… an answer, and more questions

Yesterday’s question looks like a problem about probability, involving maybe a slight inequality in the sex ratio, and maybe failure of independence; but it is not.

The answer is that, among two-child families, it is significantly more likely that the children will be of opposite sex.

As Sune Kristian Jakobsen correctly commented (and also Gordon Royle said to me), the reason given is that parents prefer to have a child of each sex; if their first two are of the same sex, there is a tendency for them to have another. Only those who stop at two are counted in the data.

Thinking about this led me to two speculations. Firstly, I don’t understand this reason. To me, people (including children) are people, and that is that. But if it is true, then a second child of the same sex as his/her older sibling would be slightly unsatisfying to his/her parents. Is there any data about this? Do such children have more problems later in life? (Of course, this would be only a slight tendency; I am certainly not saying that every child in this position would suffer. I am not, in fact, claiming anything.)

The second was to wonder about the evolutionary basis of such a preference, if (as the data seem to show) it exists. Maybe it is true that a child who grows up with a sibling of the opposite sex is less likely to regard the opposite sex as an impenetrable mystery, and so is more successful at choosing a mate. Is there any data about this?

I have no information on either of these points. Anecdotal evidence tells nothing, but careful analysis of large datasets may throw some light.

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About Peter Cameron

I count all the things that need to be counted.
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9 Responses to … an answer, and more questions

  1. How do we know that “parents prefer to have a child of each sex”? We could also explain the data with “some (pairs of) parents wants to have a girl and some (pairs of) parents wants to have a boy” (like you, I’m not claiming anything).

    It could be interesting to see if there is a difference between the probability that parents with two girls get a third child and the probability that parents with two boys get a third child (of cause, if there was a difference you could also explain that but claiming that children of one sex is more difficult to raise than the other).

    • Good point. Once again, a large dataset is our best hope of deciding this. I admit it, I swallowed the explanation I was given when I learned this factlet without being sufficiently critical.

  2. Colin Reid says:

    You don’t need to assume that parents are dissatisfied with having children all of the same sex – they might just have a straight preference for one sex over the other. Suppose for instance that there is a large group of parents whose primary goal is ‘at least one daughter’ and whose secondary goal is ‘as close to 2 children as we can manage’. 1/4 of them will stop at two daughters, 1/2 at one daughter and one son, and 1/4 will have more than two kids, so you still have a population bias towards opposite-sex siblings among two-child families.

    • Colin Reid says:

      If an equal number of parents had the corresponding bias towards sons, you wouldn’t be able to tell this situation apart from the situation ‘some people want children of both sexes’.

  3. Emil says:

    Very interesting!

    But I can’t see that there can be an evolutionary explanation here – I don’t think it is ever an evolutionary advantage to voluntarily stop having kids. The correct response in all situations is to want more kids, whether your existing family is balanced or not….

    I’d like to see this study done for a number of different cultures.

    Also, we should exclude twins.

    • This discussion, and in particular your comment, made me think:

      Parents to children that are difficult to raise will probably on averages choose (now that they have the possibility to choose) to get fewer children than parents with children that are easier. So
      the invention of contraception should make future children easier to raise!

  4. bretbenesh says:

    Hi Peter,

    My first child, a boy, was born in 2009. My second child, a girl, was born in September. We had always planned on just having two kids.

    However, I have received a lot of comments from people that basically said, “It’s a girl? Congratulations! Your family is now complete.”

    This baffled us, since we think about kids as you do—we would not have kept trying for a girl if it had been a boy. But we heard it enough times that we figured that it must be some sort of “thing” that people think that we were not aware of.
    Bret

  5. Walter Sinclair says:

    After hearing a recent news item about the scarcity of females in China after its one child policy, I was expecting the answer. However, my reasoning was that if parents wanted a boy, and got a girl (or vice versa: wanted a girl and got a boy), they would try again. If that were the case, and they got the desired result the second time, there would be less incentive to try for a third child. But then suppose parents wanted all their children to be the same sex, but didn’t care which it was. In that case they would stop at two because there would now be no way they could achieve that goal, or else press on for three in order to get a better weighting. And if it is the case that parents could have one preference initially, and then shift strategy after the first child, having discovered that it wasn’t what was wanted after all, then you’d again end up with this result. Thus you’d achieve the same result no matter what motive you assign the parents. Only if all parents had no motive at all would you get any other result.

  6. More research needed …

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