<p>I recently completed an analysis of the USNWR Top 50 ranked colleges. I sorted the schools by the size of their graduate enrollments and then looked at the PA scores of the various colleges. </p>
<p>Of the 25 colleges that had the highest number of graduate students, only 3 failed to receive a PA score of 4.0 or higher. </p>
<p>Of the 25 colleges that had the fewest number of graduate students, 15 failed to receive a PA score of 4.0 or higher.</p>
<p>Thus, Top 50 USNWR universities that had above the median number of graduate students were five times more likely to score at the 4.0 level or higher. </p>
<p>Here is the full data set (graduate school numbers taken from collegeboard.com):</p>
<p>Rank in absolute number of grad students, # of grad students, PA score, college</p>
<p>1 , 17740 , 4.6 Columbia
2 , 16477 , 3.8 NYU
3 , 14526 , 4.5 U Michigan
4 , 13950 , 4 USC
5 , 11439 , 3.6 U Florida
6 , 11101 , 4.1 U Texas
7 , 10901 , 4.2 UCLA
8 , 10285 , 4.9 Stanford
9 , 10211 , 4 U Illinois
10 , 10010 , 4.9 Harvard
11 , 9886 , 3.9 U Washington
12 , 9007 , 4.8 UC Berkeley
13 , 8832 , 4.1 U Wisconsin
14 , 8254 , 4.2 U North Carolina
15 , 7824 , 4.3 Northwestern
16 , 7693 , 4.3 U Virginia
17 , 6712 , 4.5 U Penn
18 , 6180 , 3.8 Penn State
19 , 6126 , 4.9 MIT
20 , 5834 , 4.6 U Chicago
21 , 5575 , 4 Georgia Tech
22 , 5350 , 4.4 Duke
23 , 5181 , 4.6 Cornell
24 , 4852 , 4.8 Yale
25 , 4715 , 4.1 Wash U
26 , 4589 , 3.8 UCSD
27 , 4490 , 4 Georgetown
28 , 4451 , 4.2 Carnegie Mellon
29 , 4088 , 3.6 UC Irvine
30 , 4080 , 4 Emory
31 , 4072 , 3.8 UC Davis
32 , 3928 , 3.5 Case Western
33 , 3925 , 4 Vanderbilt
34 , 3842 , 3.6 Boston Coll
35 , 3539 , 3.4 U Rochester
36 , 2977 , 3.6 Tufts
37 , 2870 , 3.5 UC Santa Barbara
38 , 2646 , 3.9 Notre Dame
39 , 2305 , 3.3 Tulane
40 , 2240 , 3.5 Rensselaer
41 , 2115 , 3.2 Lehigh
42 , 2070 , 4 Rice
43 , 2010 , 4.9 Princeton
44 , 2009 , 3.6 Brandeis
45 , 1756 , 4.4 Brown
46 , 1646 , 4.6 Johns Hopkins
47 , 1393 , 3.5 Wake Forest
48 , 1360 , 3.7 W&M
49 , 1352 , 4.3 Dartmouth
50 , 1222 , 4.7 Caltech</p>