Geoscience Reference
In-Depth Information
required for any variable. However, if this is not possible within the available
resources, then some smaller size might need to be used, and some variables
might have to be estimated with less precision than was originally desired.
EXAMPLE 2.3 Determining the Sample Size for Strip Transect
Sampling
In a pilot study of winter mortality of deer in central Wyoming, strip
transects 1 km long by 60 m wide were walked to look for dead animals.
In 36 randomly
se
lected transects, 12 dead deer were counted to give a
sample mean of =
y
12/36 0.333
dead deer per transect, with a sample
standard deviation of
s
= 0.828. The estimated percentage CV of counts
per transect was therefore
=
CV(
·
100 × 0.828/0.333 = 248.6%.
Suppose that it was determined that the target CV for estimating the
population mean number of dead deer per transect for the main study
was 15%. There were about
N
= 50,000 possible transects, so Equation
(2.14) shows that the number of transects needed to be sampled to reach
this target is
n
= 2.486
2
/{0.15
2
+ 2.486
2
/50,000} = 273.2 transects, say 273
transects. Because the population size
N
is so large, Equation (2.15) gives
almost the same result, with
n
= 2.486
2
/0.15
2
= 2 74 . 7.
y
=
2.6 Errors in Sample Surveys
In general, there are four sources of error or variation in scientific studies
(Cochran, 1977). First, the observations vary with the sample units, and as a
result, different random samples will generally produce different estimates
of population parameters. This variation is just because of sampling errors.
Second, there may be errors caused by the lack of uniformity in the man-
ner in which a study is conducted. The measurement procedure might be
biased, imprecise, or both biased and imprecise. This type of measurement
error results solely from the manner in which the observations are made.
For example, a fisher might report incorrect lengths and weights of the fish
caught, human subjects might lie about their age or weight, or a measure-
ment instrument might not be correctly calibrated. Third, there might be
missing data because of the failure to measure some units in the sample.
This will introduce a bias if the missing values are unusual in some way. For
example, in a study of vegetation, some sample plots might be inaccessible,
and in fact these plots have high densities of the plants of interest. Finally,
errors might be introduced in recording, typing, and editing data.
An understanding of sampling errors and their effects is the basis of statis-
tical inference procedures, with the assumption that these errors are far more
important than the other errors. In reality, however, the other three types of
error might be more important than the sampling errors unless great care is
