Of Beauty, Sex and Power
Too little attention has been paid to the statistical challenges in estimating small effects
A series of papers in the Journal of Theoretical Biology has found evidence that beautiful parents have more daughters, violent men have more sons, and other sex-ratio patterns (Kanazawa, 2005, 2006, 2007, 2008). These papers have been shown to have statistical errors, but the question remains how to interpret findings that are intriguing, potentially important, but not statistically significant. 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.
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