Sample size for many proportions

[cbautista]

Hi list,

Well, this is not a question on SPSS, but maybe you could have some links
or info about how to estimate a sample size for many proportions. I need
to calculate the overall sample size for four groups, assuming that the
expected proportions are 10%, 15%, 12%, and 20%.

Thanks in advance,

/Christian

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[Hector Maletta]

Sample size depends on the degree of precision you want to achieve in your
estimate of the true proportion. The standard error E of a proportion of the
estimate of a population proportion p equals p(1-p) divided by the square
root of sample size N. This means that N equals the square of p(1-p) divided
by the square of the standard error E. The 95% confidence interval of your
estimate is about 2 standard errors to each side of the estimate. If you
tolerate to be wrong by, say, 2 percentage points to each side, this means
you aspire to have a standard error E=0.01, the square of which is 0.0001.
Suppose we are talking about the group where the presumed proportion is
0.20. In this case, N=[0.20*0.80] squared / 0.0001 = 256. If you take a
random sample of this group with N=256, and obtain p=0.20, you have 95%
confidence that the population proportion is between 0.18 and 0.22. Larger
samples would give you a narrower confidence interval. The same for the
other groups. All in all, for this level of precision you would need about
900-1000 cases. The general requirement is that samples are simple random
samples. More elaborate sampling models may be different (smaller or larger
error, it depends).
Notice, besides, that there is no guarantee that your particular sample
would be among the 95% of samples which are within 2% of the true figure:
your sample may well belong with the 5% of all possible samples that give
proportions farther off the mark (2.5% would be below 0.18, and 2.5% above
0.22). If you already know the true (population) proportion of one group is
0.20, be prepared to find a (hopefully slightly) different proportion in
your sample.

Hector



-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Christian Bautista
Sent: 27 May 2008 18:13
To: [hidden email]
Subject: Sample size for many proportions

Hi list,

Well, this is not a question on SPSS, but maybe you could have some links
or info about how to estimate a sample size for many proportions. I need
to calculate the overall sample size for four groups, assuming that the
expected proportions are 10%, 15%, 12%, and 20%.

Thanks in advance,

/Christian

=====================
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[Peck, Jon]

If you use the propor extension command downloadable from SPSS Developer Central (www.spss.com/devcentral) for use with SPSS 16, you can see how the confidence interval varies with the sample size.

propor num=1 10 100 1000 10000 denom=10 100 1000 10000 100000.

for example, shows you the 95 % (by default) ci for p=.10 at different sample sizes.  If you plot the lower and upper ci's against N (better, log N)  you get a nice graph that I wish I could insert here.

HTH,
Jon Peck

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Hector Maletta
Sent: Tuesday, May 27, 2008 6:38 PM
To: [hidden email]
Subject: Re: [SPSSX-L] Sample size for many proportions

Sample size depends on the degree of precision you want to achieve in your
estimate of the true proportion. The standard error E of a proportion of the
estimate of a population proportion p equals p(1-p) divided by the square
root of sample size N. This means that N equals the square of p(1-p) divided
by the square of the standard error E. The 95% confidence interval of your
estimate is about 2 standard errors to each side of the estimate. If you
tolerate to be wrong by, say, 2 percentage points to each side, this means
you aspire to have a standard error E=0.01, the square of which is 0.0001.
Suppose we are talking about the group where the presumed proportion is
0.20. In this case, N=[0.20*0.80] squared / 0.0001 = 256. If you take a
random sample of this group with N=256, and obtain p=0.20, you have 95%
confidence that the population proportion is between 0.18 and 0.22. Larger
samples would give you a narrower confidence interval. The same for the
other groups. All in all, for this level of precision you would need about
900-1000 cases. The general requirement is that samples are simple random
samples. More elaborate sampling models may be different (smaller or larger
error, it depends).
Notice, besides, that there is no guarantee that your particular sample
would be among the 95% of samples which are within 2% of the true figure:
your sample may well belong with the 5% of all possible samples that give
proportions farther off the mark (2.5% would be below 0.18, and 2.5% above
0.22). If you already know the true (population) proportion of one group is
0.20, be prepared to find a (hopefully slightly) different proportion in
your sample.

Hector



-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Christian Bautista
Sent: 27 May 2008 18:13
To: [hidden email]
Subject: Sample size for many proportions

Hi list,

Well, this is not a question on SPSS, but maybe you could have some links
or info about how to estimate a sample size for many proportions. I need
to calculate the overall sample size for four groups, assuming that the
expected proportions are 10%, 15%, 12%, and 20%.

Thanks in advance,

/Christian

=====================
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=====================
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