Of beauty, sex, and power: Statistical challenges in estimating small effects

How do we interpret findings that are intriguing, potentially important, but not statistically significant? We discuss in the context of a series of papers in the Journal of Theoretical Biology that reported evidence that beautiful parents have more daughters, violent men have more sons, and other sex-ratio patterns (Kanazawa, 2005, 2006, 2007). These papers have been shown to have statistical errors, but the more general research questions remain. From a classical statistical perspective, these studies have insufficient power to detect the magnitudes of effects (on the order of 1 percentage point) that could be expected based on earlier studies of sex ratios. The anticipated small effects can also be handled using a Bayesian prior distribution. These concerns are relevant to other studies of small effects and also to the reporting of such studies.