Date: Thu, 9 Jun 2005 10:50:36 -0300 Hector Maletta "SPSSX(r) Discussion" Hector Maletta Re: sample size determination To: rahel kale <20050609050229.99975.qmail@web30502.mail.mud.yahoo.com> text/plain; charset="US-ASCII"

Rahel, 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 cases.

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.

Hector

> -----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 > > > hi!!!!!!!!!!!! > i want to determine the sample size from the population.Does > SPSS have any direct command for that? > > Regards, > Rahel . > > > > --------------------------------- > Discover Yahoo! > Get on-the-go sports scores, stock quotes, news & more. Check it out! >

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