There is no single simple answer to this question. It will depend on the experimental design and the hypothesis that you want to test.
It will also depend on what you want to estimate : difference of two means for instance will not require the same sample size than estimation of a single mean with a given precision.
It depends to the problem to tackle:
* For assuring a confidence interval (with quantile zb) of a certain estimator (typically mean value) you can fix this interval as an error:
e= zb * sigma/sqrt(N)
and then calculate the sample size.
* In case of a tolerance interval (i.e. guarantee that certain population proportion does not exceed a limit) with a probability “g” and a confidence level “b”. It can be used the Wilks’ formulae:
1-g^n= b
Always that none of the samples overpass the selected limit, otherwise order statistics results shall be used.
Hope it helps
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