RESEARCH METHOD COHEN ok

PROBABILITY SAMPLES 111
subjects for the sample. This can be done by
drawing names out of a container until the required
number is reached, or by using a table of
random numbers set out in matrix form (these
are reproduced in many books on quantitative
research methods and statistics), and allocating
these random numbers to participants or cases
(e.g. Hopkins et al. 1996: 148–9). Because of
probability and chance, the sample should contain
subjects with characteristics similar to the
population as a whole; some old, some young,
some tall, some short, some fit, some unfit,
some rich, some poor etc. One problem associated
with this particular sampling method
is that a complete list of the population is
needed and this is not always readily available
(see http://www.routledge.com/textbooks/
9780415368780 – Chapter 4, file 4.7.ppt).
Systematic sampling
This method is a modified form of simple random
sampling. It involves selecting subjects from a
population list in a systematic rather than a
random fashion. For example, if from a population
of, say, 2,000, a sample of 100 is required,
then every twentieth person can be selected.
The starting point for the selection is chosen at
random (see http://www.routledge.com/textbooks/
9780415368780 – Chapter 4, file 4.8.ppt).
One can decide how frequently to make
systematic sampling by a simple statistic – the total
number of the wider population being represented
divided by the sample size required:
f = N sn
f = frequency interval
N = the total number of the wider population
sn = the required number in the sample.
Let us say that the researcher is working with a
school of 1,400 students; by looking at the table
of sample size (Box 4.1) required for a random
sample of these 1,400 students we see that 302
students are required to be in the sample. Hence
the frequency interval (f) is:
1, 400
= 4.635 (which rounds up to 5.0)
302
Hence the researcher would pick out every fifth
name on the list of cases.
Such a process, of course, assumes that the
names on the list themselves have been listed in a
random order. A list of females and males might
list all the females first, before listing all the males;
if there were 200 females on the list, the researcher
might have reached the desired sample size before
reaching that stage of the list which contained
males, thereby distorting (skewing) the sample.
Another example might be where the researcher
decides to select every thirtieth person identified
from a list of school students, but it happens that:
(a) the school has just over thirty students in each
class; (b) each class is listed from high ability to
low ability students; (c) the school listing identifies
the students by class.
In this case, although the sample is drawn
from each class, it is not fairly representing the
whole school population since it is drawing almost
exclusively on the lower ability students. This is
the issue of periodicity (Calder 1979). Not only is
there the question of the order in which names
are listed in systematic sampling, but also there
is the issue that this process may violate one of
the fundamental premises of probability sampling,
namely that every person has an equal chance
of being included in the sample. In the example
above where every fifth name is selected, this
guarantees that names 1–4, 6–9 etc. will be
excluded, i.e. everybody does not have an equal
chance to be chosen. The ways to minimize this
problem are to ensure that the initial listing is
selected randomly and that the starting point for
systematic sampling is similarly selected randomly.
Stratified sampling
Stratified sampling involves dividing the population
into homogenous groups, each group
containing subjects with similar characteristics.
For example, group A might contain males and
group B, females. In order to obtain a sample
representative of the whole population in
Chapter 4