Is it gathered or publicly available?
This could be a case of weak Google skillz, but my wife and I were unable to find the data to back up or refute this statement:
There are eight possible combinations of gender and birth order (from B/B/B to G/G/G); G/G/B is more common than B/B/G.
The background: my wife and I have three children, two girls and a boy. Many, many people (particularly my parents) assume this represents a “trying for the boy” scenario. They are not subtly implying it either: when my wife got pregnant for #2, they would say things like “I hope it’s a boy so you can stop at two children” before we reached the sonogram stage.
It’s not just the “traditional Chinese desire for a boy” thing (though that’s certainly my parents’ angle). We hear this all the time from people of all backgrounds and age groups when we introduce them to our family: they nod knowingly and make some joking remark about our boy being the third and youngest child. (“Finally got the boy, eh?”)
A good friend and his wife just had their second child, and now have 2 girls, and are beginning to get the pressure (at least the expressed expectation) to “try one more time for the boy”.
A few families I know of have three girls, and every now and then the comment is made that “they must have been trying for the boy and struck out”. They are not Chinese.
Nobody, it seems, feels it’s reasonable to go beyond 3 kids in the Quest For A Son.
Based on these observations, my wife posited that in a country like the USA where birth control is readily available and widely used and the birth rate is well below 3, that a significant number of families with exactly three children will reflect a skew towards the desire to have a son. (Having more than three children could reflect a lack of practice of birth control, as among certain religious groups.)
Assuming equal odds for a girl or a boy, one would expect G/G/B about 12.5% of the time (1/8). (I say “about” because I’ve read that in reality, girls are slightly more common than boys, at about a 52/48 ratio.) We made a bet: she thinks the occurrence of G/G/B will end up much higher, nearly double that frequency, between 20-25% (actually she said 50% at first, then backed down).
[FTR: no, we were not “trying for a boy”; truth be known, The Boy was an Accident and we have taken steps to ensure he is the last off the assembly line.]