There is a possibility to perform a limited number of experiments. Then take each experiment and probabilisticaly change randomly changed parts of it. In this way you can create several different sets of data.

Take data, input them into evaluation and observe resulting statistical properties. Under certain number of experimental data taken from each set separately, the statistical properties sharply change.

It is not fool proof method but when you generate modified data with sufficient care, it can give you an estimate of dynamics of results with respect if sample size.

Be sure that different sets are evaluated independently and that they all converge to the roughly same results.

You can test your approach by creating some statistically compromised sets where you know that they should give strange results.

Your targeted minimal lopulation size of the experimental data is above the range where statistical data change sharply.

Tell me your opinion about this approach.

Attached is a formula (along with a calculation) that shows a large sample size calculation for the binomial dist. simple hypoptheses H0: p = p0 vs H1: p = P0 + d, where d > 0. It applies with minor modifications for a two sided test of H1: p = p0 +- d. One can apply this formula with a small modification by assuming the large sample variances of a continuous variances (with a central limit approximation, which in practice means first and second moments of the iid variables exist). However, one must assume that variances are equal or not and face the same problems that occur in two sample t-tests where the variances are assumed the same or different.

I think correct answer is given by Steven Douglas Moffitt..