Monday, October 11, 2010

Elite universities and human capital mongering

In an earlier post I discussed the advantages of attending an elite university. A related question is: what fraction of the total population of top students in the US attend an elite university? The answer is a function of where we put the lower cutoff for top students.

One interesting population to consider is the subset of National Merit Semi-Finalists who are awarded scholarships directly funded by the National Merit Corporation. Semi-Finalists are themselves the top percent of PSAT/SAT takers, so this subset is an especially elite group. From my experience I would guess that only the top 10-20 percent (see *** below) of National Merit Semi-Finalists are offered these portable awards, as opposed to other "National Merit Scholarships" that are funded by individual colleges. (Almost all non-elite colleges use these self-funded NMS to increase the enrollment of talented students; any Semi-Finalist is eligible for such an award. The most elite universities do not need to offer self-funded scholarships of this type, as discussed below.)

About 2300 NMS scholarships funded by the corporation are awarded each year. It turns out that just 10 elite universities account for well over half of these awardees. The vast majority of universities in the US have zero students from this select population! Data from this report. (Thanks to a reader of the blog for sending it to me.)

Number of NMS in entering class / size of entering class.

Caltech       42 / 200
Harvard     266 / 1600
Yale         234 / 1300
Princeton     196 / 1300
Stanford     110 / 1600
MIT         110 / 1000
Brown       91 / 1500
Duke         105 / 1600
Penn         125 / 2000
Berkeley     91 / 6000

Total 1270

Note, large numbers of Semi-Finalists who are not in this top group (i.e., not among the top 10-20 percent or so) do not receive a National Merit Scholarship because they choose to attend an elite university that does not self-fund additional awards. Just by looking at average SAT scores one would guess that as many as half the students at some of the schools listed above were Semi-Finalists. Apparently, the marginal value to these schools of "just another Semi-Finalist" does not warrant the expenditure of a few thousand dollars in additional scholarship funds. ("If we wanted to, we could fill our entire freshman class with Semi-Finalists!" etc. etc.)

*** If Semi-Finalists are in the top .5 percent of the population (assuming some selection in PSAT takers relative to the general population), the threshold IQ is +2.5 SD (137 or so). The NMS population discussed above is perhaps another SD higher (IQ 150 or so). You can directly estimate the number of students at the Semi-Finalist level: if 4M students graduate from HS each year in the US, that means about 20K above the 99.5th percentile. If the 2.3K NMS are the elite of this population, they would constitute the top 12 percent or so.


n/a said...

"The NMS population discussed above is at least another SD higher (IQ > 150 or so)."

You must have picked up this idea from the confused Asian who started spreading it at Steve Sailer's blog a while back for reasons that elude me (the commenter in quesion clearly having no personal history with the NMSC). There's no basis on which to assume "portable scholarship" awardees average higher IQs than Finalists. The $2500 scholarships are awarded by "a committee of college admission officers and high school counselors" on the basis of non-test score criteria similar to those used in college admissions (essay, GPA, recommendations). The aim is to select the most conscientious and striverish Finalists -- not the most intelligent Finalists. Of course this population will be more likely to attend elite schools (though your denominator should be something like 3400, since around 1100 corporate-sponsored National Merit scholarships are awarded each year).

RKU said...

Well, it's nice to see that the relative rankings of the elite schools with respect to their high-elite fractions are almost exactly what I would have expected from back when I used to pay attention to such things. The only (slight) surprise is that Yale seems a bit higher than I would have expected, being above Harvard and well above Princeton. This tends to reinforce the complaints of "corrupt practices" at Harvard I've sometimes heard.

Guest said...

Lots of amusing info in that document. Did you know Oral Roberts U. got more than U. of Oregon? By your own criterion Steve, you teach at an institution that is less elite than Oral Roberts. :) I know, I know, statistics of small numbers and all that.

steve hsu said...

"The NMS population discussed above is at least another SD higher (IQ > 150 or so)."

No, I picked this up from my own high school experience (see link in post) and also experience at Caltech.

I knew the scores of the S-Fs and (portable) NMS winners at my high school over several years, and I also discussed it with teachers and administrators there who had seen many cohorts pass through the school. Out of around 20 SFs per year only a few would get the (portable) NMS, and they tended to have much higher average SAT scores than the average SF. My high school has quite a long and proud academic tradition, and around graduation time there was a special awards reception in which the school honored all the kids who have won scholarships, contests, etc. In printing up the program for the event they were always careful to distinguish the (portable) NMS winners from the other type, and it was always the top kids in the class SAT- and brainpower-wise who won it. You can imagine that the top couple of kids out of a class that produces 20 S-Fs are pretty bright.

I also knew the SAT scores of lots of my Caltech classmates and who had the NMS and who were S-Fs without NMS. There was a definite difference in average ability between NMS winners and S-Fs.

I can't say for sure how things work today, but at high confidence I would say my description is accurate of the deep past, when I was a kid :-) Remember, in those days the SAT had a much higher ceiling. If the average S-F was somewhat below 1400, and you had a sub-population of kids who scored, say, well above 1500 (>1 SD higher, and clearly a qualitatively different population), who do you think the NM committee would award the NMS to? These days I'm not sure how they do it. Does the SAT have enough ceiling to select the top 2-3K kids in the country? How many 2400 scores are there each year?

steve hsu said...

I was a bit surprised that Stanford and MIT were so low and Duke so high. Otherwise about right.

Perhaps engineers are at a disadvantage with the double verbal weighting of the new SAT?

BTW, I have it on good authority that Duke's strategy for climbing the rankings is to not discriminate as much as the other schools against Asians -- a quick way to build up their SAT averages ;-)

n/a said...

It's not impossible that the $2500 scholarship winners average slightly higher SAT scores than Finalists in general. What's absolutely not true is that they are the top 1/7 of Finalists in terms of SAT scores or IQ.

Yan Shen said...

Regarding the scholarships awarded by the NMSC itself.

"Every Finalist competes for these single payment scholarships, which are awarded on a state representational basis."

It seems like even if they selected the top NMSFs from each state in terms of scores, the disparity in scores amongst states would dictate that, as before, the 2.3k students wouldn't represent the top 2.3k scoring students overall.

steve hsu said...

Not claiming you really get the top 2.3k in a rank-ordered sense, but that you get a (significantly) more elite group if you consider the (portable) NMS awards.

Yan Shen said...

"Not claiming you really get the top 2.3k in a rank-ordered sense, but that you get a (significantly) more elite group if you consider the (portable) NMS awards. "

I think that's fairly likely.

By the way, I noticed that the cutoff this year for Iowa for NMSF was "only" a 209. I wonder how stable the IQ demographic in Iowa has been over the past 20 years or so. Perhaps you were one of the smartest people in the entire state during your day? :)

n/a said...

Test scores are supposedly one of the factors taken into account, but as I expected: "Often recommendations or essays are the determining factors".

steve hsu said...

Again, I can't make any global statement about how the selection works (esp. today), but based on what I know from HS and Caltech I would say that the characterization I made in the post at *** was correct at the time.

BTW, I followed your link and your quoting and interpretation seem selective. In an earlier paragraph it specifically says only the top scorers in each state qualify for consideration for the portable NMS award. Even in a moderately small pop. 5M state (say, 60K HS grads per year) the top scorers (say, the top 30) are a much more select group than the top 99.5th percentile. We're talking 1 in 2000, as opposed to 1 in 200.

n/a said...

"specifically says only the top scorers in each state qualify for consideration for the portable NMS award."

It's poor writing, but the author is simply referring to the fact that only Finalists are considered (this is clear from the next section in which Semifinalist cutoffs for different states are listed). There's no additional cutoff for "portable scholarships".

Retard said...

According to Wikipedia the PSAT and SAT score aren't enough to be a finalist. An "excellent academic record" is also necessary.

Retard said...

There was no pre-prep era unless you mean an era before test prep companies (which are total frauds by the way).

Walking into a high stakes test cold having no idea even of the format?

Ruchira Datta said...

I'm surprised that that the short list of elite schools you picked for your sample didn't include Chicago, Cornell, or Columbia, while including some others. The list I usually use is here:

Kristen Mendez said...

What an excellent information here. I am really happy to see that my school really do well. Thank you for sharing this essay writing services essay for us. Keep on writing.

Kristen Mendez said...

I need more essay about PSAT and SAT, I hope I can get more information here. Is there any essay writing services that can give me some idea or essay about this topic?

Blog Archive