This is self-selection error. You remember this example because it’s memorable, and because families with a “regular” distribution of children don’t bring it up at as a dinner conversation because it isn’t interesting. You may have known lots of families with boys going back 19 generations, but you know a LOT more families that don’t spark such interest.
However, when the statistics are taken over a large population, even slight biases can be significant. Over the whole world, the human birth sex ratio is about 105 boys born for every 100 girls. There can be some quibbling over the exact number, but there is no doubt that more boys are born than girls.
Here’s a study that suggests gender is affected by a woman’s menstrual cycle (the length of the follicular stage in particular). If a woman tends toward a particular cycle length, then she’d be predisposed to one gender or another.
This study not only states that normal male births are 51.5%, but that the number is slightly higher in southern Europe compared to northern Europe, with a possible connection to temperature.
On the other hand, we’re splitting hairs. The conventional wisdom spread by old wives does not say a family with three boys already has a 55% chance of another boy. They tend to assume it’s a near certainty and that it’s affected by diet, sex position, magical herbs and all kinds of ridiculous factors. If any of that would be true, scientists would not be interested in a 0.7% difference in ratios between northern and southern Europe.
Someone did a study that said women who eat more grains have more boys. It worked for us, my wife eats a lot of oatmeal and we had 2 boys.
My dad produced 5 boys and 0 girls. When his and his brothers’ offspring are all totaled up you get 16 boys and 3 girls. It seems the subsequent generation is heavily male as well though I don’t have the numbers. It’s hard not to think that there could be a factor at work in my family that skews the odds in favor of males. It could all just be a coincidence tough.
There could be social explanations for this. Perhaps parents with two girls are more willing to have a third child than parents of two boys.
I’m going to go look at data. I need a good procrastination project today…
I agree that there could be something to it. However, just to play devil’s advocate, we need to look at the statistics.
If I flip a fair coin 100 times, I’m almost guaranteed a string of at least six heads or tails in a row. So out of every 20 families of 5 kids, we’d expect at least one (maybe two or three) to have all girls or all boys if the distribution is near 50/50. When we’re talking about 20 million families, we’ll expect some that have 16 boys and 3 girls. The odds of 10 boys in a row is only 1/1000.
That’s one of those things about statistics that is so challenging to the human mind. Often, our evidence that something is not random is actually evidence that it is.
Do a search on previous threads. At some point in the last few months, there was a discussion about it.
This made the scientist in me pull out the shotgun.
Just as a side note, the evolution of sex is one of my personal interests. It’s fascinating, because you have two competing strategies (one for males, one for females) fighting it out evolutionarily in a single genome. There’s cheating and dirty tricks galore if you look for them. There’s meiotic drive in females, for instance. Or the proteins in fruit fly semen that go to the females’ brains and try to get them to stop breeding…all kinds of cool stuff that could (and here I’m getting back to the topic) theoretically mess up the gender ratio. I’ve seen nothing to prove that anything like that is happening in humans, but it’s not theoretically impossible.
Data!
I pooled all of the folks who were in their first month of the Current Population Survey between May 2001 and July 2006. For those of you unfamiliar with the CPS, this is the Bureau of Labor Statistics’ big survey that is used to calculate the unemployment rate, among other things. It is nationally representative with some subgroups oversampled. I did not bother to do any weighting with my analysis, so some geographical regions (sparsely populated states) and racial/ethnic groups are over-sampled here. I’m inclined to think this doesn’t matter for the question at hand. The CPS is a household survey, which means that it has information on all inhabitants of a given household, but no information on persons who live outside of the household.
In the 5+ years of data I examined, there are 278,582 unique households. Of those, 24,489 had three or more children under the age of 18. I looked at the sex of the three oldest kids. Here are the frequencies of the 8 possible birth order combinations:
frequency percent
bbb 3635 14.87
bbg 3256 13.32
bgb 2834 11.60
bgg 2740 11.21
gbb 2854 11.68
gbg 2752 11.26
ggb 3235 13.24
ggg 3134 12.82
Basically, what we can take away from that is that parents who have one boy and one girl are less likely to have a third child than are parents who have two of a kind. It looks like parents with two boys might be more likely to keep going than parents of two girls, too. (Went back and tested this and yes, there are significantly more 3 sibling sets that start off bb than gg.)
Among families with 2 boys who have a 3rd child, 47% have a girl as the third child. This is statistically significant.
Among families with 2 girls who have a 3rd child, 49% have a girl as the third child. This is not statistically significant. (where significant means p < .05)
One caveat with this analysis is that only children aged 0-17 and living in their parent’s household were included. With this dataset, I have no way of knowing if the parents have older children who no longer live in the household. I suppose that could influence the results, but I have no hypothesis as to how it would affect them.
So, to answer the original question, it looks as though parents who start off with two boys are (very slightly) more likely to have a boy for number three. Parents who start off with two girls have an even shot at having a third girl.
[The following is something that I remember reading about a long time ago. I have no cites, and I might be remembering wrong. Take with a lot of salt.]
The theory was that male sperm are sprinters, and female sperm are marathoners. If the mother is well lubricated and the sperm is deposited close to the target, it’s more likely that a male sperm will win the race. If the trip is long and difficult, then it’s more likely that a female sperm will. Whatever I read was suggesting that you could improve (but I don’t recall it saying by how much) your chances of having whichever gender you wanted by screwing appropriately. [I apologize for all of the technical jargon.]
Now, if this were true, then I would think that unintended pregnancies would skew more towards females. I’m not sure how easy it would be to get data on this.
The thing is that it is mostly a purely academic question since there seems not to be a whole lot that can be done about it whether it turns out to be true or not. Can’t be changed, can’t be sold, can’t be funded for research. Esoteric it is.
There is approximately a 92% chance that this will not happen.
Well, other than the fact that in the entire history of the universe, this has never, ever happened with a fair coin. If you can flip a fair coin 100 times per nanosecond, and you keep doing this (with 100 billion flips every second), and you keep doing this for, say, a billion years, the odds of ever getting 100 heads in a row are roughly 40,000 to 1 against.
Somewhat related puzzle: a certain despotic king felt that his kingdom didn’t have enough hot chicks for him to deflower, so he enacted a new decree: families were permitted to keep having children as long as they had only girls, but as soon as they had a single boy child, they were forever forbidden from having any more children. If boys and girls are equally likely to be born, and if families continue having children as long as they are legally allowed to, what effect does the king’s decree have on the gender ratio of the population?
The whole point of this thread is that you have to also add the assumption (very close, at least, to accurate in practice) that all births are independent. If you add that assumption, then the answer is that the population will still be split evenly. If you instead assume that some couples are predisposed one way or the other, then the balance will shift towards females.
If this were true, and assuming the male climaxes at full penetration, wouldn’t well-endowed men have more boys than girls? Presumably, the father’s would pass on “well-endowed” genes on to their sons who would then go on to have more sons. etc. etc.
Men would be looking like elephants.
Well, those well-endowed sons would have to impregnate the daughters of less-endowed men. So wouldn’t it balance out?
[ETA: I ask this not so much as a defense of this theory, but as an exercise in logic.]
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I’m too modest to ask strangers personal questions. 
[BTW, I’ve never mentioned this theory to my uncle that has 3 girls.]
This is basically what I’ve read recently in Taking Charge of Your Fertility - the male sperm are fast & light, but die faster - so if you have sex right near ovulation, they’d reach the egg first. The female-producing sperm are heavier and slower, but heartier - so if you had sex maybe 4 days before ovulation, the male sperm would die off before there was an egg to fertilize, but the female sperm would live to get to the egg.
Not really, if you’re having sex ejaculate is getting shot straight at a woman’s cervix, the guy’s length really isn’t going to make much of a difference - the stuff comes out pretty fast and can get shot pretty far, after all 
This is faulty analysis. In 100 flips there are 96 different possible runs of 5: 1-5, 2-6, … 96-100. Now these are not independent, clearly, but they’re still there. In 20 families of 5 kids, there are only 20 groups of five. At 50-50 the probability of getting 5 boys in a family of 5 is 2^(-5) = 1/32. So the chance of having no family of five boys in 20 families of 5 children is (31/32)^20 = almost 53%. The probability of no 5 boy or 5 girl family in 20 families of 5 kids is 27.5%
I think your analysis backs up what I said, though with more precision and specifics. There is a 72.5% chance of having at least one family with all 5 kids of the same gender. How is it faulty to say we’d expect to see that result? I didn’t say we were guaranteed or assured of that result, just that we’d expect it.