Why gender at birth is not a coin toss

I love analogies. As analogies go, many things are well approximated by the “toss of a coin”. Gender at birth is not. And it’s not for two reasons, only one of which you can probably guess.

The sex ratio at birth is not 1 boy to 1 girl. As of 2017, according to World Bank data, it was 1.073 male births for every 1 female birth. In my mind, I still operate on the heuristic of 1.05:1. (It was 1.062:1 in 1962, which probably dates some of my professors rather than me. The US is currently at 1.048:1.)

There are several postulated reasons, including generally higher mortality of males, but also under-registration of female births, and sex-selective abortion and infanticide of female babies. Both of those last two could be attributed to China’s one-child policy. China’s ratio is still 1.15:1 compared to Sierra Leone at 1.018. (Zimbabwe is close to bottom at 1.02 with South Africa not much greater at 1.03.)

The second reason gender at birth is not a coin toss is less well known. The gender of a child is not independent of the gender of the previous child. The impact is small and best-studied on (non-human) animals. One thought is that the “condition” of the mother has an impact on the gender of the child. Other possible factors include frequency of intercourse and paternal age.

Since many of these factors are not independent, the probability of same-gender children is slightly higher than a pure coin toss would indicate, even if it were a biased 1:073:1 coin.

This post was prompted by the interesting analysis of 12 consecutive girl births in a tiny village in Poland. The “statistics lecturer” who explained quite well why this isn’t actually a surprise glossed over some, interesting to me, and arguably important distinctions that demographers (and parents) care about perhaps a little more.

The next Really Interesting Question is what happens to sex ratios, and births and genetic characteristics and selection for children in the coming decades. I can easily imagine that my own children will be the last in “my line” to be all-natural, unedited, unmodified, naturally selected genetic offspring.

Published by David Kirk

The opinions expressed on this site are those of the author and other commenters and are not necessarily those of his employer or any other organisation. David Kirk runs Milliman’s actuarial consulting practice in Africa. He is an actuary and is the creator of New Business Margin on Revenue. He specialises in risk and capital management, regulatory change and insurance strategy . He also has extensive experience in embedded value reporting, insurance-related IFRS and share option valuation.

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