Tony Baglioni writes:

> I've forgotten so many basics. Can anyone tell me how to > calculate the needed sample size for a simple query? I > know the probability of an event is 3/10,000. What sample > size is needed to verify there are no cases present?

You need to be a bit more precise in your research hypothesis. If you already know the probability of an event, why are you running a test at all?

I'll make a guess that you want to find a sample large enough so that you can exclude the possibility that the true proportion is 3/10,000. In other words, you want to prove that the true proportion is less than 3/10,000.

The rule of three is helpful here. If you observe zero events out of n, then 3/n is an approximate 95% confidence interval for the true probability. Solve the equation

3/n < 0.0003

to get n > 10,000.

A more formal power calculation could be done, and it would probably demand an even larger sample size. You need to be more explicit with your hypothesis before you can do a power calculation. I understand that StatXact will do a power calculation for you, although I do not have the latest version which does this. The traditional formulas for power fall apart because the event is very rare.

Steve Simon, ssimon@cmh.edu, Standard Disclaimer. The STATS web page has moved to http://www.childrens-mercy.org/stats.