What are the stats for gender distribution of 3 children?

Factual Questions
1

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.]

2

I think this is going to be just another case of a statistical problem not clearly defined or understood where people will be discussing how to interpret the OP more than anything else.

Having said that, let me also say: If you take any group of 3 children families the odds that the third is a male are 50%. If you take only the subset where the two first are girls the odds are still 50%. Same with any other subset. The sex of the third child (or any of the others) is not affected by the sex of the previous ones.

This reminds me of the problem recently discussed here of the results of a family planning policy of stopping at the first male or number X, whichever comes first. The result, not obvious to some people, is that you get more females than males. Sometimes “common sense” can be misleading.

3

Just to add some data, that seem to skew what you’re going for:

My parents had: BGB
My dad is the last of: BBB (but admittedly, the grandparents were gunning for a girl)
My aunt has: GGG
My uncle has: BBB (in his first family, he has two more (GB) with another woman)
My friends who have two siblings are: BBG, BGB

But then again, most of my buddies seem to have just one sibling (of the others sex).

All these anecdotal numbers from Scandinavia.

4

It would be difficult to judge it statistically because some people, for whatever reason, tend towards making either girls or boys, not both.

5

I agree that our approach is open to refinement, but to address your second point, we understand that well – the odds for B/B/G should be equal to that for G/G/B based on pure odds (an independent series). That’s exactly the reason we’re interested in comparing this: she’s saying it’s NOT an independent series because more people will stop after two children with a boy in the series than will go on to even have a third one.

Basically, turn your statement around and you have what we’re looking for: if the occurrence of G/G/B is significantly higher than that of any other pattern, then that shows there is selection bias (“trying for a boy”) because it so far away from what is predicted by an independent series.

6

Shouldn’t we rather compare two children families then? If there are fewer with only girls than random probablility would have it would mean those with only girls went on to have another child and became three child families.

Or, if we compare three-child families we should look only at the two first children, the third one is irrelevant. Among the first two we would find more G-G than 25%.

The thing also is that you need to include only families which have finished breeding because you cannot know if the 2-child family of today is the 3 or 4 child family of tomorrow.

These things get tricky.

7

This is true if you make the simplifying assumptions that any birth is equaly likely to be a boy or a girl and that the sexes of subsequent births are independent. You’d have to look at the statistical data to see whether these assumptions are valid or not. I interpreted the OP as asking whether there was such data available.

8

I think you just need to look at families that finished at two children.

Randomness says you should have 1/4 BB, 1/2 BG, and 1/4 GG

If there are significantly fewer GGs, then it’s like that the desire for a boy is behind it.

9

I do not think the OP is asking that at all.

10

Well part of the musing was that it was common for people to want two children, so long as one of them was a boy. The idea is that having one boy and one girl is the sought-after ideal, but if a family ends up with two boys, it’s less likely to see them “try for the missing piece” than if they have two girls.

That’s why we’re also excluding cases of 4+ children families: if you’re not practicing birth control at all (as is common with subset communities of Orthodox Jews and Catholics, for example), then we would expect to see the random distribution probabilities play out. By focusing on specifically the three-children case we hope to focus on the scenario we are thinking of.

In other words, it’s NOT a case of “do it until you have a boy”, but rather, “if after two we don’t have a boy, give it one and only one last go”.

As for sailor’s comment about the OP – Thudlow Boink has it exactly right. I am looking for data to back up or refute my wife’s claim. We agree that the mathematically expected distribution would be about 12.5% for a G/G/B pattern; she expects to find a significant deviation from this in the real world, one that she would attribute to "gender preference sexism.

Whether or not that would be the appropriate conclusion to draw is entirely dependent on the data.

11

One would certainly expect that GGB would be less than half, since even if a significant portion of three-child families were “trying for a boy”, you’d expect just as many “struck out” as “finally got the boy”, so GGG should be just as common as GGB.

You’d also have to make sure that you only looked at families that have finished, if you go this route, since at least some two-child families will eventually become three-child families.

12

Except that what he said is

He is questioning and seeking confirmation for whether any birth is equaly likely to be a boy or a girl and that the sexes of subsequent births are independent which, as I understand it, is a given in your OP. To see if any birth is equaly likely to be a boy or a girl you do not care about the previous or succesive siblings. It is just statistical data and I understood that we were accepting the simplification that both sexes were equally likely although we know for a fact that there is a slight preponderance of female births.

13

I read recently that women who eat a lot of grains like oatmeal for breakfast have more boys than girls. My wife has oatmeal every day and we had 2 boys.

14

I gotta say I’m skeptical of the assumption that couples would try for a boy more often than they’d try for a girl nowadays. Women tend to be the ones who are uh - driving the breeding (wanting kids more), and more women, imhe, are going to be upset at the idea of a family of all men with no daughters than vice versa.

Even if you look at it from a security in old age scenario (why boys used to be favored), now that women are working, your best bet is having at least one daughter. Daughters tend to stay more involved, close and do more caretaking for aging parents. I don’t think many people are basing their decisions on that, but if they are, I also think most people get that.

15

Except for the family who lived behind us when I was a kid . . . they used to literally pray for a son. When we moved from there, they had seven girls. I assume they kept trying.

16

We had a similar experience as the OP, two girls then a boy. I was amazed at how many women congratulated my wife on “finally getting her boy”. I would’ve been fine with another girl but my wife was hoping for a boy.

17

Maybe, but I wonder if the same thing happened if it had been the other way around - two boys and then a girl. It’s also pretty common for women to sympathize with mothers of only boys.

18

Yes, I agree: to see if any birth is equally likely to be a boy/girl, it does not matter what the previous siblings were.

BUT, I am trying to analyze the proposition that it is NOT equally likely to be a boy or a girl, BASED ON what the previous siblings were. And that it matters exactly what the previous siblings were: exactly G/G, and not B/G or G/B or B/B.

To do this (and feel free to criticize the method of analysis here), we are comparing the expected distribution based on an presumption of independence (1/8, or 12.5%) to what is really observed.

If, for example, we were to find a significant difference over a significant data sample – say, that 25% of three-children famillies had a G/G/B pattern – then it becomes a matter of attributing the disparity. Her explanation would be that they were “trying for a boy”. You could certainly argue for alternate explanations in that case… BUT, if the observed distribution were actually about 12.5%, it would pretty much shoot down her proposition right there.

To recap: I am primarily looking for a source of this data, which I thought might be in the US Census but maybe not (I could well believe the Census only keeps track of “total number of children in household” and not gender or birth order).

I do also think it’d be interesting to discuss a better way to go about looking for data to back up or refute this supposition.

For the record, I am more inclined to uglybeech’s viewpoint that even if it’s talked about a fair amount (“trying for a boy after 2 girls”), it’s not really nearly as prevalent as my wife thinks it is. Sort of like the “Irish twins” thing, it’s a standard cultural image for some people and not so much a reflection of current reality.

19

Oh, I see. I think you’re right about that. I’m sure that if our situation had been reversed my wife would’ve wanted a girl, FWIW.

20

I think it is fairly well established that the odds are always the same, regardless of previous births but I have no hard data so I’ll leave it to others.