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<p>Precisely what I was going to say.</p>
<p>Regardless, I think we can give the LACs this. They don’t get much of the spotlight otherwise. =p</p>
<p>I am assuming Barrons does not indeed have a PhD and majored in something practical.</p>
<p>No but many friends went on to PhD’s. I settled for two master’s. Even in my “practical majors” I had several friends who went on for PhD’s in business and are now teaching at major schools. At much higher salaries than most profs make.</p>
<p>Could someone explain the mathematics behind the belief that percentage of students who go on to PhD’s favors smaller institutions?</p>
<p>If 10% of the class at a small place and 10% of the class at a large place get doctorate degrees, then why does this somehow favor the small place? The smaller college will have a less precise estimate of the percentage looking at data from only one year, since a change in plans by one or two students might alter the percentage substantially. But this could alter the percentage up or down. If there is a consistent pattern of higher percentage from a smaller institution, year in and year out, then this is not measurement error.</p>
<p>By this logic, one would expect a higher percent of Amherst than Michigan graduates in the NFL. After all, Amherst is much smaller…</p>
<p>
if you want a ranking based on quantitative results (SATs, etc) this is a really good one:
[College</a> Rankings - Academics - Data](<a href=“http://www.ordoludus.com/6.html]College”>http://www.ordoludus.com/6.html)
if you search around the site, you can customize your preferences on what feature you find more important. but…rankings are really getting annoying.</p>
<p>“If 10% of the class at a small place and 10% of the class at a large place get doctorate degrees …”</p>
<p>That’s not the comparison being made here, and 10% vs. 10% would indeed make it a wash.</p>
<p>The comparison here is that, e.g., the top four or the top seven out of 10 small schools in this list (crunched by interesteddad) have significantly higher percentages than some large more well known schools, e.g., Berkeley at #49. Don’t ignore the self-selection issue; HS students interested in a future PhD may seek out colleges that historically excel in that area.</p>
<p>interesteddad has from time to time posted lists for various disciplines; you can find his posts via Advanced Search with his User Name and Key Words “ipeds” and “phd” and use “Any Date” and then scan the results.</p>
<p>Percentage of PhDs per graduate</p>
<p>Academic field: ALL</p>
<p>PhDs and Doctoral Degrees:
ten years (1994 to 2003) from NSF database</p>
<p>Number of Undergraduates:
ten years (1989 to 1998) from IPEDS database</p>
<p>Note: Does not include colleges with less than 1000 graduates over the ten year period
Note: Includes all NSF doctoral degrees inc. PhD, Divinity, etc., but not M.D. or Law. </p>
<p>1 35.8% California Institute of Technology<br>
2 24.7% Harvey Mudd College
3 21.1% Swarthmore College<br>
4 19.9% Reed College<br>
5 18.3% Massachusetts Institute of Technology<br>
6 16.8% Carleton College<br>
7 15.8% Bryn Mawr College<br>
8 15.7% Oberlin College
9 15.3% University of Chicago<br>
10 14.5% Yale University
11 14.3% Princeton University<br>
12 14.3% Harvard University<br>
13 14.1% Grinnell College<br>
14 13.8% Haverford College<br>
15 13.8% Pomona College<br>
16 13.1% Rice University
17 12.7% Williams College<br>
18 12.4% Amherst College
19 11.4% Stanford University
20 11.3% Kalamazoo College<br>
21 11.0% Wesleyan University
22 10.6% St John’s College (both campus)
23 10.6% Brown University<br>
24 10.4% Wellesley College<br>
25 10.0% Earlham College
26 9.6% Beloit College<br>
27 9.5% Lawrence University
28 9.3% Macalester College<br>
29 9.0% Cornell University, All Campuses<br>
30 9.0% Bowdoin College
31 8.9% Mount Holyoke College<br>
32 8.9% Smith College<br>
33 8.8% Vassar College<br>
34 8.7% Case Western Reserve University
35 8.7% Johns Hopkins University<br>
36 8.7% St Olaf College
37 8.7% Hendrix College
38 8.6% Hampshire College<br>
39 8.5% Trinity University<br>
40 8.5% Knox College<br>
41 8.5% Duke University
42 8.4% Occidental College<br>
43 8.3% University of Rochester
44 8.3% College of Wooster<br>
45 8.3% Barnard College
46 8.2% Bennington College<br>
47 8.1% Columbia University
48 8.0% Whitman College
49 7.9% University of California-Berkeley<br>
50 7.9% College of William and Mary
51 7.8% Carnegie Mellon University<br>
52 7.8% New Mexico Institute of Mining and Technology<br>
53 7.7% Brandeis University
54 7.6% Dartmouth College<br>
55 7.5% Wabash College<br>
56 7.5% Bates College<br>
57 7.5% Davidson College<br>
58 7.2% Rensselaer Polytechnic Institute<br>
59 7.2% Franklin and Marshall College<br>
60 7.1% Fisk University</p>
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<p>I’d be happy to explain. Consider a two schools - one called Tiny College and another called Mondo State U. Tiny graduates a total 10 students a year in one specialized field. Mondo graduates 10,000 every year in many fields. So if Tiny has on average two motivated grads who go on to get a Ph.D. they will have 20% Ph.D. production rate. Mondo would have to produce 2,000 Ph.D.s every year to get the same percentage. So what’s the easier task to pull off - producing two smart, motivated students or producing a thousand times that many?</p>
<p>Percentage or per capita analyses are a great way for very small countries, schools, religions, companies, or other small organizations to come up with a number to make them feel good about themselves. But they mask important factors about the true picture. At the extremes they become a contest to see which is smallest institution that can produce just one.</p>
<p>Here’s a real life example: at the 1996 Olympic games in Atlanta the USA, being the home team, did unusually well and won 101 medals. Tonga on the other hand won only one. However, if you look at a percentage or per capita analysis you find that population-wise Tonga won medals at a rate 25 times greater than that of the US. So which is the greater sporting nation? Should athletes hoping to win at Olympics forsake their modern facilities and coaches in the US and go train in Tonga? Probably not. What has really happened is that this analysis favors very small countries over big ones. The same thing can happen with schools.</p>
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<p>Idad is so obsessed with this sort of data - and the fact that, surprise, it appears to show (as do these Reed lists) a certain small Pennsylvania college in a flattering light - that it’s nearly impossible to avoid the very strong suspicion that the OP is simply Idad posting under another name. (Why - who knows?)</p>
<p>Oh, well - carry on.</p>
<p>“Here’s a real life example: at the 1996 Olympic games in Atlanta …”</p>
<p>To guard against such a statistical fluke, only schools with at least 1000 graduates over 10 years are included in these PhD percentages.</p>
<p>Bah. Berkeley can get the spotlight. The big Us can get the spotlight. Good for you guys! Bask in it! Berkeley is more famous. Berkeley is more renowned. Berkeley is more prestigious, and Berkeley is BETTER. (Maybe you guys should create a slogan - “Berkeley - it’s just Better.” =p) Ok then. </p>
<p>We like our LACs, we know we’re getting a good, solid, and to me the best education, and we think it’s a better fit than being in a big university. One does not go into an LAC for its ‘global’ prestige or name. It has regional, or selective prestige, or whatever you call it. (Otherwise, I guess all us folks are going to have to work the shrinking fields of corn eh without any other job offers)</p>
<p>That said, I see the mathematical logic behind this thinking. Is there a threshold of students, beyond which will percentage figures actually become meaningful?</p>
<p>To barrons: PhD in business??? Which uni offers that?</p>
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<p>Well, if you have a thousand times as many students, faculty members, labs, etc, then it should be about equally difficult. If the larger institution has some inherent advantages, perhaps simply size, or being “better known”, perhaps better resources, then it should be easier.</p>
<p>The athlete who wants to medal in the sport (or sports?) in which Tonga excels might be better off training there. Of course, if they are better than the US at that sport, then it might be more difficult to make that team. Which is the better sporting nation? Depends on how you define it. Might have nothing to do with the outcome of the Olympics. Which nation has more fit citizens? Before adjusting for population age, probably Tonga. Which has more professional athletes? Certainly US.</p>
<p>I am not debating the importance of prominence of universities, that is done to death on CC. I really am asking a mathematical question. Do lawyers who try a small number of cases consistently win a higher proportion of them? Do doctors who do a small number of operations consistently have higher success rates? Do pitchers who throw a small number of innings consistently have better ERA’s?
In other words, how does having a small number of cases produce higher success rates?</p>
<p>If this effect holds for PhD’s, should the smaller institutions also produce a higher percentage of MDs, JDs, MBA’s, NBA players, members of the National Academy of Sciences, the Supreme Court, or the Hall of Fame? A higher percentage of CEO’s and masters of the universe financiers? Or is this effect unique to PhD’s? If the latter, it becomes an even more challenging mathematical problem. If the former, then it is starting to sound like an argument in favor of simple smallness. </p>
<p>But smallness leaves lots unexplained. There are many small colleges that never appear high on these lists, and it is the same group of LAC’s that top the lists year after year. They are not the smallest LAC’s, and there are some small universities with excellent students (like Dartmouth) that are not consistently higher than other universities that are larger. </p>
<p>Does smallness only favor colleges when they are below a certain enrollment? Caltech is small enough, but Dartmouth is too large? </p>
<p>But Carleton is larger than Amherst. Yet year after year Carleton produces a higher percentage of PhD’s. By the small-favors-PhD-production argument, Amherst should be higher. </p>
<p>If smallness only works within a certain size range, why? </p>
<p>So, again, a mathematical question: “How does smallness bias in favor of high rates of PhD’s?”</p>
<p>I think coureur’s point is that even with a college size of 1600 students versus one with 16000, if both send 10 percent of their student populations to go on an achieve PhDs, it does not necessarily follow that both schools are of an “equal” caliber academically. The small college with the population of 1600 needs only to send 160 students to grad school to meet that benchmark (10 percent). The big U, otoh, has to send 1600 students to grad school, which may or may not be a bigger/smaller achievement, but is evidence that at the end of the day, this translates to a greater presence of big U grads in grad schools, and results in greater influence, networks and etc.</p>
<p>Remember that there is also not accounting for the quality of PhD programs that students go to, and also that the population in small colleges are more self-selective in the direction of academia.</p>
<p>Since networks are more important than real education, sounds like Mondo U has an edge.</p>
<p>vossron- to be honest, I’d rather come from a school with a department that doesn’t have a bunch of students applying for PhD… competition… competition… but at the same time, it is annoying not to have anyone to freak out with over the graduate school applications.</p>
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<p>I don’t know about doctors and lawyers, but keeping with the example of the tiny countries winning the Olympic medal percentage, that almost always holds up. The percentage or per capita winner is pretty much always a tiny country winning just one or two medals. To extend the example given, in 1996 the top four countries by percentage were all tiny countries. Australia was the first country of any size on the list - in 5th place.</p>
<p>Now using these stats to compare Australia to US is legitimate: big compared to big. But to compare Tonga or those other tiny countries to US or Russia or Germany is bogus. It’s apples and oranges. You just watch, at the the Beijing Olympics this year, the medal winner on a per capita basis will be a tiny country</p>
<p>As I said, at the extremes, a percentage comparison becomes a contest to find the tiniest country that can win just one medal, or perhaps the tiniest college that can produce just one PhD.</p>
<p>coureur, but in the case of overall PhD production, that simply isn’t true. Unless you are talking about a truly tiny school (a la Deep Springs), even the small schools have a big enough sample size of graduates for the results to mean something. We’re not talking about 1 of the 5 chemistry graduates last year going on to get a PhD, and producing a 20% rate; we’re talking about 1000 of the 5000 graduates in all fields over the past 10 years. If the effect were due to one or two individuals (and thus chance), then, though you would expect small colleges at the top, it would be very unlikely to see the same small colleges at the top year after year. But we do see the same colleges at the top of PhD production year after year, so it’s not a fluke - students at Caltech are simply more likely to get PhDs than students at Berkeley.
One student can’t bias these results, even at small colleges, the way one athlete can in the Olympics example. That makes the Olympics example a very flawed analogy.</p>
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<p>Is it always the SAME tiny country? If so, then that tiny country really does produce world class athletes at a high per capita rate. Maybe a Nordic country where, until global warming, everyone would cross country ski to school everyday. The great African running nations are not that small, but perhaps the same phenomenon. </p>
<p>If it is a different tiny country each time, then it is sampling error, and not particularly interesting.</p>
<p>The argument here seems to be that even if it is the SAME small colleges that produce high per capita PhD rates year after year, this is somehow misleading because smallness alone leads to high rates. </p>
<p>I am just trying to understand how this works, and whether the same mechanism applies to professional degrees or any of these other career metrics. Is it something unique to PhD’s? If so, why? </p>
<p>Why does smallness lead to high rates for a handful of colleges, but apparently not apply to small colleges overall?</p>
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<p>I think it’s more that Berkeley simply has more students who don’t care about getting a PhD. But it also has a lot of students who do want one, and who do get one.</p>
<p>Can you really normalize for size differences by simply multiplying by the %? I’m not sure it ever works that way, logically.</p>
<p>afan makes a good point: it’s the same schools, over many decades, that have a track record of sending students on to Ph.D. programs. BTW, I don’t think that it’s good to infer that a school that doesn’t send many graduates on to Ph.Ds is somehow inferior to schools that do. Many schools simply have a culture of placing government and econ grads in the private sector through strong networks, sending their science majors on to do MDs, placing many grads in law school, etc…</p>
<p>PhD in business???–only most of them. From Harvard on down. </p>
<p>[Programs</a> - HBS Doctoral Programs](<a href=“http://www.hbs.edu/doctoral/programs/]Programs”>PhD Programs - Doctoral - Harvard Business School)</p>
<p>[Wharton</a> Doctoral Programs: Finance](<a href=“http://www.wharton.upenn.edu/doctoral/programs/finance/]Wharton”>http://www.wharton.upenn.edu/doctoral/programs/finance/)</p>