Are 80% of Harvard Students First Borns? | Hacker News Reader

Are 80% of Harvard Students First Borns?

larrycheng.com

16 pointslwc12323 comments

Eh, thats not very good evidence of the claim, and wouldn't over 50% be first born anyway? I dont know the average distribution of child-sizes but I would assume almost half of people in the US are first borns (including only-children).

The "average number of own children under 18 per family" for "familes with own children under 18" was 1.86 in 2009 (and has been within 0.1 of that since 1978), which means about 1/1.86=~54% of all children are first-borns...

I don't think we have enough information here to actually verify but I suspect 80% vs 54% is still a statistically significant difference.

But it's pretty obvious that the 80% number is an arbitrary guess, so I'm not sure exactly where I stand here.

source: http://www.census.gov/population/socdemo/hh-fam/fm3.csv

No, it depends on the distribution. Let's say (as a first guess) that number of children follow a poisson distribution. A poisson distribution with mean of 1.84 has 74% of children being first borns.

There are a lot of reasons why a poisson model probably isn't great, but it's worth pointing out that a model with more density near zero is probably likely and implies that first borns are more popular than the they look.

74% versus 80% isn't anything to write home about.

Moreover, as Mz points out, only-children are a totally different case.

A Poisson distribution with a mean of 1.84 results in about 45% of children being first born. In fact, the best you can do with any distribution is 54%. For example, if there are 10k couples, then there will be 18.4k children born, at most 10k of which can be first born; and 10/18.4 = 54%.

In fact, the only thing that matters for the distribution (once you know the mean) is the number of childless families, since they could have had a first born but didn't.

I haven't been able to figure out where 74% comes from. Is there some way to sample on a per-family basis to come up with this?

edit: spelling

More like a fundamentally stupid mistake of inverting my parameters when I checked the number, getting a result in tune with the article, and then not thinking it through at all. It'd be possible to have a whole great deal of families with 0.1st children, but that's just the egg on my face.

Isn't Poisson rate-based, ie events over a fixed time period? I'm having trouble seeing where you got the rate from (children per lifetime? but that's hardly a "fixed time period") - all we have is a single number "children/household" with no time dimension.

And most other distributions, ie other than the uniform I'm assuming and the Poisson you're using, require >1 parameters. Since we only have one piece of data (the mean) we would have to make assumptions with these distributions that make no more sense than simply assuming a uniform distribution to begin with.

You'll have to excuse me for any incredibly stupid intuitive leaps; I haven't had a chance to wake up fully yet.

I crunched the numbers from the GSSS once. 42% of Americans are first born children.

Inferring temperament from birth order is largely pseudoscience. Wikipedia has a good summary: http://en.wikipedia.org/wiki/Birth_order

"Birth order is defined as a person's rank by age among his or her siblings. Birth order is often believed to have a profound and lasting effect on psychological development. This assertion has been repeatedly challenged by researchers, yet birth order continues to have a strong presence in pop psychology and popular culture."

There are many obvious problems with this argument:

1. The 80% number seems to be pulled out of the air. It could be a counting error or a statistical aberration of that class, and the real Harvard number could revert to the mean.

2. The type of parents who could send a child to Harvard is a biased sample of the general population. It will mostly tend towards rich, white (or asian) families, who generally will have less children.

There's definitely not enough information to infer that first-borns are any different.

Or maybe if they're not rich, they can't afford to send child #2 there.

I figured it was because the second and third born were too busy working their butts off in the military and the clergy to have time to spare.

Interesting that although I am the second of two, the "Only Child" description matches me much, much more accurately than the others.

It's always the way that statistics are fine in aggregate, but for the exception, it's 100%. For me, the descriptions of the characteristics of the "child-by-place" are simply all wrong.

I hesitate to say it, but maybe a lot of them are 'only' children and it relates (at least in part) to parental ability to afford Harvard? Just like big cities in America tend to have fewer kids because they are expensive to live in, so families move someplace they can afford to raise their kids.

This was my first thought as well, but my understanding is that if you are accepted at Harvard they will provide financial aid for 100% of need, which means parents pay what they can afford -- it can actually be cheaper to go to Harvard than a state school that doesn't have the funds to meet 100% need.

Maybe single children have better academic preparation? Should be easy to look at that.

Need is a hazy thing. They will meet all of what they define as your need, but what you "can pay" often means a substantial sacrifice when it comes to standard of living. This is especially bad if your parents have been paying what they "can pay" for the last 4 years for an older sibling.

Also, it's gotten a lot better in the last few years, which is after he moved through Harvard.

About 3(?) years ago, they, along with a few other upper-echelon colleges (I know Stanford did) moved to a much more liberal definition of need and totally got rid of loans from financial aid programs. Now, theoretically, if your family makes <$60k, you pay nothing, and <$100k you pay no tuition, but pay room & board and such. There's more variables than just family income, and you always have to add to the "nothing" or the "no tuition" a reasonable figure for the student to make from having a part-time job during the year and full-time over the summer, but it's still substantially more generous than it was.

It would be interesting to see if those policies changed the percentage that are only children.

That's quite a liberal definition of "need".

Yes, it is. It used to be substantially worse, though, and other than a few top colleges, it still is.

Example of the difference: my "estimated family contribution" according to the FAFSA is about $10k more than what Stanford estimates they'll make me pay (though I haven't seen the final number, yet).

Some random-ish thoughts:

Cambridge is expensive to live in even if you aren't paying tuition.

All other factors being equal, going off to college elsewhere is both more expensive and logistically harder to arrange than going to the local college where you happen to already be.

I happen to think there is a little truth to the "birth order" theories. My first born older sister has always been more interested in getting societal validation of the sort that sends people to Harvard than I have been. But then I also believe in astrology. :0 (No, not "sun sign" astrology.)

These descriptions reminded me of horoscopes... I saw characteristics of myself in each one.

Yeah, that's the Forer Effect[1] at work.

[1] http://en.wikipedia.org/wiki/Forer_effect

Back when I took calculus in high school, the instructor asked for a show of hands for first-borns. All hands but one went up--well above 80%. I've wondered why that was so ever since. Why weren't middle and younger children pushing themselves to get into the "advanced" math classes?

Because parents put much more pressure on the first born.

Epic fail. All his descriptions do not even remotely describe me and my brother.

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