RESEARCH METHOD COHEN ok

106 SAMPLING
would be insufficient to construct a sample consisting
of ten female classroom teachers of Arts
and Humanities subjects.
Quantitative data
For quantitative data, a precise sample number
can be calculated according to the level of accuracy
and the level of probability that researchers require
in their work. They can then report in their
study the rationale and the basis of their research
decisions (Blalock 1979).
By way of example, suppose a teacher/researcher
wishes to sample opinions among 1,000 secondary
school students. She intends to use a 10-point
scale ranging from 1 = totally unsatisfactory to
10 = absolutely fabulous. She already has data
from her own class of thirty students and suspects
that the responses of other students will be
broadly similar. Her own students rated the
activity (an extracurricular event) as follows: mean
score = 7.27; standard deviation = 1.98. In other
words, her students were pretty much ‘bunched’
about a warm, positive appraisal on the 10-point
scale. How many of the 1,000 students does she
need to sample in order to gain an accurate (i.e.
reliable) assessment of what the whole school
(n = 1, 000) thinks of the extracurricular event
It all depends on what degree of accuracy and what level
of probability she is willing to accept.
AsimplecalculationfromaformulabyBlalock
(1979: 215–18) shows that:
if she is happy to be within + or − 0.5 of a scale
point and accurate 19 times out of 20, then she
requires a sample of 60 out of the 1,000;
if she is happy to be within + or − 0.5 of a
scale point and accurate 99 times out of 100,
then she requires a sample of 104 out of the
1,000
if she is happy to be within + or − 0.5 of a scale
point and accurate 999 times out of 1,000, then
she requires a sample of 170 out of the 1,000
if she is a perfectionist and wishes to be within
+ or − 0.25 of a scale point and accurate 999
times out of 1,000, then she requires a sample
of 679 out of the 1,000.
It is clear that sample size is a matter of
judgement as well as mathematical precision; even
formula-driven approaches make it clear that there
are elements of prediction, standard error and
human judgement involved in determining sample
size.
Sampling error
If many samples are taken from the same
population, it is unlikely that they will all have
characteristics identical with each other or with
the population; their means will be different. In
brief, there will be sampling error (see Cohen
and Holliday 1979, 1996). Sampling error is often
taken to be the difference between the sample
mean and the population mean. Sampling error
is not necessarily the result of mistakes made
in sampling procedures. Rather, variations may
occur due to the chance selection of different
individuals. For example, if we take a large
number of samples from the population and
measure the mean value of each sample, then
the sample means will not be identical. Some
will be relatively high, some relatively low, and
many will cluster around an average or mean value
of the samples. We show this diagrammatically in
Box 4.2 (see http://www.routledge.com/textbooks/
9780415368780 – Chapter 4, file 4.4.ppt).
Why should this occur We can explain the
phenomenon by reference to the Central Limit
Theorem which is derived from the laws of
probability. This states that if random large
samples of equal size are repeatedly drawn from
any population, then the mean of those samples
will be approximately normally distributed. The
distribution of sample means approaches the
normal distribution as the size of the sample
increases, regardless of the shape – normal or
otherwise – of the parent population (Hopkins
et al. 1996:159,388).Moreover,theaverageor
mean of the sample means will be approximately
the same as the population mean. Hopkins et al.
(1996: 159–62) demonstrate this by reporting
the use of computer simulation to examine the
sampling distribution of means when computed
10,000 times (a method that we discuss in