Independence of sexes of children born to a couple

Suppose $100p\%$ of babies born are male. Sometimes one reads that $p\approx 0.505$ or something like that. If a couple has $n$ children, it is often assumed that the sex of each child is independent of those of the children born earlier to the same couple.

Has that hypothesis of independence been tested? What can be said based on data, about the nature of the dependence?

• Identical twins (triplets, etc.) discredits independence right off the bat. Commented Jul 10, 2015 at 20:21
• @MarkL.Stone : True, but the more interesting question is about independence within families without such multiple births. Commented Jul 10, 2015 at 20:29
• Some of us explicitly do not make this assumption. It's not hard to search the Web for such studies. One early hit I found is at phys.org/news/2008-12-boy-girl-father-genes.html. This issue seems off-topic here, because it concerns a matter of biology and not statistics or even statistical analysis. What statistical question do you have in mind?
– whuber
Commented Jul 10, 2015 at 21:05
• The existence of multiple births within a family is itself not independent. Pre-in vitro fertilization, answer was somewhat different, and on the verge of changing with selection and manipulation techniques. Also distribution of sex conceived is not the same as those born due to abortions based on sex of baby, which didn't exist in any significant numbers prior to ultrasound. Etc. Of course you can say none of this counts, in which case just assume anything you want, and under those assumptions, anything you want can be true. Commented Jul 10, 2015 at 23:14
• I do not have an answer, but this reminds me of a recent article on the gambler's fallacy and how hard it is to unlearn it with finite samples: poseidon01.ssrn.com/… Commented Jul 10, 2015 at 23:53

A classic dataset of interest is the Saxony dataset of about 6000 12-child families, which was used as example here: How do I compute the estimated values of x for a beta-binomial distribution? If there is variation in $$p$$ between families, the distribution of number of boys will not be binomial, maybe beta-binomial could fit closer. Below is a plot from simulations based on a binomial model, with the Saxony data overlaid: