Critical sample sizes for determining the statistical significance of mutation frequencies

Based on the assumption that the numbers of mutations observed in an untreated and treated sample of individuals are binomial random variables, a method is presented to compute the probability of observing a specific number of mutations as a function of the sample sizes and the number of mutations in the untreated control sample. Knowledge of the true mutation frequencies is not required. The formalism is then used to compute critical sample sizes for testing hypotheses concerning mutation frequencies in the two populations.