RESEARCH METHOD COHEN ok

THE SAMPLE SIZE 105
rapidly generate the need for a very large sample.
If subgroups are required then the same rules for
calculating overall sample size apply to each of the
subgroups.
Further, determining the size of the sample
will also have to take account of non-response,
attrition and respondent mortality, i.e. some
participants will fail to return questionnaires,
leave the research, return incomplete or spoiled
questionnaires (e.g. missing out items, putting
two ticks in a row of choices instead of only
one). Hence it is advisable to overestimate rather
than to underestimate the size of the sample
required, to build in redundancy (Gorard 2003:
60). Unless one has guarantees of access, response
and, perhaps, the researcher’s own presence at
the time of conducting the research (e.g. presence
when questionnaires are being completed), then
it might be advisable to estimate up to double the
size of required sample in order to allow for such
loss of clean and complete copies of questionnaires
or responses.
In some circumstances, meeting the requirements
of sample size can be done on an evolutionary
basis. For example, let us imagine that you
wish to sample 300 teachers, randomly selected.
You succeed in gaining positive responses from
250 teachers to, for example, a telephone survey
or a questionnaire survey, but you are 50 short of
the required number. The matter can be resolved
simply by adding another 50 to the random sample,
and, if not all of these are successful, then
adding some more until the required number is
reached.
Borg and Gall (1979: 195) suggest that, as a
general rule, sample sizes should be large where
there are many variables
only small differences or small relationships are
expected or predicted
the sample will be broken down into subgroups
the sample is heterogeneous in terms of the
variables under study
reliable measures of the dependent variable are
unavailable.
Oppenheim (1992: 44) adds to this the view
that the nature of the scales to be used also exerts
an influence on the sample size. For nominal data
the sample sizes may well have to be larger than
for interval and ratio data (i.e. a variant of the
issue of the number of subgroups to be addressed,
the greater the number of subgroups or possible
categories, the larger the sample will have to be).
Borg and Gall (1979) set out a formuladriven
approach to determining sample size (see
also Moser and Kalton 1977; Ross and Rust 1997:
427–38), and they also suggest using correlational
tables for correlational studies – available in most
texts on statistics – as it were ‘in reverse’ to
determine sample size (Borg and Gall 1979:
201), i.e. looking at the significance levels of
correlation coefficients and then reading off the
sample sizes usually required to demonstrate that
level of significance. For example, a correlational
significance level of 0.01 would require a sample
size of 10 if the estimated coefficient of correlation
is 0.65, or a sample size of 20 if the estimated
correlation coefficient is 0.45, and a sample size of
100 if the estimated correlation coefficient is 0.20.
Again, an inverse proportion can be seen – the
larger the sample population, the smaller the
estimated correlation coefficient can be to be
deemed significant.
With both qualitative and quantitative data,
the essential requirement is that the sample
is representative of the population from which
it is drawn. In a dissertation concerned with
a life history (i.e. n = 1), the sample is the
population!
Qualitative data
In a qualitative study of thirty highly able girls
of similar socio-economic background following
an A level Biology course, a sample of five or
six may suffice the researcher who is prepared to
obtain additional corroborative data by way of
validation.
Where there is heterogeneity in the population,
then a larger sample must be selected on
some basis that respects that heterogeneity. Thus,
from a staff of sixty secondary school teachers
differentiated by gender, age, subject specialism,
management or classroom responsibility, etc., it
Chapter 4