RESEARCH METHOD COHEN ok

108 SAMPLING
The formula assumes that each sample is drawn
on a simple random basis. A small correction factor
called the finite population correction (fpc) is
generally applied as follows:
√
(1 − f)P × Q
SE of proportions =
where f is the
N
proportion included in the sample.
Where, for example, a sample is 100 out of 1,000,
fis0.1.
√
(1 − 0.1)(66 × 34)
SE of proportions =
= 4.49
100
With a sample of twenty-five, the SE = 9.4. In
other words, the favourable vote can vary between
56.6 per cent and 75.4 per cent; likewise, the unfavourable
vote can vary between 43.4 per cent
and 24.6 per cent. Clearly, a voting possibility
ranging from 56.6 per cent in favour to 43.4 per
cent against is less decisive than 66 per cent as opposed
to 34 per cent. Should the school principal
enlarge her sample to include 100 students, then
the SE becomes 4.5 and the variation in the range
is reduced to 61.5 per cent−70.5percentinfavour
and 38.5 per cent−29.5percentagainst.Sampling
the whole school’s opinion (n = 1, 000) reduces
the SE to 1.5 and the ranges to 64.5 per cent−67.5
per cent in favour and 35.5 per cent−32.5 per cent
against. It is easy to see why political opinion surveys
are often based upon sample sizes of 1,000 to
1,500 (Gardner 1978).
What is being suggested here generally is that,
in order to overcome problems of sampling error,
in order to ensure that one can separate random
effects and variation from non-random effects,
and in order for the power of a statistic to be
felt, one should opt for as large a sample as
possible. As Gorard (2003: 62) says, ‘power is an
estimate of the ability of the test you are using
to separate the effect size from random variation’,
and a large sample helps the researcher to achieve
statistical power. Samples of fewer than thirty are
dangerously small, as they allow the possibility of
considerable standard error, and, for over around
eighty cases, any increases to the sample size have
little effect on the standard error.
The representativeness of the sample
The researcher will need to consider the extent
to which it is important that the sample in fact
represents the whole population in question (in
the example above, the 1,000 students), if it is
to be a valid sample. The researcher will need
to be clear what it is that is being represented,
i.e. to set the parameter characteristics of the
wider population – the sampling frame – clearly
and correctly. There is a popular example of
how poor sampling may be unrepresentative and
unhelpful for a researcher. A national newspaper
reports that one person in every two suffers
from backache; this headline stirs alarm in every
doctor’s surgery throughout the land. However,
the newspaper fails to make clear the parameters
of the study which gave rise to the headline.
It turns out that the research took place in a
damp part of the country where the incidence
of backache might be expected to be higher
than elsewhere, in a part of the country which
contained a disproportionate number of elderly
people, again who might be expected to have more
backaches than a younger population, in an area
of heavy industry where the working population
might be expected to have more backache than
in an area of lighter industry or service industries,
and used only two doctors’ records, overlooking
the fact that many backache sufferers went to
those doctors’ surgeries because the two doctors
concerned were known to be overly sympathetic
to backache sufferers rather than responsibly
suspicious.
These four variables – climate, age group,
occupation and reported incidence – were seen
to exert a disproportionate effect on the study,
i.e. if the study were to have been carried
out in an area where the climate, age group,
occupation and reporting were to have been
different, then the results might have been
different. The newspaper report sensationally
generalized beyond the parameters of the data,
thereby overlooking the limited representativeness
of the study.
It is important to consider adjusting the
weightings of subgroups in the sample once the