THE THREE RANKINGS USED 

 
ACADEMIC RANKING OF WORLD UNIVERSITIES 
Institute of Higher Education, Shanghai Jiao Tong University, 2004.

This ranking was compiled using "several indicators of academic or research performance, including alumni and staff winning Nobel Prizes and Fields Medals, highly cited researchers, articles published in Nature and Science, articles in Science Citation Index-expanded and Social Science Citation Index, and academic performance with respect to the size of an institution." A Further Analysis about This Ranking has been given by Da Hsuan Feng.  
WORLD UNIVERSITY RANKINGS
[
London] Times Higher Education Supplement (THES), 2004.
This ranking was compiled "with the help of findings from a survey for the THES of 1,300 academics in 88 countries. They were asked to name the best institutions in the fields that they felt knowledgeable about." 
TOP AMERICAN RESEARCH UNIVERSITIES,
The Center at the University of Florida, 2004.
This website is not a ranking but a collection of data for ranking research universities. Our ranking was compiled solely from data provided by this website with the exception of SAT and ACT scores obtained from US News and World Report.

METHODOLOGY USED

 
We use a procedure involving z-scores (the z-score of a number in a list is the distance, in standard deviations, between this number and the average of the list) and a linear transformation to make lists (usually given as columns) of numbers (oftentimes points awarded to universities) more compatible by forcing the average of the largest twenty-five numbers in each list to be 75 and the largest number in each list to be 100; our choice of the numbers 75 and 100 was arbitrary but perhaps based on aesthetic considerations. In general, our procedure will change the numbers on a list but will not change the ordering (for example, if University A is ranked seventh on a survey, after applying our procedure, University A will still be ranked seventh).  We did this procedure on each of the three rankings used, on the sum of these three rankings, and on the nine columns of data collected in the Top American Research Universities. We spare you the calculations. 

EXPLANATION OF SYMBOLS USED
 
 ABBREVISIONS
          USED 
                     EXPRESSION
     
            AR    Academic Ranking of World Universities
             LT    World University Rankings (London Times)  
            Rev    Our revision of the points awarded
            SC    Point total on our ranking
            UF    Top American Research Universities


 
INFORMATION ABOUT THE RANKINGS USED
 
     AR        AR
 Revised
   LT  

    LT
Revised

   UF       UF
Revised
                         
 Number of Universities Ranked       500        200          50        50
 Number of Universities
 Receiving Points  
    100        200                50
 Number of USA Universities
 (excluding medical schools)
 Receiving Points
     48        48     61        61           50
 Points Received by USA
 University Ranked One (Harvard)
   100       100   1000      100          100 
 Points Received by  USA
 University Ranked Two 
   77.2        87.5     880      95.0         91.8
 Points Received by USA
 University Ranked 48
   25.1      58.9    131      64.0         53.8 
 Points Received by Lowest
 Scoring University
   25.1      58.9    103      61.8         49.1
 The Average of the Twenty-five
 highest Ranking USA Universities
   54.5      75.0    413      75.0          75.0
 Standard Deviation of the 
 Twenty-five Highest Ranking 
 USA Universities
   15.3      8.42    238      10.1         8.01

 

OUR RANKING OF AMERICA'S
BEST RESEARCH UNIVERSITIES

 
In the first three columns after UNIVERSITY, we give the position that the top-scoring universities were ranked by each of our three rankings. In the next three columns, this table gives the points the university received from each of our three rankings (as always, we modify each of these numbers so that the average of the twenty-five highest numbers in this column is 75 and the highest score of 100. For example, on the World University Rankings (London Times) ranking, denoted by LT, we see that MIT ranked fourth and received, by our calculation, 91.0 points. The last column (SCORE) gives the number that determines our graduate school rank. The first step in calculating this last column SCORE  is to add the numbers in the three preceding columns; this sum is slightly modified so that the average of the twenty-five highest numbers in this last column is 75 and the highest score of 100.
   

UNIVERSITY

AR

 

LT

 

UF

 

 

AR

 

LT

 

UF

 

SCORE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

Harvard

1.0

 

1

 

1

 

 

100

 

100

 

100

 

100

2

 

Stanford

2.0

 

5

 

2

 

 

87.5

 

86.7

 

91.8

 

88.8

3

 

UC Berkeley

3.0

 

2

 

4

 

 

85.8

 

94.9

 

81.0

 

87.4

4

 

MIT

4.0

 

3

 

5

 

 

84.8

 

91.0

 

79.9

 

85.4

5

 

Cal Tech

5.0

 

4

 

21

 

 

83.0

 

88.9

 

68.3

 

80.2

6

 

Yale

9.0

 

6

 

6

 

 

77.3

 

82.2

 

78.4

 

79.5

7

 

Princeton

6.0

 

7

 

16

 

 

80.0

 

81.1

 

71.5

 

77.8

8

 

Columbia

7.0

 

10

 

10

 

 

78.7

 

73.8

 

76.4

 

76.5

9

 

Johns Hopkins

17.0

 

13

 

3

 

 

71.2

 

71.5

 

82.5

 

75.3

10

 

Cornell

10.0

 

11

 

11

 

 

75.6

 

72.2

 

75.8

 

74.8

11

 

U Chicago

8.0

 

8

 

22

 

 

78.3

 

76.3

 

68.2

 

74.5

12

 

UCLA

13.0

 

14

 

7

 

 

73.4

 

70.9

 

77.9

 

74.3

13

 

U Pennsylvania

12.0

 

15

 

8

 

 

73.5

 

70.5

 

77.0

 

73.9

14

 

U Michigan

15.0

 

16

 

12

 

 

72.2

 

69.9

 

75.7

 

72.9

15

 

U Wisconsin

14.0

 

24

 

9

 

 

72.5

 

65.2

 

77.0

 

71.9

16

 

UC San Diego

11.0

 

12

 

20

 

 

74.6

 

71.5

 

68.4

 

71.8

17

 

U Washington 

16.0

 

27

 

13

 

 

72.0

 

64.9

 

73.0

 

70.3

18

 

U Texas

27.0

 

9

 

18

 

 

64.2

 

75.3

 

69.7

 

70.0

19

 

U Illinois

18.0

 

17

 

17

 

 

68.9

 

69.4

 

70.5

 

69.9

20

 

Duke

21.0

 

20

 

14

 

 

66.4

 

66.4

 

72.2

 

68.7

21

 

Northwestern

20.0

 

26

 

19

 

 

66.8

 

65.1

 

69.1

 

67.3

22

 

Washington U

19.0

 

39

 

23

 

 

68.8

 

63.8

 

68.0

 

67.2

23

 

U Southern Calif

31.5

 

55

 

15

 

 

62.9

 

62.1

 

72.0

 

66.0

24

 

U Minnesota

23.0

 

31

 

27

 

 

66.1

 

64.6

 

64.5

 

65.4

25

 

New York U

22.0

 

29

 

29

 

 

66.3

 

64.8

 

63.7

 

65.3

26

 

Pennsylvania SU

29.0

 

44

 

26

 

 

63.5

 

63.3

 

64.6

 

64.1

27

 

U North Carolina

35.0

 

42

 

25

 

 

62.2

 

63.5

 

65.3

 

64.0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

28

 

Vanderbilt

26.0

 

50

 

33

 

 

64.4

 

62.7

 

60.8

 

63.0

29

 

U Maryland

36.0

 

45

 

31

 

 

62.2

 

63.2

 

62.3

 

62.9

30

 

U Colorado

24.0

 

38

 

44

 

 

65.8

 

63.9

 

56.3

 

62.4

31

 

UC Davis

28.0

 

56

 

36

 

 

63.5

 

62.1

 

60.2

 

62.3

32

 

Boston U

46.0

 

28

 

34

 

 

59.5

 

64.9

 

60.5

 

62.0

33

 

Brown U

45.0

 

22

 

40

 

 

59.8

 

65.4

 

58.4

 

61.6

34

 

UC Santa Barbara

25.0

 

25

 

48

 

 

65.4

 

65.1

 

53.8

 

61.8

35

 

Purdue

40.0

 

21

 

42

 

 

60.8

 

65.7

 

57.3

 

61.6

36

 

U Arizona

43.0

 

57

 

39

 

 

60.5

 

62.1

 

58.8

 

60.9

37

 

Rice

42.0

 

49

 

41

 

 

60.6

 

62.9

 

57.8

 

60.8

38

 

Michigan State

44.0

 

41

 

43

 

 

59.9

 

63.6

 

56.8

 

60.5

 
Why stop at 38? Thirty-eight universities did well enough to receive a score on all three of the rankings. By our calculations, are these 38 the top thirty-eight? This is not so clear but we can say that, by our calculations, the top twenty-seven are the top twenty-seven.
Is it possible that a university that did not receive a score by one or more of the three rankings we used is in the top thirty-eight? A university that did not receive a score from one or more of the three rankings we used could rank, by our calculations, as high as twenty-eighth.  
How is this possible? As we can see from the preceding table, World University Rankings (London Times) awarded 61.8 points to its  lowest scoring  university. Thus a USA university not ranked by World University Rankings (London Times) could have received as many as 61.7 points. Now the University of Florida received 61.2 points from Academic Ranking of World Universities (AR) and 65.6 points from the Top American Research Universities (UF). The University of Florida point total from World University Rankings was not given but conceivable could have been as high as 61.7. With these 61.7 points, the University of Florida could have a score on our ranking of 63.7. This would put the University of Florida in the twenty-eighth position; note that the University of Florida could have scored much less than 61.7 from World University Rankings. In twenty-seventh position is the University of North Carolina with 64.0. No university that received points from less than three of our rankings couldd score more than 63.7 points: ipso facto, no university that received points from less than three of our rankings could be in our top twenty-seven. Thus we can state our rankings of the top twenty-seven research universities is unambiguous (this is not the same as correct).  


 

HOW THIS WEBSITE'S RANKING OF
THE TWENTY-SEVEN BEST AMERICAN
RESEARCH UNIVERSITIES COMPARES
WITH THE THREE GIVEN RANKINGS
AND COMMENTS

 
       Agree    Differ
 by 1 
   Differ
 by 2
  Differ
 by 3
  Differ
 by 4
  Differ
  by 5
  Differ
  by 
6-7
  Differ
  by
8-9   
   Larger 
  Differ-
ences
                                       
 Academic Ranking of
 World Universities
        6     11      0      5      0      1      0     4    None
 World University 
 Rankings
 (London Times)
        4      5      4      2      3      1     1     2    10,15,
 17, 18,
    22
 Top American
 Research Universities
        5      4      5      1      3      2     3     2    11,16
The Academic Ranking of World Universities differs from this website's ranking by eight or nine (never by more) for four universities. In all of these four cases, the Academic Ranking of World Universities  gives a less favorable ranking. The four universities are Johns Hopkins University, the University of Texas, the University of Southern California, and the University of North Carolina. 
  
The World University Rankings (London Times) differs from this website's ranking by eight or more for seven universities. In six of these cases, the World University Rankings (London Times) gives a less favorable ranking. These six universities are the University of Wisconsin, the University of Washington, Washington University (St. Louis), the University of Southern California, the Pennsylvania State University, and the University of North Carolina. A more favorable ranking is given to the University of Texas.
 
The Top American Research Universities differs from this website's ranking by eight or more for four universities. In three of these cases, the Top American Research Universities gives a less favorable ranking. These three universities are the California Institute of Technology, Princeton University, and the University of Chicago. A more favorable ranking is given to the University of Southern California.

Note that there is wide disagreement about the University of Southern California (given rankings of  31.5, 55, and 15); our website compromised and gave USC a ranking of 23). There was also wide disagreement about the University of Texas (given rankings of 27, 9, and 18); our website compromised and gave the University of Texas a ranking of 18). In addition, there was also wide disagreement about the University of North Carolinas (given rankings of  35, 42, and 25); our website compromised and gave the University of North Carolina a ranking of 27. 


COMMENTS ON OUR RANKING OF
AMERICA'S BEST RESEARCH UNIVERSITIES

 
Most surprising ranking. The World University Rankings (London Times) ranked the University of Massachusetts number 19 among American research universities. None of our other two rankings made mention of the University of Massachusetts. 
Universities with the most consistent rankings. Our three rankings thought Harvard was number one; we ranked Harvard number one. Our three rankings thought Cornell was number 10 or number 11; we ranked Cornell number 10.  Our three rankings thought the University of Illinois was number 17 or 18; we ranked it number 19.  
Number of branches of the University of California in the top forty-one. Five. Berkeley (3), Los Angeles (12), San Diego (16), Davis (31-35), and Santa Barbara (34-41). Academic Ranking of World Universities ranked Irvine number 34 and World University Rankings (London Times) ranked Santa Cruz 54. Let us not forget UCSF, the San Francisco branch of the University of California; this branch is primarily a medical school. Academic Ranking of World Universities ranked UCSF number 14, World University Rankings (London Times) ranked number 11. The Top American Research Universities would have ranked UCSF in the top thirty (we did not run the numbers for medical schools). 
The ranking that agrees with this website's ranking of the top five (in the same order). The Academic Ranking of World Universities 
Number of branches of the University of California in the top forty-one. Five. Berkeley (3), Los Angeles (12), San Diego (16), Davis (31-35), and Santa Barbara (34-41). Academic Ranking of World Universities ranked Irvine number 34 and World University Rankings (London Times) ranked Santa Cruz 54. Let us not forget UCSF, the San Francisco branch of the University of California; this branch is primarily a medical school. Academic Ranking of World Universities ranked UCSF number 14, World University Rankings (London Times) ranked number 11. The Top American Research Universities would have ranked UCSF in the top thirty (we did not run the numbers for medical schools). 
The ranking that agrees with this website's ranking of the top twenty-three (although not necessarily in their order). This website and the Top American Research Universities agree on the top one and the top twenty-three. This website and the Academic Ranking of World Universities agree on the top one, the top five, and the top seventeen. [London] Times Higher Education Supplement (THES) and this website agree on the top one, the top five, and the top seven.  
The research university that ranks number one. Who's Number One? There seems to be no doubt that Harvard is number one. 
Research university that ranks number two. Who's Number Two? It is reasonably clear, especially looking at the data given by The Center at the University of Florida, that a medical school taking in big bucks, as many do, will greatly help the ranking of the corresponding university on The Center at the University of Florida ranking. If the Stanford University School of Medicine were ignored, the University of California, Berkeley, which has no medical school, would probably be number two.  
The author's opinion of the top eight. I agree that Harvard is number one. I agree that Cal Tech, MIT, Stanford, and UC Berkeley are numbers two through five in some order. I also agree that Yale and Princeton are number six and number seven in some order. I believe that Columbia may be number eight. 


 

THE RESEARCH UNIVERSITIES THAT
SCORED ON EXACTLY TWO OF
THE THREE RANKINGS USED

 

 

UNIVERSITY

AR

 

LT

 

UF

 

 

 

 

 

 

 

 

Carnegie Mellon

37.0

 

18

 

28

 

U Virginia

 

 

43

 

 

 

U Rochester

33.0

 

32

 

 

 

U Florida

39.0

 

 

 

24

 

Case Western Reserve

38.0

 

33

 

 

 

Rutgers

30.0

 

59

 

 

 

Emory

 

 

52

 

32

 

Texas A and M

 

 

36

 

35

 

Ohio State

41.0

 

 

 

30

 

U Pittsburgh

31.5

 

 

 

37

 

Tufts

48.0

 

35

 

 

 

U Utah

47.0

 

48

 

 

 

World University Rankings (London Times) ranks The University of Alabama 34. From what I have read, including the University of Alabama's website, University of Alabama refers exclusively to the Tuscaloosa campus. The Top American Research Universities ranks the University of Alabama - Birmingham 49; there is a medical school on this campus.  





THE RESEARCH UNIVERSITIES THAT
SCORED ON EXACTLY ONE OF
THE THREE RANKINGS USED

 

UNIVERSITY

AR

 

LT

 

UF

 

 

 

 

 

 

 

 

U Massachussetts

 

 

19

 

 

 

Georgia Institute

 

 

23

 

 

 

U Iowa

 

 

37

 

 

 

Brandeis

 

 

40

 

 

 

SUNY Stoney Brook

 

 

46

 

 

 

Georgetown

 

 

51

 

 

 

UC Irvine

 

 

34

 

 

 

Indiana

 

 

53

 

 

 

UC Santa Cruz

 

 

54

 

 

 

Tulane

 

 

58

 

 

 

VPI

 

 

60

 

 

 

Rensselaer

 

 

61

 

 

 

U Georgia

 

 

 

 

45

 

U Notre Dame

 

 

 

 

46

 

U Arkansas

 

 

 

 

50

 

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