What are the stats for gender distribution of 3 children?

[LSLGuy]

I’m having a hard time understanding why so many people cannot understand the OPs question.

Do a lot of people who have two girls keep trying to have a boy? Yes or no? This has zero to do with the statistical likelihood of the 3rd child’s sex. It has everything to do with the parents’ decision to get & stay pregnant the third time.

So: Do people with two girls already get and stay pregnant at a rate different from people with two children already where at least one is a boy?

For this strictly cultural question I think it’s fair to say the answer may differ in rural India versus, say, Hollywood or Dusseldorf.

The reason the OP’s question will be hard to answer (but not to understand), is that what we really need to know is:

1. Of those people with two children who don’t have a third, why did they not have a third?
2. Of those people with two children who did have a third, why did they have a third?
   Interestingly, given that the sex outcome of the third child is 50/50 (or is assumed to be so by the terms of the OP’s simplifications), then we actually need to look at GGG as well as GGB. Both of those may represent an attempt to break the GG cycle; only one was a successful attempt and the other not.

IOW, the smoking gun would be that GGX is more significantly common than GBX or BGX or BBX. That would show an over-representation of GG beginnings among 3-child families.
My own take is you won’t find it, but not because the try-for-a-boy effect doesn’t exist in many cultures.

Across the whole human population the sex ratio is about 52/48. We can simplify that to 50/50 for discussion purposes, as long as keep that in the back of our minds.

But (in my non-expert understanding) the odds for any given couple are not 50/50. Some couples are much more likley to produce boys than girls. And viec versa.

There also seems to be an effect where the sex ratio changes under economic/social stress and also across birth order. I’ve forgotten the details, but the concepts are like “Good times favor boys, hard times girls.” And first-births are 52/48 boys, 8th births are 54/46 boys". Again those are made up numbers, but the issue is real.

The sum of both these facts is that even IF you could find summary stats on the 4 patterns of birth order for 2 kids, 8 patterns for 3 kids and 16 patterns for 4 kids, you could not validly deduce that an excess of GGX represented try-for-a-boy behavior versus some other cause related to the GG-producing parents situation.

[sailor]

@LSLGuy

I’m having a hard time understanding why so many people cannot understand the OPs question.

Do a lot of people who have two girls keep trying to have a boy? Yes or no?

That is not how I interpret

@robardin

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.

[LSLGuy]

Missed edit window. Substitute these expanded paragraphs for their originals above …

IOW, the smoking gun would be that GGX is more significantly common than GBX or BGX or BBX. That would show an over-representation of GG beginnings among 3-child families. Finding unusually few GGBX among 4-child families would also be a clue that GGB parents are less likely to have a fourth than other birth orders. That would give credence to the idea that the B represented a completed goal.

…
But (in my non-expert understanding) the odds for any given couple are not 50/50. Some couples are much more likely to produce boys than girls. And vice versa. That difference will muddy the stats to uselessness. You can’t dissect a sum of very different items to say something useful about a 2nd order effect (differing parental preference) when the first order effect (differing individual sex-of-offspring) tendency dominates.

[Rigamarole]

@robardin

(I say “about” because I’ve read that in reality, girls are slightly more common than boys, at about a 52/48 ratio.)

Is this accurate? I always assumed the slightly greater prevalence of women in the population was due to women having longer life expectancies, not because they are more likely to be born.

[MandaJo]

I have to agree with uglybeech that “trying for variation” is more prevalent than trying for any particular sex: people often like to have both. I have known people with a strong preference for one gender or another, but IME that has most often followed the pattern of their own childhood: women with only sisters often tend to strongly prefer girls, and men with only brothers often tend to strongly prefer boys–I assume that’s because their own childhoods were dominated by that gender, and it’s just what they know.

My two brothers had between them five boys, all of which are being raised very close together. When my sister-in-law had a surprise late pregnancy, all of them were hoping for a girl–but alas, they added a 6th boy!

[Kent_Clark]

If I were going to design this from scratch, here’s how I’d do it.

Take the set of all families with two children. How many are BB, GG and BG?

Then take the subset of 2+ children families. How many of them started with BB, GG, or BG (for the sake of the study, assume BG=GB)? If the BB and/or GG birth order is significantly higher than BG, then one might assume that “trying for X” comes into play.

If the BG, BB and GG distribution of the first two children is statistically similar, then one might assume people just want to have more children.

[happiness]

@Rigamarole

Is this accurate? I always assumed the slightly greater prevalence of women in the population was due to women having longer life expectancies, not because they are more likely to be born.

According to the CDC, the birth rate for boys is higher than that for girls, with about 1050 males born for every 1000 females born.

http://www.cdc.gov/nchs/data/nvsr/nvsr56/nvsr56_06.pdf

[robardin]

@LSLGuy

Do a lot of people who have two girls keep trying to have a boy? Yes or no? … Do people with two girls already get and stay pregnant at a rate different from people with two children already where at least one is a boy?

Interestingly, given that the sex outcome of the third child is 50/50 (or is assumed to be so by the terms of the OP’s simplifications), then we actually need to look at GGG as well as GGB. Both of those may represent an attempt to break the GG cycle; only one was a successful attempt and the other not.

IOW, the smoking gun would be that GGX is more significantly common than GBX or BGX or BBX. That would show an over-representation of GG beginnings among 3-child families.

Bingo, that is exactly what I am considering and yes, you are right, it’s really GGX not GGB per se. I recognize the cultural element and that is why I am focusing on the current US population (being that I live in the US), hence my original unsuccessful desire to find US Census figures.

As for your comment that “some couples are much more likely to produce boys than girls”, well, is that really true? I have always seen birth gender given as an example of an essentially random process on the order of coin flips. And just as with coin flips, in any big sample size you’ll see some occurrence of the outliers (i.e., some families with 6 boys). While it’s possible that there’s a biological basis for this, it could still be the tail of a normal distribution. I’d be interested in reading about what kind of study drew that conclusion.

And even if that were a biological possibility, perhaps it’s a rarity in and of itself (some genetic mutation that causes a man to produce significantly more Y- than X-chromosomed sperm cells) that could be ignored.

[robardin]

@kunilou

If I were going to design this from scratch, here’s how I’d do it.

Take the set of all families with two children. How many are BB, GG and BG?

Then take the subset of 2+ children families. How many of them started with BB, GG, or BG (for the sake of the study, assume BG=GB)? If the BB and/or GG birth order is significantly higher than BG, then one might assume that “trying for X” comes into play.

If the BG, BB and GG distribution of the first two children is statistically similar, then one might assume people just want to have more children.

I like this (using the real-world distribution of two-children patterns as a baseline instead of the a priori odds of 1-in-8 for three-children sequences), though as I said earlier, I’m inclined to limit the analysis to exactly three children to eliminate the “just wanted a lot of kids” or “don’t use birth control” factor.

[Thudlow_Boink]

I managed to Google up a site that may be the kind of thing you’re looking for.

Did previous children’s gender influence whether to have a third child?

Parents are 6% more likely to stop having children if the first two children are a boy and a girl.

Of parents with two same-gender children, parents of two girls are 3% more likely to stop having children than parents of two boys.

And, if all previous children are of the same gender,

The odds of having a girl seem decrease after having each boy, but only very slightly. Even after 3 boys, you are only 6.4% more likely to have a 4th boy than a girl.

The odds of having a boy seem to increase after having girls, except after 2 girls, when a 3rd girl is more likely.

Specifically, according to their data, when the first two children were a boy, 47.7% of the time the third child was a girl. When the first two children were girls, 46.0% of the time the third was a boy.
The same Google search turned up various references to factors that supposedly can have some influence on whether a child turns out to be a boy or a girl (the mother’s diet, the father’s genetics, etc.).

[Thudlow_Boink]

…although it doesn’t look like that site provides data on the number of G/G/B vs. B/B/G families, allowing you to compare them directly.

After further Googling, the only thing like that that I could find was this: see “Data Set #2” at the bottom of the page, which, if I’m interpreting it correctly, shows a ratio of 1.060 B/B/G to 949 G/G/B three-children families.

[robardin]

@panache45

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.

Which is how you get people named “Octavius” in this day and age, I suppose. (I once found a keychain consisting of that name written in brass.)

[robardin]

@Thudlow_Boink

I managed to Google up a site that may be the kind of thing you’re looking for.

Indeed it is. I bow to your superior Google-fu!

[OldGuy]

@sailor

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.

This is not true at all assuming 50-50 and independence.

Suppose X = 1, then all families will have one child and half will be boys.

Suppose X = 2, then families will be from oldest to youngest:
B 50% stop
G B 25%
G G 25%
which is again 50-50.

Now use induction: Suppose the rule results in 50-50 for X = n. Consider changing the rule to X = n+1. This lets the families with n girls try once more. We know (by the assumption of induction) that the children so far are distributed 50-50. We know by the assumption of independence that the families that try once more will have half boys and half girls.

[uglybeech]

@LSLGuy

IOW, the smoking gun would be that GGX is more significantly common than GBX or BGX or BBX. That would show an over-representation of GG beginnings among 3-child families.

The problem with using GGX is that an increase in GGX from the GGB subset might be offset by a decrease in GGG if those with three girls and no boy are motivated to go for a fourth.

Agree with Oldguy too - unless there’s something I’m missing, this should have no impact on the absolute ratio of girls to boys. It should stay 50/50 or so.

[Palo_Verde]

It’s not just families of girls who are assumed to want the opposite sex. After my first 2 boys were born, everyone kept asking me if I was going to try again to ‘finally get my girl.’

When #3 came and was a girl, a lot of people said dumb things like, “Kept trying until you got your girl, eh?” and I always replied, “Nope, just wanted another baby!” It really bothered my boys when people said that, it made them feel like there was something wrong with being boys.

When we had #4 (a boy) many were just confused. They assumed I only had a third in order to get a girl, and I had one, so what was the point of another. My husband and I just wanted another baby… not complicated.

[YamatoTwinkie]

personal anecdote: My mom had BBG. She was very much hoping for a girl the third time around, but if she had a boy, my parents probably would have stopped at 3.

[Indistinguishable]

@sailor

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.

It’s already been pointed out that this is not true. Indeed, it was pointed out in the thread you refer to that this is not true. Allow me to re-emphasize: this is not true.

You can think of the stork as flipping a fair coin whenever any family decides to conceive a child, and then writing the result down in a logbook while assigning the gender of the family’s new baby accordingly. The coin being fair, the results in the logbook are expected to contain an equal number of heads and tails, which means, correspondingly, that there will have been an equal number of boys and girls delivered by the stork unto the world. Human mating practices cannot change any of this; they can change who gets which babies when, they can make the stork flip faster or slower or only on Tuesdays, but they can’t alter the basic fact that the stork’s gender-deciding coin will come up heads as often as it comes up tails.

[StarvingButStrong]

@Indistinguishable

. The coin being fair, the results in the logbook are expected to contain an equal number of heads and tails, which means, correspondingly, that there will have been an equal number of boys and girls delivered by the stork unto the world. Human mating practices cannot change any of this; they can change who gets which babies when, they can make the stork flip faster or slower or only on Tuesdays, but they can’t alter the basic fact that the stork’s gender-deciding coin will come up heads as often as it comes up tails.

This isn’t completely true, given today’s technology.

It’s been possible to separate ‘y’ sperm from ‘x’ sperm for years. It’s mainly done to avoid certain sex-linked diseases.

Also, you can ‘sex test’ embryos created in vitro, and only implant those of the desired flavor.

Again, I think there are ethical, and possibly legal, restraints against doing this purely for parental choice reasons, but there are some pretty nasty sex-linked diseases where having, say, a boy will mean a few years of suffering and then death, while a girl would be born healthy.

[Indistinguishable]

Fine. I meant “On the usual idealization that births are independent and each equally likely to produce boys as girls, no rule (e.g., ‘Crank out babies till you have 1 boy or 5 girls, whichever comes first’) can cause an imbalance in birth genders”. Naturally, if we drop the first part of that (e.g., to account for the technology you refer to), then the latter part will not follow.