Since you asked this as a general question, I can only provide a general response.  In order to do an estimation, you need to have a variance (standard deviation) estimate, the level of confidence you want to achieve (or significance), and the sample size.  By turning this around, it becomes an algebra problem and you can solve for sample size (n).  Thus, if you have the error of your estimate you are willing to accept, the confidence level you wish to achieve, and an estimate of variance (or standard deviation), you can solve for n or the sample size.  Any basic stat book has formulas for this depending on the parameter you are estimating.  Good luck!

Jim

Dear Wafaa,

If you know which test you are planning to use then this webpage might help you obtain a sample size estimate: http://www.biomath.info/power/index.htm. At least you don't need to work it out from scratch!

Your question is really general, as James said.

Maybe that book helps you:

Shein-Chung Chow, Hansheng Wang, Jun Shao

Sample Size Calculations in Clinical Research

1. compute sample size for each pairwise comparison and choose maximum sample size

2. the above depends on whether the objective  is superiority or not. For example, for arms A, B and C , if C is placebo , then A vs C and B vs C might be superiority , but A vs B might be tested for non-inferiority - in which case a different approach

3. Then think about multiplicity as you have 3 possible comparrisons - which ones are primary / secondary etc

4. There is lot sof software around to do these - PASS, NQuery and STATA and SAS code

thanks