RESEARCH METHOD COHEN ok

THE SAMPLE SIZE 101
The sample size
A question that often plagues novice researchers is
just how large their samples for the research should
be. There is no clear-cut answer, for the correct
sample size depends on the purpose of the study
and the nature of the population under scrutiny.
However, it is possible to give some advice on this
matter. Generally speaking, the larger the sample
the better, as this not only gives greater reliability
but also enables more sophisticated statistics to be
used.
Thus, a sample size of thirty is held by many
to be the minimum number of cases if researchers
plan to use some form of statistical analysis on
their data, though this is a very small number
and we would advise very considerably more.
Researchers need to think out in advance of any
data collection the sorts of relationships that they
wish to explore within subgroups of their eventual
sample. The number of variables researchers set
out to control in their analysis and the types
of statistical tests that they wish to make must
inform their decisions about sample size prior
to the actual research undertaking. Typically an
anticipated minimum of thirty cases per variable
should be used as a ‘rule of thumb’, i.e. one must
be assured of having a minimum of thirty cases
for each variable (of course, the thirty cases for
variable one could also be the same thirty as for
variable two), though this is a very low estimate
indeed. This number rises rapidly if different
subgroups of the population are included in the
sample (discussed below), which is frequently the
case.
Further, depending on the kind of analysis to
be performed, some statistical tests will require
larger samples. For example, less us imagine that
one wished to calculate the chi-square statistic,
a commonly used test (discussed in Part Five)
with cross-tabulated data, for example looking at
two subgroups of stakeholders in a primary school
containing sixty 10-year-old pupils and twenty
teachers and their responses to a question on a
5-point scale (see diagram below).
Here one can notice that the sample size
is eighty cases, an apparently reasonably sized
sample. However, six of the ten cells of responses
(60 per cent) contain fewer than five cases.
The chi-square statistic requires there to be five
cases or more in 80 per cent of the cells (i.e.
eight out of the ten cells). In this example only
40 per cent of the cells contained more than
five cases, so even with a comparatively large
sample, the statistical requirements for reliable
data with a straightforward statistic such as chisquare
have not been met. The message is clear,
one needs to anticipate, as far as one is able,
some possible distributions of the data and see if
these will prevent appropriate statistical analysis;
if the distributions look unlikely to enable reliable
statistics to be calculated then one should increase
the sample size, or exercise great caution in
interpreting the data because of problems of
reliability, or not use particular statistics, or,
indeed, consider abandoning the exercise if the
increase in sample size cannot be achieved.
The point here is that each variable may need
to be ensured of a reasonably large sample size (a
minimum of maybe six–ten cases). Indeed Gorard
(2003: 63) suggests that one can start from the
minimum number of cases required in each cell,
multiply this by the number of cells, and then
double the total. In the example above, with six
cases in each cell, the minimum sample would be
120 (6 × 10 × 2), though, to be on the safe side,
to try to ensure ten cases in each cell, a minimum
Chapter 4
Variable: 10-year-old pupils should do one hour’s homework each weekday evening
Strongly disagree Disagree Neither agree Agree Strongly agree
nor disagree
10-year-old pupils in the school 25 20 3 8 4
Teachers in the school 6 4 2 4 4