Sib redux

[undyingking]

Well, that was quite interesting. I asked a few days ago about birth order among people who read my LJ, and have now got 47 responses, which is probably enough to get on with.
First of all, sibling group sizes:

Only child	10
One of two	18
One of three	15
One of more than three	4

Note that these are not 'official' family sizes, but the number of siblings you grew up with: for some people, the two are different. This makes it rather difficult to compare with general family size data, to see whether you lot are odd in that respect. Apparently the mean UK family has about 1.8 children these days, down from 2.0 in 1970 (I guess most of you were born nearer to that date), compared with 2.3 above. But the mean figure I guess ignores the fact that some families surveyed will be as yet incomplete, which doesn't (presumably) apply to this sample. So not really sure what to make of that. (I do have a few people on my flist who are from the same sibling group, but fortunately in no case has more than one of them has answered the poll, which would have made analysis a bit trickier.)

Now the bit I was more interested in: where people are/were in their sibling group.

Elder of two	15
Younger of two	3

Eldest of three	10
Middle of three	3
Youngest of three	2

Eldest of four or more	3
Not eldest	1

This is pretty striking I think. A mighty 76% of those of you who aren't only children are the elder/st sibling in your group. And the proportion is fairly similar across the group sizes. I'm no statistician, but it looks significant to me.

I suppose there are several possibilities:

• this is actually the sort of distribution found in the general population (seems doubtful);
• or is typical of LiveJournal users generally;
• (or of some other appropriate generic category of geekdom;)
• or is typical of the subset of my friends group who are active on LJ and who respond to polls, but that's not necessarily going to apply to my friends group in a more general sense;
• (etc.)

celestialweasel pointed out in a comment to the earlier post that there has been observed to be a preponderance of first/only-borns among SF fans, which quite a few of you are. Don't know if that's true of gamers (which even more of you are), but it wouldn't surprise me.

There's also I believe a finding that first/only-borns were in my generation more likely to go to university, which as I did (and met many of you through it) that would obviously skew things. But I haven't been able to locate a link to that result yet.

One possibility I was slightly intrigued by was the psychological one that somehow I unconsciously seek out firstborns to be my friends, to fill some particular social role vis-a-vis me.  It would be interesting if other middle children could do the same exercise to see if they get the same result; and, come to that, if those of you who are firstborns could see if you have a preponderance of middle children. At first guess I would say it looks unlikely, because out of my own group of firstborn friends, lots of you are also friends of each other. But worth investigating I think.

Any thoughts?

Comments

[bateleur.livejournal.com]

Any thoughts?

Well first, I'm slightly skeptical of some of your maths. The mean number of kids across the population isn't relevant, because what you're doing is sampling random kids. So in particular, you have families with three kids weighted three times higher than families with one kid. This will skew your mean.

Also, when you say that it "seems doubtful" whether the sibling distribution you have there is correct for the population, I'd go a bit further and say it's clearly not possible. For every pair of children who grew up together, one must be eldest and the other not. It's slightly more complex for threes and fours, but for the majority of families an analogous result will apply.

Second, I would be curious to know what the statistical significance of these results are. It looks very significant to me, but statistical intuition can be misleading!

[bateleur.livejournal.com]

A quick calculation suggests that the probability of your eldest-vs-youngest of two data with a null hypothesis of 50-50 is around 1 in 314.

(Assuming I've remembered the relevant stats stuff correctly...)

[undyingking.livejournal.com]

That kind of magnitude does 'sound' right. This is where a professional would be useful… (_alanna?)

[mr-malk.livejournal.com]

You couldn't explain that in layman's could you? I thought I was more or less keeping up until you got to the bit about 1 in 314, at which point I realised that I clearly hadn't got the faintest idea what you were talking about!

[bateleur.livejournal.com]

Sure...

According to my null hypothesis we should see responses from an equal number of responses from first-of-two and second-of-two people. So the question we need to ask is: If I take 18 people who grew up with exactly one other sibling and each is 50-50 to be the eldest, what is the probability that 3 or fewer from my sample are youngest?

This probability is (I claim): (0.5^3 x 0.5^15 x 18C3) + (0.5^2 x 0.5^16 x 18C2) + (0.5^1 x 0.5^17 x 18C1) + (0.5^0 x 0.5^18 x 18C0)

This simplifies in an obvious way to: 0.5^18 x (18C3 + 18C2 + 18C1 + 18C0)

Because I'm lazy, I just Googled for a big picture of Pascal's triangle and pulled the last four digits off the 18th row without checking them. They are (allegedly): 680, 136, 17 and 1.

So our probability is (680 + 136 + 17 + 1) / 2^18.

Which is 834 / 262144.

This is approximately 1/314.

(Feel free to poke holes in this - it's been well over 15 years since I last did this stuff and I may have messed it up!)

[mr-malk.livejournal.com]

Not sure about poking holes in it. I rate my mathematical skills as "Quite good at mental arithmetic, and not bad at percentages", so I'm not really equipped with a very sharp scaplel!

I was momentarily confused by "0.5^18 x" becoming "/2^18", but I've got it now.

Thanks. Most enlightening!

[undyingking.livejournal.com]

This will skew your mean.

Good point! (I said I wasn't a statistician&hellip and I was right.)

Hmm, in that case I'm not sure if it's possible to get a figure form my data that can sensibly be compared with the population mean quoted. That seems a pity, but maybe someone else can see how to.

[bateleur.livejournal.com]

There's no way to compare with the population mean unless we can find population stats for distribution of family sizes.

[ar-gemlad.livejournal.com]

I have no thoughts, as my brain is too busy looking forward to a pint of beer in an hour.

However, I will point out that metame and ar_boblad have been conspiring to make your analysis trickier by being brothers :P

[undyingking.livejournal.com]

Gah, I hadn't noticed that ar_boblad had responded too. In that case, I've got no idea how to make that affect the maths…

[ar-boblad.livejournal.com]

We mucky up your mean family size whatsits but judging from other comments those are fairly mucked up in any case.

For the "surprisingly many of my friends are eldest children rather than not" does it mess with your analysis? It's a feature of the people you know that some of them are related to each other, if we ignore that we aren't modelling your friend space accurately. And yes, if you tend to know sibling groups you will tend to know a smaller proportion of exclusively eldest types. "Skewing" the maths by doing nothing to it in order to model a complexity for free is all good.

[undyingking.livejournal.com]

Mm, yes, I think it's legit for the latter stuff, it was the mean size I was worried about. Seems a pity that that is so screwed, you'd think there would be something useful that could be done with it.

[floralaetifica.livejournal.com]

I've noticed over the years that most of my friends have been firsts or onlys. I'm a first (with a hint of only, as my sister is 5 years younger than me), and I'd always assumed that I had so many first/only friends because we were drawn to other people with similar personalities.

[undyingking.livejournal.com]

That seems reasonable, although doesn't leave me wiser as to why I'm also drawn to you :-)

[floralaetifica.livejournal.com]

Oh, well that's cos I'm awesome. :)

[undyingking.livejournal.com]

Hold that thought! :-)

[mr-malk.livejournal.com]

Well, as bateleur clearly knows something about the dark arts of statistomancy, I'm not even going to attempt to reach any mathematical conclusions, but it is at the very least curious that the number of first-borns is as high (relatively) as it is. It sounds like the sort of subject that Robert "Quirkology" Wiseman would research.

It would be quite interesting to know what the demographic splits are in this context, not just in terms of geekiest, but in terms of the sorts of jobs people do, academic achievements, interests, social groups. Perhaps those data have been collected by someone already...

[undyingking.livejournal.com]

Ooh, interesting, I shall have to look at that Quirkology stuff when I have some time.

I'm sure the extra data you mention will have been gathered, but digging out the relevant research is probably going to be a non-trivial task. Maybe another thing for when I have some time...

[mr-malk.livejournal.com]

I'm surprised you've not encountered Robert Wiseman/Quirkology before. I think it would be right up your street. I had seen the website and a few experiment/trick videos he has on Youtube (also worth looking at), and I was given the book "Quirkology" for Christmas last year. Very interesting and entertaining read. One for your book group perhaps. Could be interesting/entertaining/contentious if any of them like their astrology.

[undyingking.livejournal.com]

Mm, as far as I know they're all pretty rational, but this might be a good way of flushing out the closet loons!

[dr-bob.livejournal.com]

The mean UK family size presumably includes those families with no children (as well as those whose family is incomplete). The former group is not going to show up in your avg no of kids analysis, so may in part explain why it's 2.0 vs 2.3.

[undyingking.livejournal.com]

It hadn't even occurred to me that they might be incuding 0-child families. Oh well, it's hopeless to try and compare, in that case.