RESEARCH METHOD COHEN ok

THE SAMPLE SIZE 103
that population must be which appears in the
sample. The converse of this is true: the larger
the number of cases there are in the wider,
whole population, the smaller the proportion
of that population can be which appears in the
sample (see http://www.routledge.com/textbooks/
9780415368780 – Chapter 4, file 4.2.ppt). They
note that as the population increases the proportion
of the population required in the sample diminishes
and, indeed, remains constant at around
384 cases (Krejcie and Morgan 1970: 610). Hence,
for example, a piece of research involving all the
children in a small primary or elementary school
(up to 100 students in all) might require between
80 per cent and 100 per cent of the school to be
included in the sample, while a large secondary
school of 1,200 students might require a sample
of 25 per cent of the school in order to achieve
randomness. As a rough guide in a random sample,
the larger the sample, the greater is its chance of
being representative.
In determining sample size for a probability
sample one has to consider not only the population
size but also the confidence level and confidence
interval, two further pieces of terminology. The
confidence level, usually expressed as a percentage
(usually 95 per cent or 99 per cent), is an
index of how sure we can be (95 per cent
of the time or 99 per cent of the time)
that the responses lie within a given variation
range, a given confidence interval (e.g. ±3 per
cent) (see http://www.routledge.com/textbooks/
9780415368780 – Chapter 4, file 4.3.ppt). The
confidence interval is that degree of variation or
variation range (e.g. ±1 per cent, or ±2 percent,
or ±3 percent)thatonewishestoensure.For
example, the confidence interval in many opinion
polls is ±3 percent;thismeansthat,ifavoting
survey indicates that a political party has 52 per
cent of the votes then it could be as low as 49 per
cent (52 − 3) or as high as 55 per cent (52 + 3).
Aconfidencelevelof95percentherewould
indicate that we could be sure of this result within
this range (±3percent)for95percentofthetime.
If we want to have a very high confidence level
(say 99 per cent of the time) then the sample size
will be high. On the other hand, if we want a
less stringent confidence level (say 90 per cent of
the time), then the sample size will be smaller.
Usually a compromise is reached, and researchers
opt for a 95 per cent confidence level. Similarly,
if we want a very small confidence interval (i.e. a
limited range of variation, e.g. 3 per cent) then the
sample size will be high, and if we are comfortable
with a larger degree of variation (e.g. 5 per cent)
then the sample size will be lower.
Afulltableofsamplesizesforaprobability
sample is given in Box 4.1, with three confidence
levels (90 per cent, 95 per cent and 99 per cent)
and three confidence intervals (5 per cent, 4 per
cent and 3 per cent).
We can see that the size of the sample reduces at
an increasing rate as the population size increases;
generally (but, clearly, not always) the larger
the population, the smaller the proportion of
the probability sample can be. Also, the higher
the confidence level, the greater the sample, and
the lower the confidence interval, the higher the
sample. A conventional sampling strategy will be
to use a 95 per cent confidence level and a 3 per
cent confidence interval.
There are several web sites that offer sample
size calculation services for random samples. One
free site at the time of writing is from Creative
Service Systems (http://www.surveysystem.
com/sscalc.htm), and another is from Pearson
NCS (http://www.pearsonncs.com/research/
sample-calc.htm), in which the researcher inputs
the desired confidence level, confidence interval
and the population size, and the sample size is
automatically calculated.
If different subgroups or strata (discussed below)
are to be used then the requirements placed on
the total sample also apply to each subgroup. For
example, let us imagine that we are surveying
a whole school of 1,000 students in a multiethnic
school. The formulae above suggest that
we need 278 students in our random sample, to
ensure representativeness. However, let us imagine
that we wished to stratify our groups into, for
example, Chinese (100 students), Spanish (50
students), English (800 students) and American
(50 students). From tables of random sample sizes
we work out a random sample.
Chapter 4