Sample size and power for different distribution types

Question

I received this question from a  customer:

" ... Is there a way to calculate the sample size for a binomial or hypergeometric distribution?  For instance, we have some working on FDA programs and they need to determine the number of samples they need to test to determine whether they can get an error rate of 1 out of 10000. ..."

Have you come across this question before? any solutions? It looks like there is also a similar open question at the community on the topic: Sample Size and Power Analysis for Negative Binomial or Poisson Distributions

Thanks in advance,

calking · Answer

Hey @kemal_oflus!

A simple approach for a Binomial test utilizes the following formula: 1-a = (1-p)^N which you can rearrange to get N = Log(1-a)/Log(1-p), where a=confidence level and p=probability of interest. The idea is that you determine N so as to claim the probability of some event of interest happening is no more than p so long as all N samples do not experience said event of interest. You can think of it as defining a one-sided confidence bound where p is set as the upper bound. The formula is derived straightforward from the probability of observing no events in N samples with a Binomial Distribution.

You could easily do something similar with a Hypergeometric distribution if that's more appropriate. Same idea: just find the probability of seeing no events in a sample from a specific lot. It's not a nice closed form as the Binomial case, but it should get the job done. You can also extend the concept to allow for a few events to occur, though the computation gets more tricky. For the small probability they're looking at, I think the Binomial formula approach should work just fine.

Hope that helps!

Emmanuel_Romeu · Answer

Hello @kemal_oflus , while working at Beckman-Coulter on Blood Virus diagnostic assays I had to resolve this question for FDA submissions. I used Wilson score method which is the FDA's recomended method (not the exact method i.e. Clopper-Pearson). To be honest I did it from the formula using an EXCEL spreadsheet but we can certainly do a JMP script to automize that.

Phil_Kay · Answer

Hi @kemal_oflus ,

Not quite the same but I have come across a customer in Marketing in the insurance industry. They were doing simple DOEs to optimise response rate for promotional mail they were sending out.

They used simulation in JMP Pro to determine the sample size for the experiment.

Here is a thread answering a question that they had: Testing - Sample sizes for a full factorial