Determining Sample Size The sample size needed to estimate the difference between two population proportions to within a margin of error E with a confidence level of 1 2 a can be found as follows. In the expression replace n1 and n2 by n (assuming that both samples have the same size) and replace each of p1, q1, p2, and q2 by 0.5 (because their values are not known). Then solve for n.