Sex at birth could well be a biological coin toss.... Beware of conditioning on post-baseline information

Abstract

Wang et al. (2025) use statistics to argue that sex at birth is not a biological coin toss, by noticing that repeated patterns such as Male Male Male and Female Female Female occur in the Nurses Health Study more often than patterns like Male Female Male, Male Female Female, Female Male Female, or Female Male Male. This letter shows that this over-representation is likely due to a statistical artifact, arising from parent preferences for mixed-sex children. As noticed in Angrist and Evans (1998) and supported by the data in Wang et al. (2025), parents are more likely to have a third child if their first two children are of the same sex. We show mathematically and statistically that mixed-sex preferences lead to the over-representation of patterns like Male Male Male and Female Female Female. In fact, the patterns seen in the Nurses Health Study are perfectly consistent with sex at birth being a random coin toss.