|Date: ||Thu, 9 Jun 2005 10:50:36 -0300|
|Reply-To: ||Hector Maletta <firstname.lastname@example.org>|
|Sender: ||"SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>|
|From: ||Hector Maletta <email@example.com>|
|Subject: ||Re: sample size determination|
|Content-Type: ||text/plain; charset="US-ASCII"|
There is no "command" for that. There is, on the other hand, a well-known
formula to determine the size of a simple random sample based on a desired
margin of error, which you may easily compute by hand calculator or by
spreadsheet. The formula for a 95% significance level is approximately n=4 *
variance/e**2. The 4 stands for the square of 1.96, or approximately 2,
which is the number of standard deviations encompassing 95% of the area
below the normal curve. For instance, if you want to estimate a population
proportion p (such as the proportion of Republicans in an electorate), and
you would accept an error e= +/- 0.02 in the estimated proportion, you only
need to know the population variance of the proportion, p(1-p). The worst
case scenario, giving the highest variance, is p=0.50. In that case, the
variance is p(1-p)=0.25. This multiplied by 4, and divided by the square of
0.02 gives the necessary sample size, namely 4 * 0.25/0.0004= 2500 cases.
The number may be lower if you expect the population proportion to be
significantly below or above 0.5: for example if you guess the true
population proportion is likely to be in the vicinity of p=0.4 your sample
should be 4*0.4*(1-0.4)/0.0004=2400 cases.
Now this is just for simple random sampling, like drawing numbers from a
box, but that is seldom the case in large populations. You may resort to
stratified sampling, which reduces the variance (since each stratum is more
homogeneous than the whole population, or should be), and/or you may first
select some kind of clusters such as neighbourhoods or city blocks, and then
select your cases within each cluster, which INCREASES the error (since you
are throwing your lot on a few neighbourhoods ignoring the others). For this
kind of complex sample the formula must be corrected to take account of the
increased or diminished margin of error. All sampling textbooks (including
such classics as Cochran or Kish for instance) give the formulas for those
Besides all that, all the above formulas refer to a population which is many
times larger than the sample (say, at least 100 times larger, possibly much
more), which in practical terms is regarded as an "infinite" population. For
small populations, where your sample would make a sizeable proportion of all
cases, it is wise to multiply the above formula by (N-n)/(N-1). This is only
worthwhile if N is large relative to n. For instance, if N=100000 and n=1000
this ratio is 99000/99999=0.99. Multiplying 2500 by 0.99 would reduce the
necessary sample by only 25 cases, to 2475, hardly worth the effort. If
instead your sample size n is, say, 20% of total population N, this ratio is
approximately 0.80, thus reducing the necessary sample by 20%, say from 2500
to 2000, allowing for significant savings in field costs (or giving more
precision if the sample is kept at 2500).
Hope this helps.
> -----Original Message-----
> From: SPSSX(r) Discussion [mailto:SPSSX-L@LISTSERV.UGA.EDU]
> On Behalf Of rahel kale
> Sent: Thursday, June 09, 2005 2:02 AM
> To: SPSSX-L@LISTSERV.UGA.EDU
> Subject: sample size determination
> i want to determine the sample size from the population.Does
> SPSS have any direct command for that?
> Rahel .
> Discover Yahoo!
> Get on-the-go sports scores, stock quotes, news & more. Check it out!