<p>Calculated below are the average rankings (over all simulations) of the schools in the Revealed Preference study, December 2005 version. For example, Harvard was outranked by Caltech in 30 percent of trials and Yale in 2 percent, so its average rank is 1.32.</p>
<p>From this and the table of confidence “probabilities” in the article, we can conclude the following about the simulations in the study:</p>
<p>-Harvard is never out of the top 3</p>
<p>-In all simulations, either HYPSMC are (in some order) the top 6, or HYPSM are (in some order) the top 5 and some school other than Caltech is number 6. This reflects the fluky nature of Caltech’s inclusion in the top 6. </p>
<p>-There is some bunching in the top 6, reflecting what are basically ties between schools. The bunching would increase if Caltech were properly deflated and some of its points redistributed. Princeton is seen to be in a tie for the 4-5-6 or possibly 3-4-5-6 spots, and is only nominally in sixth place. Other than Harvard it is hard to say that any of the top 6 really outrank each other in the RP model.</p>
<p>-First tier (1-6) and second tier (7+) are quite well separated. </p>
<p>-Brown ranks at the head of its tier (ie., the next after HYPSM(C) ) at least 34 percent of the time.
-However, there is very little mathematical room for Brown to head its tier more than 50 percent of the time. For instance, if Brown always ranks first or second in its tier, it has to come in second 66 percent of the time. Under plausible scenarios Brown heads its tier a bit less than 50 percent of the time; alternatively, it spends a lot of time at ranks 9-10 or below. Either way there isn’t much of a case for Brown to be the clear champion of its group, and little or nothing to separate it from Columbia.</p>
<p>SCHOOL – (RANK) – AVG.RANK.IN.ALL.SIMULATIONS
Harvard (1st) 1.32
Caltech (2nd) 2.60
Yale (3rd) 3.11
MIT (4th) 4.35
Stanford (5th) 4.62
Princeton (6th) 5.04
Brown (7th) 7.65 [not 9.67 as previously reported]
Columbia (8th) 9.21
Amherst (9th) 10.33
Dartmouth (10th) 10.43
UPenn (12th) 11.64</p>