**[StATS]:** **Sample size for a binomial confidence
interval (October 3, 2005)**

Someone asked me for some help with a homework question. I hesitate to offer too much advice in these situations because I don’t want to disrupt the teacher’s efforts to get the students to think on their own.

If it is not too much trouble, I would really appreciate your kind assistance on how best to determine and calculate for sample size if the only information given to me is the estimate (i.e. 10% of all male patient in the study population likely to be screened for prostate cancer at the medical clinic) and the precision of this estimate (i.e. 5%).

This sure sounds like they want a sample size that will produce a 95% confidence interval that has a width of plus or minus 5%. The confidence interval is based on a single binomial distribution, I suspect, rather than a difference in two binomial proportions. There’s a bit of ambiguity in the wording, so it always helps to get a bit of clarification.

I have a spreadsheet that does confidence interval calculations for a single binomial proportion and you can play some “what-if” games to arrive at an appropriate sample size. But there are also formulas that you can use. Here are two web sites that provide simple and easy to follow guidance.

- http://www.itl.nist.gov/div898/handbook/prc/section2/prc243.htm
- http://www.anu.edu.au/nceph/surfstat/surfstat-home/4-2-3.html

You can also browse for pages similar to this one at Category: Sample size justification.

You can find an earlier version of this page on my website.