In a previous post, I argued that philosophy undergraduate students are pretty smart; indeed, they are approximately as smart as the physics and mathematics undergraduates. Now, I want to ask a question that naturally extends from my first post: just how smart are philosophy graduate students?
We can make some inferences using GRE scores. However, we must first have a sample of philosophy graduate students. I will use the Philosophical Gourmet Report, which has a profound impact on undergraduates selecting philosophy graduate programs. The ranking has come under some criticism, notably by Zac Ernst, on how well the report ranks the educational ability of the departments; but I find for my purposes that the ranking is excellent at ranking the faculty quality in terms of publication, both in quantity and quality. In short, the better the professional philosophers (on average) are, the better ranked the graduate department is. And it’s reasonable to assume that the better the philosophy undergraduate (on average) is, the better the program (on average) the student will be admitted to.
Let’s restrict the number of graduate schools to the United States. It’s a manageable number, and they require GRE scores more often than Canadian, Australasian, and British graduate programs. There are approximately 100 U.S. philosophy graduate programs. So finding a school that is ranked around 50 is going to be a good approximate of the average philosophy graduate department, and of the average philosophy graduate student. I could only find GRE scores for the following departments, starting with our approximate average:
(51st) University of Missouri-Columbia: 650 verbal, 700 quantitative, 1350 total, 10%-15% acceptance, and 3.9 GPA.
(46th) University of Washington-Seattle: 660 verbal, 710 quantitative, 1370 total, and 6%-8% acceptance.
(40th) University of Virginia: 650 verbal, 690 quantitative, 1340 total, 10% acceptance, and 3.87 GPA.
(38th) University of California-Davis: 684 verbal, 743 quantitative, 1427 total, and 3.62 GPA.
(28th) University of Colorado-Boulder: 708 verbal, 741 quantitative, 1449 total, 6% acceptance, 3.87 GPA.
(22nd) University of Chicago: They don’t currently post their information, but I do recall that as early as last year the average was 710 verbal, 740 quantitative, 1450 total.
(21st) University of California-San Diego: 705 verbal, 750 quantitative, 1455 total, and 12.7% acceptance.
(20th) University of Texas-Austin: 1470 total, and 3.86 GPA.
For a comparison, the average GRE for the total test-taking population is a 465 verbal (117 SD), 584 quantitative (149 SD), and 1049 total. The average GRE score for the philosophy undergraduate test-taking population is a 590 verbal, 638 quantitative, and 1228 total.
Let’s use the differences in standard deviation to gain a better idea of how much smarter the graduate students are from the undergraduates. Philosophy undergraduates are roughly 1.07 standard deviations above the verbal mean, and .36 standard deviations above the quantitative mean. Averaging them together yields that the undergraduates are roughly .72 standard deviations above the general test-taking mean. Recall from my above list that students from the University of Missouri-Columbia are good approximate representations of the average philosophy graduate student; they tested at 1.58 standard deviations from the general verbal mean, and .78 standard deviations from the quantitative mean. Averaging this yields that they place at 1.18 standard deviations from the general test-taking mean. The University of Colorado-Boulder philosophy graduate students tested at 2.08 standard deviations from the general verbal mean, and 1.05 standard deviations from the general quantitative mean. The average yields that they tested at 1.57 standard deviations from the general test taking mean. the University of California-San Diego philosophy graduate students tested at 2.05 standard deviations from the general verbal mean, and 1.11 standard deviations from the general quantitative mean. The average yields that they tested 1.58 standard deviations from the mean.
I couldn’t find any programs past Texas that has available, ready-made, easily interpretable scores. So we don’t know the average GRE scores of the students in the top-nineteen programs. But most will surely be better than the 1470 total of Texas. So I’ve decided to perform a linear regression analysis to predict the top-ten philosophy graduate programs’ GRE average scores.
I’ve thrown out the Texas score to do separate regressions on the verbal and quantitative scores against the ranking. The verbal y-value is 756.62348459 and the slope is -2.151887773; the quantitative y-value is 782.06927607 and the slope is -1.6279853. I stick with the simpler values of 756.62, -2.15, 782.07, and -1.63. We find the corresponding equations to be Verbal = 756.62 – 2.15(Rank), and Quantitative = 782.07 – 1.63(Rank). These equations predict a 713.62 average verbal score, and a 749.47 average quantitative score for Texas, which adds to a 1463 total average (with rounding). This is seven points off from the 1470 reported total. You might not think the equations’ predictive power is very accurate—they seem to be on the conservative side—but the conservativeness shall work well for my purposes; it’s better to be conservative for my following predictions.
Here are some predicted average GRE scores for the graduate students at the following departments (with their standard deviations from the total test-taking population):
(15th) City University of New York Graduate Center: 724 verbal (2.21 SD), 758 quantitative (1.17 SD), and 1482 total (1.69 SD).
(10th) University of California-Berkeley: 735 verbal (2.31 SD), 766 quantitative (1.22 SD), 1501 total (1.77 SD).
(5th) University of Michigan-Ann Arbor: 746 verbal (2.4 SD), 774 quantitative (1.28 SD), 1520 total (1.84 SD).
(3rd) Princeton University: 750 verbal (2.44 SD), 777 quantitative (1.3 SD), 1527 total (1.87 SD).
(1st) New York University: 754 verbal (2.47 SD), 780 quantitative (1.32 SD), 1534 total (1.9 SD).
These predictions are probably on the conservative side; If these average GRE scores approximate the real ones, then all I can say is “WOW!” You might be wondering why the student quality is so high; the reason is that the job market for professional philosophers is abysmal, which forces graduate departments to have minimal funding for graduate students, which forces the departments to accept the best of best, which forces an acceptance rate that is roughly 3%-5% for the top-ten departments. I highly doubt that the best physics departments in the United States have acceptance rates this small.
To conclude this post with a side note, you probably believe that philosophy graduate students tilt towards verbal ability given the above standard deviations. Verbal tilt is usually calculated as having verbal scores the fall more than one standard deviation beyond the quantitative scores. If this true, then you can tell from above that philosophy graduate students don’t tilt towards verbal ability. You can read here about ability tilt concerning highly gifted adolescents taking the SAT.
Will Dwinnell
27 February 2009
Your analysis is interesting, though I wonder:
1. Whether linear regression is an appropriate choice for this data, since linear functions are unbounded, yet GRE scores have hard lower and upper limits. Perhaps logistic regression would have been a better choice?
2. What effect does regressing on ranks have? Ranking throws away a great deal of data and, notably, masks the underlying distribution. I worry that inferences made toward the extremes of a rank-based model will be seriously biased.
3. Whether your use of the standard deviation to make inferences about a population which, by definition, cannot be normally-distributed might not lead to estimates which are too approximate.
Still, it is an interesting subject to explore quantitatively. Thanks!
Lover of Wisdom
27 February 2009
Hi Will:
Those are good points, so let’s take them each in turn:
1. My short answer is: you are probably right. When I put the available data into a scatter plot, it was only enough to give me (just by sight) an almost perfectly straight linear line; my reasoning is that it might be enough to give me an idea on what’s going on in the top twenty rankings, predictability-wise. However, I know from what other’s have told me is that the top-ten programs have a bunching effect with student quality. The departments themselves are almost indistinguishable quality-wise, and the students are likely indistinguishable quality-wise too.
There is a problem with the GRE’s having hard upper- and lower-limits. But I wonder whether that matters; the verbal section is more difficult than the quantitative section. The verbal subtest correlates highly with traditional IQ tests; the quantitative subtest does less so. It might be easier to see a bunching effect with the quantitative section near the upper-limit, because that section can’t distinguish the top 4%-6% in that ability. The verbal section does a much better job distinguishing up to the top 1%, and I bet it can do a good job distinguishing graduate students across the board.
I’ll give the logistic regression a try and see what happens.
2. I have no doubt that my inferences about the extreme end of the ranking are wrong, but I wonder by what degree. They very well could be biased, and the ranking does certainly hide a great deal of data, such as the underlying distribution. But I think that it can be appropriate to assume some kind of distribution, just to get the ball rolling. Would you suggest anything in particular?
3. Could you explain this some more, perhaps by an example? The only inference with the standard deviation that I wish to make is to see how far the philosophy undergraduates and graduates place from the general mean. Is that problematic in itself?
My real goal in doing this analysis is to see if someone else with much better data can take what I’ve done and clean it up. The real easy thing, of course, would be all the top twenty programs posting their admitted graduate students’ average GRE scores, broken down by subtests. I do know from what some professors in top-ten programs have told me off the record is that their graduate students average a 1500 total and higher. I’d just like to know how far off my predictions are.
maggi mee
27 February 2009
woot, an update.
couple of points:
i) this analysis is, at best, significantly flawed. The post above says it all, albeit a bit too gently. You are essentially drawing from central statistics to attempt inferences about extreme statistics, which would be iffy at best even if we had a good idea of the joint distribution function. But you have no reason to believe your distributional assumptions (ie conditional normality) are valid! In fact, we know that your distributional assumptions are wrong in ways that will seriously affect your inferences – for example, since GRE scores are upper-bounded, we should (taking your estimates seriously for the moment) expect a significant downward correction in scores for the top ranked schools. I wouldn’t be surprised to see predicted scores >1600 if you used another sample for inference.
ii) I’m not a physics grad student, but I would be surprised if the median GRE math score was <800, and if the average was less than 780, for any of the top 5 (and obviously the same would hold for the top 5 math programs.) Do we have any numbers about this?
iii) you had a previous post about philosophy undergrads that I commented on (wrt your claim being flawed). The issue was whether using LSAT scores to infer ability would downward bias our inferences about math/physics undergrads relative to philosophy undergrads, because of their differing outside options. I think you mentioned that you’d have a follow-up post modifying your analysis – I assume this is the post in question, but it hasn’t really addressed any of the flaws in the previous post (in addition to bringing up new ones).
Lover of Wisdom
27 February 2009
Hi maggi mee:
I’ll address your points a little later. Have to run off now. But just quickly about (iii). This isn’t a response to your comment in the previous post. I’m sorry. I got caught up in other things that I was thinking about, and I just forgot. I’ll try to respond to it ASAP.
maggi mee
27 February 2009
thanks
look forward to it
Lover of Wisdom
27 February 2009
Hi maggie mee:
I’m going to have to answer your questions piece-meal, starting with (ii). I took a look at the US News Physics graduate department rankings and found the following (probably unhelpful) information by tediously looking through all the links, etc..
Out of the top five, only one, Caltech, posted general GRE average scores: of (V) 600, and (Q) 780. This is the average, so we don’t know the median, and the verbal includes internationals. I then looked for some lower ranked schools. 12th place Yale posted an unhelpful range of (V) 310-800, and (Q) 670-800. 15th place UPenn posted averages of (V) 626, and (Q) 780. The verbal average doesn’t include internationals, only native English speakers. 18th place Texas-Austin posted averages for internationals-only of (V) 500 and (Q) 785, for natives of (V) 602 and (Q) 766, and everyone combined for (V) 564 and (Q) 774.
I would say your hunch about the quantitative averages of the top-five physics departments is right. But all I could quickly provide were averages, not medians. So the above is probably useless.
Here is an interesting side note, which might not mean anything: compare the GRE total of the Texas physics native graduate students with the Texas philosophy graduate students, and we get 1368 to 1470. Using the internationals’ higher quantitative score plus the natives’ verbal score will yield 1387 to 1470. Compare the Texas philosophy graduate students to UPenn’s physic graduate students, and we get 1470 to 1406.
maggi mee
27 February 2009
thanks for the numbers.
As you imply, it’s somewhat inappropriate to compare aggregate GRE scores – it is clear that philosophy grad students have higher verbal scores than physics grad students, and the reverse (less clearly) holds for math. However, because of compression at the upper bound for math scores, it’s harder to tell whether the gap in math between phlisophy and physics students is similar to the gap in verbals scores. It is high time for GRE scoring to be rescaled to create separation at the top for math scores.
I eagerly await your next post on the subject.
The Undiscovered Jew
28 February 2009
In a previous post you said linked to a report showing LSAT scores for students in 29 different areas of study.
Do you want to try and incorporate ethnic differences in majors such as philosphy, economics, physics, etc, in order to determine IQ by ethnicity and which ethnic groups prefer which major?
Lover of Wisdom
28 February 2009
Hi TUJ:
I would like to try something of that sort. Do you have any suggestions on how to do that? My hunch tells me the following for ethnic group preference of major: Physics, math, economics, engineering, and other math-heavy disciplines will, unsurprisingly, pull from Caucasian, Jewish, and East Asian groups (I wonder if you would find more Jews in pure math and economics than in the other fields). the humanities will pull much less so from the East Asians, and more from other minorities; but there is a fast growing minority of East Asians in philosophy. In my department, for example, Koreans and Chinese make up roughly 1/4th of the graduate student population. The rest is Jewish and Caucasian. Blacks and hispanics are virtually non-existent. This kind of breakdown is typical for most good philosophy graduate departments.
Lover of Wisdom
28 February 2009
maggi mee:
A quick question about your point (i): You would argue that even if I performed a logistic regression on the data points I have, the result itself would still be highly iffy, correct?
I would still like to do the logistic regression, but I need to buy plug-ins for Excel. Do you happen to know if there any plug-ins for free?
The Undiscovered Jew
28 February 2009
“I would like to try something of that sort. Do you have any suggestions on how to do that?”
I think data based on GRE is sparse. The best place to look would probably be statistics derived from the LSAT.
If you find good data from the LSAT maybe you can convert those scores to correlate with GRE scores and then try to come up with IQ estimates based on ethnic group.
maggi mee
1 March 2009
Hi,
Yes – I wouldn’t consider such an extrapolation to be reliable.
Unfortunately, I have no clue about performing statistical analysis in Excel. if you want to put in the time, I would guess that your school has server-based stat packages like stata (or even matlab) that you can access via command line – but of course that would be a pretty big time investment for you.
Lover of Wisdom
2 March 2009
maggi mee:
I responded to you on my other post.
I’ll check if my school has a server-based stat package, but I certainly don’t what to make that huge time investment.
Socrates
8 August 2009
I don’t know what this means for your findings, but both the University of California, Riverside (ranked 30th) and the University of Wisconsin, Madison (ranked 23rd) have notes on their respective websites about the average GRE score. Riverside puts the average GRE score at around 1300. Madison puts theirs a little higher, at 1325.
I note these schools because they seem to go against the pattern you describe. Madison, a school close to Chicago in its rankings, has its average nearly 130 points below Chicago. I’m not sure what explains this. Any ideas?
http://www.philosophy.ucr.edu/graduate/index.html
http://philosophy.wisc.edu/graduate/faqdoc.html#gre
Lover of Wisdom
9 August 2009
Thanks for bringing that to my attention, Socrates.
Douglas J. Bender
9 August 2009
Socrates,
“I note these schools because they seem to go against the pattern you describe. Madison, a school close to Chicago in its rankings, has its average nearly 130 points below Chicago. I’m not sure what explains this. Any ideas?”
Cheese.
jax
23 August 2009
“I couldn’t find any programs past Texas that has available, ready-made, easily interpretable scores. So we don’t know the average GRE scores of the students in the top-nineteen programs.
But most will surely be better than the 1470 total of Texas. ”
You should have been more cautious about making this inference. This is just not true. I have friends that go to NYU, and there scores are know way near this range. Of course, this is a bias sample. However, the very reasoning is dubious. As you can see with undergraduate statistics, a higher ranked program does not necessarily equate to higher scores, or higher selectivity. You would have to factor in, for example, location, prestige, and etc. Just looking at the us news world report illustrates that higher ranked schools do not necessarily have higher stats. U of chic is significantly easier to get into than others schools of similar rankings. Georgetown is highly selective for its current rank. Of course, you could say these are mere aberrations, but their are other examples that are less pronounced. Also, I think, actually I know, you overestimate the importance of GRE scores. They are not in any stretch of the imagination as important as SAT’s were for college. Some top schools, like john hopkins and MIT say they are optional. They seems to be too many variables absent in your project to draw such correlations, and this is discounting your mathematical speculation.
In any case, while I will take what you said with a grain of salt, thank you for compiling the scores for those select few schools. It was very informative.
ryan
20 October 2010
http://graduate-school.phds.org/rankings/philosophy
This site provides some data that might interest you LOW
ryan
20 October 2010
note that it has data on verbal gre scores for all of the humanities
Lover of Wisdom
21 October 2010
Cool beans. Thanks Ryan.
Jordan Feenstra
7 April 2012
Off the subject, and far past the release date, I have a pertinent question: what accounts for the average (American) test-taker doing better on math (quantitative) than language arts (verbal, analytic)? I’ve never been able to understand why my verbal and analytic scores were so highly regarded, yet my quantitative scores were such a joke. I’ve taken the GRE three times now, and every time I’ve scored in the mid 80th percentile (or maybe I’ve saying that backwards, but hopefully all will understand what I mean to say) on analytic, high 70th percentile on verbal, and, literally, anywhere from the 6th to 16th percentile range for quantitative. People look at me like I’m some sort of challenged wizard when I talk about my scores, and I can’t say I’m necessarily happy with that. Do you, or does anyone, know of any studies, or in any special area of expertise, that could point me to some information on how it is that your average college undergraduate, taking the GRE–without even studying the first time, somehow remembers all of elementary, middle school, and high school mathematics, and I can’t even remember the first step to long division, but, miraculously, can give you the /real/ answer as to why one uses “well” instead of “good” (where appropriate), or where semi-colons and double-dashes are appropriate?
douglasjbender
8 April 2012
Obviously, Jordan, you are an English major. : )
Lover of Wisdom
8 April 2012
Jordan:
You have to remember that positive correlations between verbal, mathematical, and analytical ability appear at the group level. So you have individuals that can be great at one ability (e.g., verbal) and not at the other. You’ll also find other individuals that are great at all and not at any.
There isn’t anything that you can do. It’s just how your cognitive profile is set up.
Ryan
5 May 2012
What do you make the the discrepancy between your estimates and the reported averages?
Ryan
5 May 2012
of*
Anonymous
7 May 2012
douglasjbender: Haha; actually I’m a philosophy major, but the comment makes just as much sense. The odd thing, however, is that my peers in philosophy exemplified the same averages as those reported by ETS for the GRE.
Lover of Wisdom: Thank you (and very true)–I suppose I hadn’t really considered that. However–unless institutions are outright lying, my situation still strikes me as odd since most philosophy departments /that do report/ what their average applicants look like on paper (their GRE scores, undergraduate GPA, etc.) typically report that their average applicants will score around 600-700 on the quantitative portion (and not nearly as high on the verbal or analytic portions)–the same averages reported by ETS.
Ryan: I’m not sure; it could be the case that I spend a lot of time worrying about very specific grammatical cases (e.g., whether, and in what cases, a comma comes before “not…but rather”), but because I worry about these where my peers might not would not mean that I wouldn’t spend that time instead on practicing my arithmetic regarding fractions, for example, or even that they /do/ spend their time doing this rather than solving or practicing obscure or esoteric grammatical discrepancies. So perhaps it is simply the case that I never properly nor committed to long term memory my arithmetic and algebra but rather simply ran through the motions to get the grade (or lack thereof, haha).
BoredOutOf MyMind
30 July 2012
Those GRE projections are way off. If you go to http://graduate-school.phds.org/rankings/philosophy and search under GRE you will see Princeton has the highest average Verbal GRE(they don’t give quant) which was 727 for 2006.
I really would like to see the Total GRE for these various Philosophy programs and not just
verbal simply because I think it would be interesting. I also would be very interested in the
average GRE scores for UC Berkeley’s Group in Logic and the Methodology of Science which is mainly an interdisciplinary program between Math and Philosophy(Computer Science
department is to some degree involved as well but not on the level of the Math and Philosophy departments) and is supposedly quite competitive. I would expect that program
to have a high average GRE score.
Lover of Wisdom
16 August 2012
Bored:
Compare the scores from 2006 to more recent scores at each school. You’ll find remarkable improvements at each school, and the improvements are found (at least with the departments that reveal their current scores) from the bottom of the top 50 to the top. The scores alone from 2003-2006, as indicated by that website, don’t track with the current talent of philosophy graduate departments. You can find a percentage of current graduate students towards the bottom of the top 50 that would match and surpass the talent of the top 5 from just ten years ago.
TucoAndTioFromBB
13 December 2012
Lover of Wisdom
can you direct me to any website that has the more recent GRE scores rather than the ones
for 2006?
or if you don’t know of such a website post those new updated GRE scores for at least some
of the top 50(particular interested in Princeton, Rutgers and NYU)
Lover of Wisdom
26 December 2012
The newest information is only available on the departments’ websites, if they are available at all. Some don’t update their information for years.