ABSTRACT
Consider a population containing N individuals, and let M denote the unknown number of individuals in the population possessing a particular characteristic. A large number of data sets are not based upon random sampling. In such cases, a binomial assumption can only be justified subjectively, and all conclusions are at best subjective. The reader might be alarmed by the large sample sizes needed to estimate population proportions under random sampling. In practice, a large number n of replicated observations will be needed to identify the extra parameters accurately in any probability distribution generalizing the Poisson. Quite surprisingly, random samples for the evaluation of genotype frequencies appear to have seldom been collected. The newspaper announcements to the effect that Landon had won by a landslide proved to be incorrect.
