RESEARCH METHOD COHEN ok

102 SAMPLING
sample of 200 might be better (10 × 10 × 2),
though even this is no guarantee.
The issue arising out of the example here is
also that one can observe considerable variation
in the responses from the participants in the
research. Gorard (2003: 62) suggests that if a
phenomenon contains a lot of potential variability
then this will increase the sample size. Surveying
avariablesuchasintelligencequotient(IQ)for
example, with a potential range from 70 to around
150, may require a larger sample rather than a
smaller sample.
As well as the requirement of a minimum
number of cases in order to examine relationships
between subgroups, researchers must obtain the
minimum sample size that will accurately represent
the population being targeted. With respect to size,
will a large sample guarantee representativeness
Not necessarily! In our first example, the
researcher could have interviewed a total sample
of 450 females and still not have represented
the male population. Will a small size guarantee
representativeness Again, not necessarily! The
latter falls into the trap of saying that 50 per
cent of those who expressed an opinion said that
they enjoyed science, when the 50 per cent was
only one student, a researcher having interviewed
only two students in all. Furthermore, too large
asamplemightbecomeunwieldyandtoosmall
asamplemightbeunrepresentative(e.g.inthe
first example, the researcher might have wished to
interview 450 students but this would have been
unworkable in practice, or the researcher might
have interviewed only ten students, which, in all
likelihood, would have been unrepresentative of
the total population of 900 students).
Where simple random sampling is used, the
sample size needed to reflect the population value
of a particular variable depends both on the size of
the population and the amount of heterogeneity
in the population (Bailey 1978). Generally, for
populations of equal heterogeneity, the larger the
population, the larger the sample that must be
drawn. For populations of equal size, the greater
the heterogeneity on a particular variable, the
larger the sample that is needed. To the extent
that a sample fails to represent accurately the
population involved, there is sampling error,
discussed below.
Sample size is also determined to some extent
by the style of the research. For example, a survey
style usually requires a large sample, particularly if
inferential statistics are to be calculated. In ethnographic
or qualitative research it is more likely that
the sample size will be small. Sample size might
also be constrained by cost – in terms of time,
money, stress, administrative support, the number
of researchers, and resources. Borg and Gall (1979:
194–5) suggest that correlational research requires
asamplesizeofnofewerthanthirtycases,that
causal-comparative and experimental methodologies
require a sample size of no fewer than fifteen
cases, and that survey research should have no
fewer than 100 cases in each major subgroup and
twenty–fifty in each minor subgroup.
Borg and Gall (1979: 186) advise that sample
size has to begin with an estimation of the smallest
number of cases in the smallest subgroup of the
sample, and ‘work up’ from that, rather than vice
versa. So, for example, if 5 per cent of the sample
must be teenage boys, and this subsample must be
thirty cases (e.g. for correlational research), then
the total sample will be 30 ÷ 0.05 = 600; if 15 per
cent of the sample must be teenage girls and the
subsample must be forty-five cases, then the total
sample must be 45 ÷ 0.15 = 300 cases.
The size of a probability (random) sample can be
determined in two ways, either by the researcher
exercising prudence and ensuring that the sample
represents the wider features of the population with
the minimum number of cases or by using a table
which, from a mathematical formula, indicates the
appropriate size of a random sample for a given
number of the wider population (Morrison 1993:
117). One such example is provided by Krejcie
and Morgan (1970), whose work suggests that if
the researcher were devising a sample from a wider
population of thirty or fewer (e.g. a class of students
or a group of young children in a class) then she
or he would be well advised to include the whole
of the wider population as the sample.
Krejcie and Morgan (1970) indicate that the
smaller the number of cases there are in the wider,
whole population, the larger the proportion of