Geoscience Reference
In-Depth Information
··
,
so that e
s
timates of
f
the variance and standard error are
Var(
TN y
) ar()
y
y
··
.
An approximate 100(1 − α)% confidence interval for the true population
total can also be calculated in essentially the same manner as described in
the previous section for finding a confidence interval for the population
mean. For example, an approximate 95% confidence interval is
and
SE() SE()
TNy
·
·
T
±
1.96 SE()
T
y
.
(2.11)
y
EXAMPLE 2.2 Estimation of a Total by Strip Transect Sampling
Suppose that there is interest in using strip transect sampling for esti-
mating the number of deer pellet groups in a study area. Assume that to
this end the area is covered with 5808 strip transects each with a width
of 3 m and a length 20 m, and 20 of these are randomly sampled with-
out replacement. The number of pellet groups in each sample transect is
then determined by careful searching.
If this procedure yields a mean of
y
5.55
pellet groups per tran-
sect wit
h
a standard deviati
on
of
s
= 3.75, then the estimated standard
error of
y
is found to be
·
, and
the estimated number of pellet groups in the entire study ar
ea
is
·
==
SE() [{3.75 /20}{1 20/5808}]
y
=
2
−
=
0.837
TNy
y
y
··
5808 × 0.837 = 4861.3. Finally, an approximate 95% confidence interval for
the true total number of pellet groups is 32,234.4 ± 1.96 × 4861.3, wh ich
gives the limits 22,706 to 41,763 rounded to the nearest integers.
5808 × 5.55 = 32234.4, with an estimated standard error of
SE() SE()
TNy
=
=
2.5 Sample Sizes for Estimation of Means
One of the key considerations in designing a study is the sample size that
will be used. This should be large enough to give adequate accuracy for the
estimation of the population parameters of interest but should not be unnec-
essarily large. The sample size is determined by the resources available and
the properties desired for the estimates, but in most studies the resources
available have the greatest influence. In some cases, the resources available
do not allow reasonably accurate estimation. In that case, serious consider-
ation needs to be made about whether the study should proceed or whether
there is some alternative way to obtain the desired information about the
parameters of interest.
There are various approaches for determining an appropriate sample
size for a study. For example, it might be decided it
h
at the 95% confidence
interval for the mean that is obtained should be
yd
, where
d
is some
