Tests for a biased sex ratio when the data are clustered

In behavioral ecology the overall sex ratio in a population of birds is often tested to see if it differs from a 50/50 ratio. In recent publications the binomial test or the ² test are carried out although the sexes of chicks within the same nest may not be independent. The lack of independence occurs since female birds can adjust the sex ratio in an adaptive way as demonstrated in recent studies. In order to take dependence into consideration the Wilcoxon signed rank test based on the within-brood differences between the proportions of sons and daughters was performed in a study investigating great tit hatchling sex ratios. We compare this test with a test based on an optimally weighted estimator recently proposed for medical studies with clustered binary data. According to our simulation results, this novel test is more powerful than the Wilcoxon signed rank test and should be used for the analysis of avian sex ratios. The methods are illustrated with real data from the great reed warbler.