bias. Another possible problem with stratified sampling is that after the data
are collected, it is desired to do an analysis with some other form of stratifica-
tion or some analysis that assumes that the data come from simple random
sampling. This is always a possibility, and it led Overton and Stehman (1995)
to argue strongly in favor of using simple sampling designs with limited or
no stratification.
Generally, the types of stratification that should be considered are those
based on spatial location, areas within which the population is expected to
be fairly uniform, and the size of sampling units. For example, in sampling
an animal population over a large area, it is natural to take a map and parti-
tion the area into a few apparently homogeneous strata based on factors such
as altitude and vegetation type. In sampling insects on trees, it might make
sense to stratify on the basis of small, medium, and large tree diameters. In
sampling households, a town can be divided into regions within which the
age and class characteristics are relatively uniform. Usually, the choice of
how to stratify is just a question of common sense.
Assume that
K
strata have been chosen, with the
i
ith of these having size
N
i
and the total population size being Σ
N
i
=
N
. Then, if a random sample with
size
n
i
is taken from the
i
ith stratum, the sample mean
y
i
will be an unbiased
estimate of the true stratum mean μ
i
with estimated variance
·
(1 −
n
i
/
N
i
) where
s
i
is the sample standard deviation of
Y
within the stratum.
These results follow by simply applying the results discussed previously for
simple random sampling to the
i
ith stratum only.
In terms of the true strata means, the overall population mean is the
weighted average
2
Var( )(/)
i
ys
n
i
i
