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]

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!