On Thu, 15 Jun 2000, sahar salah wrote:
> I'm a researcher at Cairo University in the field of computer science.
> Due to my PhD I'm preparing a questionnaire. But the population is
> very large. I classified it into 35 categories. All I need, is to
> determine the sample size. Is it proportional to the population size?
> How can I determine that sample size?
Not enough information to give you a well-defined answer.
Sample size ought not, in general, to be proportional to the population
size. The precision of any estimates you get (proportion of respondents
who give a certain answer, or mean score of respondents, or whatever) is
strongly dependent on the sample size, and only VERY weakly -- one may
as well say, "negligibly" -- on the population size; provided only that
the sample size is a _small_ fraction of the population size. If you
want about the same precision (or, equivalently, the same margin of
error) for the estimates you get in each of your 35 categories, aim for
equal sample sizes in all categories.
What size(s) of samples you should aim for depends also on your
method of sampling. Consult a good textbook on sampling. In any case,
you should make serious efforts to sample randomly, in as strict a sense
as possible. Simple random sampling is one method; for the same sample
size, you can usually get somewhat better precision (smaller margins of
error) by stratified random sampling; cluster sampling tends to yield
worse precision (larger margins of error).
How to calculate sample sizes depends on what you're looking for.
For the proportion of the population who fall into a certain category of
response, the desired sample size is not much affected by the value of
that proportion, so long as it's between (roughly) 0.25 and 0.75; but
for proportions nearer to 0 or 1, somewhat smaller sample sizes will do
(ceteris paribus). For the average value of some score or measure
derived from the questionnaire, sample size will depend on the
variability of responses, and this may be difficult to know in advance
(although it is often possible to set reasonable boundaries on it, if
onke thinks carefully enough about the variable and likely responses to
the relevant questions).
Essentially, you want to be able to say, afterward, something
like this, for each of your major questions:
"With 95% confidence, the proportion of Category X who [report a
certain behavior, or give a particular answer to one of your questions]
is 0.68, with a margin of error of plus or minus 0.03."
In that statement, the values "95%" and "0.03" determine the necessary
sample size. The value "0.68" has a smaller influence, being between
0.25 and 0.75; but if it turned out to be 0.05 instead of 0.68, you
would doubtless want a smaller margin of error than 0.03.
-- DFB.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
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