Geoscience Reference
In-Depth Information
of the need to base the inferences on the laws of probability. In this con-
nection, it must be appreciated that random sampling is not the same as a
haphazard selection of the units to be surveyed. Rather, it involves the selec-
tion of units using a well-defined and carefully carried out randomization
procedure that (in a simple application) ensures that all possible samples of
the required size are equally likely to be chosen.
Although this is the case, it is a fact that with ecological sampling the
strictly random selection of sample units is not always possible. This issue
is discussed further in this chapter and in other chapters as well. For the
moment, it is assumed that true random sampling can be carried out.
Because all possible samples can occur with random sampling, it is obvi-
ous that this method might produce exactly the same units as a haphaz-
ardly drawn sample. It is important therefore to appreciate that the key to the
value of random sampling is the properties of the sampling procedure rather
than the specific units that are obtained. In fact, it is not uncommon to feel
uncomfortable with the result of random sampling because it does not look
representative enough. But, this will not be a valid objection to the sample
providing that the procedure used to select it was defined and carried out in
an appropriate manner.
Simple random sampling involves giving each sample unit the same proba-
bility of selection. This can be with replacement, in which case every selected
unit is chosen from the full population irrespective of which units have
already been included in the sample, or without replacement, in which case
a sample unit can occur at most once in the sample. As a general principle,
sampling without replacement is preferable to sampling with replacement
because it gives slightly more accurate estimation of population parameters.
However, the difference between the two methods of sampling is not great
when the population size is much larger than the sample size.
EXAMPLE 2.1 Sampling Plants in a Large Study Area
Suppose that it is required to estimate the density of plants of a certain
species in a large study area. Then, one approach would be to set up a
grid and consider the area to consist of the quadrats that this produces.
Figure 2.1 indicates the type of result that might then be obtained; in this
case, there are 120 quadrats covering a rectangular study area. The quad-
rats are then the sampling units that make up the population of interest.
The list of these units is sometimes called the sampling frame.
The next step would be to decide on a sample size
n
; that is, how many
quadrats should be randomly sampled to estimate the population mean
number of plants per quadrat with an acceptable level of accuracy?
Methods for choosing sample sizes are discussed further elsewhere, but
for this example, it is assumed that a sample size of 12 is needed.
There are various ways to determine the random sample. It is defi-
nitely not allowable just to think up the numbers because human beings
do not have random number generators in their heads. One approach in
