New method to estimate the sample size for calculation of a proportion assuming binomial distribution.

Nowadays the formula to calculate the sample size for estimate a proportion (as prevalence) is based on the Normal distribution, however it would be based on a Binomial distribution which confidence interval was possible to be calculated using the Wilson Score method. By comparing the two formulae (Normal and Binomial distributions), the variation of the amplitude of the confidence intervals is relevant in the tails and the center of the curves. In order to calculate the needed sample size we have simulated an iterative sampling procedure, which shows an underestimation of the sample size for values of prevalence closed to 0 or 1, and also an overestimation for values closed to 0.5. Attending to these results we proposed an algorithm based on Wilson Score method that provides similar values for the sample size than empirically obtained by simulation.