# Required sample size to distinguish means of two binomially distributed rv

#### s0medave

##### New Member
Hello,

Currently trying to work out the best way to calculate the number of samples that would be required to get a certain confidence interval. If I have two binomially distributed data sets, which I predict to have some probability of an event p_1 and p_2.

If I were to estimate p_1 and p_2 by measuring "n" sample points from each set I would obtain some estimates p_1(n) and p_2(n). This gives me a difference [p_1(n) - p_2(n)]. If I want to show with some confidence interval "sigma" that for some delta_p I have

delta_p > |p_1(n) - p_2(n)|

what expression would I have "n" such that these conditions are satisfied in terms of p_1, p_2, delta_p and sigma?

Either that or can someone point me in the direction of some helpful literature? I assume it is some sort of inverse "t" distribution technique.

Many thanks