We assessed a randomization test frequently used in studies that aim to detect bias in primary sex ratio of avian species. Three different treatments were examined that represent simple but ecologically realistic cases of interest to researchers. The randomization test was successful in reducing Type I error when testing for a significant departure from a single binomial distribution. When brood sizes or sample sizes were low, however, the randomization test lacked power to detect departures from a population of broods with multiple binomial distributions of sons and daughters. We recommend analytical techniques available to researchers that do not require a common distribution of the sexes to broods for an entire population.