Correlation Studies of Academic Excellence and Big‑Time Athletics

(A corrected version of an article published in International Review of Sport Sociology, 3(11), Warsaw, Poland 1976, pp.57-69.)

L. David Roper (roperld@vt.edu) and Keith Snow (U.S.A.)

Abstract

Given particular measures of undergraduate excellence (U), graduate-school excellence (G), football excellence (F) and basketball excellence (B), we rank American universities in all four categories. Then the six correlation coefficients for all six pairs of the four categories are calculated: CUG=+0.033±0.053, CUF= –0.418±0.046,    CUB= –0.496±0.033, CGF= –0.540±0.032, CGB= –0.556±0.038, CFB= –0.453±0.030. Several criticisms of our study and suggestions for future studies are made. Caution is particularly given that CUG may be considerably higher than the number we obtain.

I.       Introduction

 

One occasionally hears the following justifications for the massive financial and sociological resources that are expended by universities and colleges for big‑time (i.e., highly visible) athletics:

(1) It attracts good students to the school, directly and indirectly.

(2) It attracts financial contributions (private and public) which enable programs of academic excellence.

 

It is interesting to consider whether these are the real reasons for big‑time athletics being in institutions of higher education, or whether there are other reasons along with or instead of these reasons.

To the author’s knowledge no systematic study of the veracity of these justifications has been published. The study reported here is a first attempt to do so. There are many faults with the approach adopted here. which we shall discuss later. Nevertheless, we believe that our results are valid, and we encourage others to refine or expand on our methods. Indeed, we offer aid to those who wish to do so.

In the next section we define “big‑time athletics” and specify our measure of it. In Section III we indicate our measures of graduate and undergraduate academic excellence. Section IV contains the mathematical definition of the correlation coefficient; this section may be skipped by readers who are not mathematically inclined. Finally, Section V gives our conclusions, some criticism of our approach and suggestions for further work.

II.      Big Time Athletics

 

We define “big‑time” college and university athletics to be varsity sports that receive the major attention of the news media. Occasional casual glances at newspapers will convince one that men’s football (American, not soccer) and basketball are by far the front runners. Therefore, we further restrict our definition of big‑time athletics to men’s football and basketball. Table 1 lists the Associated Press Polls and the major bowl games and tournaments winners for football and basketball for the years 1968 through 1972. From Table 1 we calculate the “score” listed in Table 2 by moving an entry up one rank when it won a major bowl game or tournament and then adding the ranks for all five years for that entry and dividing by five. (A team that was ranked in one or more years but was unranked in another year was optimistically assumed to be in the twenty-first rank in the unranked year.) An unranked entry that won a bowl game or tournament was assumed to be ranked twentieth for that year. The football and basketball rankings given in Tables 2 and 5 were then obtained by ordering the entries according to decreasing score as given in Table 2.

Table 1

Associated Press Polls and Major Bowl Game and Tournament Winners

FOOTBALL

1968

1969

1970

1971

1972

1. Ohio State

1. Texas

1. Nebraska

1. Nebraska

1. Southern California

2. Penn. State

2. Pennsylvania State

2. Notre Dame

2. Oklahoma

2. Oklahoma

3. Texas

3. Southern California

3. Texas

3. Colorado

3. Texas

4. Southern California

4. Ohio State

4. Tennessee

4. Alabama

4. Nebraska

5. Notre Dame

5. Notre Dame

5. Ohio State

5. Pennsylvania State

5. Auburn

6. Arkansas

6. Missouri

6. Arizona State

6. Michigan

6. Michigan

7. Kansas

7. Arkansas

7. Louisiana State

7. Georgia

7. Alabama

8. Georgia

8. Mississippi

8. Stanford

8. Arizona State

8. Tennessee

9. Missouri

9. Michigan

9. Michigan

9. Tennessee

9. Ohio State

10. Purdue

10. Louisiana State

10. Auburn

10. Stanford

10. Pennsylvania State

11. Oklahoma

11. Nebraska

11. Arkansas

11. Louisiana State

11. Louisiana State

12. Michigan

12. Houston

12. Toledo

12. Auburn

12. North Carolina

13. Tennessee

13. UCLA

13. Georgia Tech

13. Notre Dame

13. Arizona State

14. Southern Methodist

14. Florida

14. Dartmouth

14. Toledo

14. Notre Dame

15. Oregon State

15. Tennessee

15. Southern California

15. Mississippi

15. UCLA

16. Auburn

16. Colorado

16. Air Force

16. Arkansas

16. Colorado

17. Alabama

17. West Virginia

17. Tulane

17. Houston

17. North Carolina St.

18. Houston

18. Purdue

18. Pennsylvania State

18. Texas

18. Louisville

19. Louisiana State

19. Stanford

19. Houston

19. Washington (Seattle)

19. Washington State

20. Ohio

20. Auburn

20. Oklahoma (tie)

20. Southern California

20. Georgia Tech

 

 

20. Mississippi (tie)

 

 

[Roanoke Times

Sat. 4 Jan. 1969]

[Roanoke Times

Sun. 4 Jan. 1970]

Roanoke Times

Wed. 6 Jan. 1971]

[Roanoke Times

Tues. 4 Jan 1972]

[Roanoke Times

Thurs. 4 Jan 1973]

Bowl Winners:

Cotton-Texas

Cotton-Texas

Cotton-Notre Dame

Cotton-Pennsylvania State

Cotton-Texas

Sugar-Arkansas

Sugar-Mississippi

Sugar-Tennessee

Sugar-Oklahoma

Sugar-Oklahoma

Rose-Ohio State

Rose-Southern California

Rose-Stanford

Rose-Stanford

Rose-Southern Calif.

Orange-Pennsylvania State

Orange-Pennsylvania State

Orange-Nebraska

Orange-Nebraska

Orange-Nebraska (forfeited)

[Roanoke Times

Thurs. 2 Jan 1969]

[Roanoke Times

Fri. 2 Jan 1970]

[Roanoke Times

Sat. 2 Jan 1971]

[Roanoke Times

Sun. 2 Jan 1942]

[Roanoke Times

Tues. 2 Jan 1973]

BASKETBALL

1968

1969

1970

1971

1972

1. UCLA

1. Kentucky

1. UCLA

1. UCLA

1. UCLA

2. LaSalle

2. UCLA

2. Marquette

2. Pennsylvania

2. North Carolina St.

3. Santa Clara

3. St. Bonaventure

3. Pennsylvania

3. North Carolina

3. Minnesota

4. North Carolina

4. Jacksonville

4. Kansas

4. Louisville

4. Long Beach State

5. Davidson

5. New Mexico State

5.Southern California

5. Long Beach State

5. Providence

6. Purdue

6. South Carolina

6.South Carolina

6. South Carolina

6. Marquette

7. Kentucky

7. Iowa

7.Western Kentucky

7. Marquette

7. Houston

8. St. John’s, NY

8. Marquette

8. Kentucky

8. Brigham Young

8. North Carolina

9. Duquesne

9. Notre Dame

9. Fordham

9. Southwestern Louisiana

9. Indiana

10. Villanova

10. North Carolina State

10. Ohio State

10. Marshall

10. Maryland

11. Drake

11. Florida State

11.Jacksonville

11. Memphis State

11. Kansas State

12. New Mexico State

12. Houston

12. Notre Dame

12. Hawaii

12. Missouri

13. South Carolina

13. Pennsylvania

13. North Carolina

13. Maryland

13. Syracuse

14. Marquette

14. Drake

14. Houston

14. Florida State

14. Southwestern Louisiana

15. Louisville

15. Davidson

15. Duquesne

15. Virginia

15. Memphis State

16. Boston College

16. Utah State

16. Long Beach State

16. Minnesota

16. Jacksonville

17. Notre Dame

17. Niagara

17. Tennessee

17. Oral Roberts

17. St. John’s, NY

18. Colorado

18. Western Kentucky

18. Villanova

18. Missouri

18. St. Joseph’s, PA

19. Kansas

19. Long Beach State

19. Drake

19. Houston

19. San Francisco State

20. Illinois

20. Southern California

20. Brigham Young

20. Indiana

20. Kentucky

[Roanoke Times

Wed 5 Mar. 1969]

[Roanoke Times

Wed 10 Mar. 1970]

[Roanoke Times

Wed 16 Mar. 1971]

[Roanoke Times

Wed 7 Mar. 1972]

[Roanoke Times

Wed 7 Mar. 1973]

Tournament Winners:

NCAA-UCLA

NCAA-UCLA

NCAA-UCLA

NCAA-UCLA

NCAA-UCLA

NIT-Temple

NIT-Marquette

NIT-North Carolina

NIT-Maryland

NIT-Virginia Tech

[Roanoke Times

Wed 23 Mar. 1969]

[Roanoke Times

Wed 22 Mar. 1970]

[Roanoke Times

Wed 28 Mar. 1971]

[Roanoke Times

Wed 26 Mar. 1972]

[Roanoke Times

Wed 26 & 27 Mar. 1973]

 

 

Table 2

Football and Basketball Rankings

Football

Score

Rank

Basketball

Score

Rank

Texas

5.0

1

UCLA

1.0

1

Pennsylvania State

6.8

2

Marquette

7.2

2

Nebraska

7.0

3

North Carolina

9.6

3

Notre Dame

7.6

4

South Carolina

10.4

4

Ohio State

7.8

.5

Kentucky

11.2

5

Michigan

8.4

6

Pennsylvania

12.0

6

Tennessee

9.6

7

Long Beach State

13.0

7

Oklahoma

10.8

8

Jacksonville

14.6

8.5

Louisiana State

11.6

9

Houston

14.6

8.5

Arkansas

12.0

10

North Carolina State

15.0

10

Southern California

12.2

11

Now Mexico State

16.0

11.5

Auburn

12.6

12

Notre Dame

16.0

11.5

Arizona State

13.8

13

Louisville

16.4

13.5

Alabama

14.0

14

Minnesota

16.4

13.5

Mississippi

15.0

15

Davidson

16.6

15

Colorado

15.4

16.5

Drake

17.2

13

Stanford

15.4

16.5

Kansas

17.2

18

Georgia

15.6

18

La Salle

17.2

18

Missouri

16.8

19

Maryland

17.2

18

Houston

17.4

20

Southwestern Louisiana

17.2

18

Toledo

17.8

21

Duquesne

17.4

22

Kansas

18.2

23

St. Bonaventure

17.4

22

Purdue

18.2

23

Santa Clara

17.4

22

UCLA

18.2

23

Florida State

17.6

25.5

North Carolina

19.2

25

St. John’s, NY

17.6

25.5

Georgia Tech

19.4

26

Southern California

17.6

25.5

Dartmouth

19.6

28

Western Kentucky

17.6

25.5

Florida

19.6

28

Memphis State

17.8

28.5

Southern Methodist

19.6

28

Providence

17.8

28.5

Oregon State

19.8

30

Purdue

18.0

30

Air Force

20.0

31

Brigham Young

18.2

32

North Carolina State

20.2

33

Iowa

18.2

32

Tulane

20.2

33

Villanova

18.2

32

West Virginia

20.2

33

Indiana

18.4

34

Louisville

20.4

35

Fordharn

18.6

35.5

Washington (Seattle)

20.6

36.5

Missouri

18.6

35.5

Washington State

20.6

36.5

Marshall

18.8

37.5

Ohio

21.0

38

Ohio State

18.8

37.5

 

 

5 ties

Kansas State

19.0

39

 

 

 

Hawaii

19.2

40

 

 

 

Syracuse

19.4

41

 

 

 

Virginia

19.8

42

 

 

 

Boston College

20.0

43.5

 

 

 

Utah State

20.0

43.5

 

 

 

Oral Roberts

20.2

46

 

 

 

Niagara

20.2

46

 

 

 

Tennessee

20.2

46

 

 

 

Colorado

20.4

48.5

 

 

 

St. Joseph's, PA

20.4

48.5

 

 

 

San Francisco State

20.6

50

 

 

 

Illinois

20.8

52

 

 

 

Temple

20.8

52

 

 

 

Virginia Tech

20.8

52

 

 

 

 

 

14 ties


III. Academic Excellence

 

There are many methods one could use for measuring academic excellence. We make no attempt in this first effort to be exhaustive. In fact, we restrict ourselves to one measure of graduate-school excellence and one measure of undergraduate excellence.

1. Graduate School Excellence

 

For a graduate-school excellence measure we use the “effectiveness of graduate programs” ranking given by Roose and Andersen[1]. Scores for the entries in a field category were obtained by adding ranks for an entry that was ranked in at least one‑half of the curricula in a field category and dividing by the number of ranked curricula. The rankings in the five field categories listed in Table 3 were obtained by ranking these scores. Then a total score, also given in Table 3, was obtained for those entries ranked in three or more categories by adding the ranks and dividing by the number of ranked categories. For those ranked in only one or two categories, a score was obtained as indicated in the footnotes of Table 3. The final graduate school ranking, obtained by ordering the entries according to decreasing score, is listed in Tables 3 and 5.

 

Table 3

“Effectiveness of Graduate Program” Ranking Obtained from the Roose-Andersen Report and Graduate School Ranking

Program

Humanities

Soc. Sci.

Bio. Sci.

Phys. Sci.

Engin.

Score

Footnotes

Rank

Harvard

1

1

2

1

 

1.25

 

1

Calif. (Berkeley)

4

5

1

4

1

3.0

 

2

Calif. Inst. Tech.

 

 

4

2

4

3.3

 

3

Stanford

6

7

3

3

1

4.0

 

4

Mass. Inst. Tech.

 

 

7

6

1

4.7

 

5

Princeton

2

6

13

4

7

6.4

 

6

Wisconsin

5

8

6

7

 

6.5

 

7

Yale

3

3

11

12

 

7.25

 

8

Michigan

8

2

8

14

6

7.6

 

9

Texas

7

 

 

13

12

10.7

 

10

Chicago

9

4

21

9

 

10.75

 

11

Cornell

11

14

12

8

10

11.0

 

12

Illinois

13

16

14

10

5

11.6

 

13

UCLA

12

12

16

11

 

12.75

 

14

Rockefeller

 

 

4

 

 

13.3

*3

15

Minnesota

 

10

19

17

8

13.5

 

16

Johns Hopkins

14

17

10

 

 

13.7

 

17

Pennsylvania

10

9

 

 

 

14.3

*1

18

Columbia

15

13

 

16

 

14.7

 

19.5

Purdue

 

 

17

 

9

14.7

*2

19.5

Wash. (Seattle)

 

 

9

 

 

15.0

*3

21

Indiana

 

15

17

 

 

16.7

*2

22

Calif. (Davis)

 

 

15

 

 

17.0

*3

23

Carnegie Mellon

 

30

 

 

11

17.7

*4

24.5

Northwestern

 

11

 

 

 

17.7

*4

24.5

Mich. State

 

 

20

 

 

18.7

*3

26

Calif. (San Diego)

 

 

 

15

 

19.0

*4

27

Brown

16

 

 

 

 

19.3

*4

29

Case Western Res.

 

 

22

 

 

19.3

*3

29

Wash. (St. Louis)

 

 

22

 

 

19.3

*3

29

 

 

 

 

 

 

 

 

3 ties

Footnotes: *1: Added 24 & ÷3;  *2: Added 18 &   ÷3;  *3:  Added  (18+18) & ÷3;  *4: Added (24+18) & ÷3

 

Undergraduate Excellence

 

Since often the justification for involving educational institutions with big‑time athletics is that it attracts good students, we restrict ourselves to some measure of the academic excellence of the students attracted to an institution; i.e., incoming freshmen. Because the SAT scores of entering freshmen are available in Singletary's[2] compendium, we use the average SAT score (average of verbal and mathematical scores) as a ranking measure.

 

Table 4 lists the average SAT score for a selection of schools. The Singletary compendium does not give SAT scores for some schools. Our selection includes all those available in Singletary that are ranked in Tables 2 and 3 and most colleges and universities with average SAT scores higher than 599. (We say “most” because we did not attempt to find all such schools.) By excluding schools which are both unranked in Tables 2 and 3 and have SAT scores below 600 we bias our results toward larger correlations between undergraduate quality and the other qualities. Similarly, by not systematically searching for all schools unranked in Tables 2 and 3 with average SAT scores higher than 599, we again bias toward larger correlations.

 

Table 4

Undergraduate Freshmen Average SAT Score Ranking

 

SAT

Rank

 

SAT

Rank

 

SAT

Rank

Calif. Inst. Tech.

715

1

Washington (St. Louis)

611

40

North Carolina State

536

79

Mass. Inst. Tech.

714

2

Stevens Inst. Tech.

610

41

Delaware

535

81

Harvard

695

3

Carnegie Mellon

609

42.5

La Salle

535

81

Yale

690

4

Case West. Res.

609

42.5

Vermont

535

81

Rice

684

5

SUNY (Stoney Brook)

607

44

Southern Methodist

534

83

Brandeis

669

6

William & Mary

606

45

Providence

530

84

Brown

665

8

Northwestern

604

46.5

St. Bonaventure

523

85

Chicago

665

8

Wabash

604

46.5

Auburn

522

86

Reed

665

8

Boston U.

600

48.5

Mass. (Boston)

520

87

Carleton

662

11

Michigan

600

48.5

Cincinnati

517

89

Dartmouth

662

11

SUNY (Buffalo)

595

50

Detroit

517

89

Williams

662

11

Georgia Tech.

593

51

Texas A&M

517

89

Columbia

661

13.5

New York

589

52

San Francisco State

516

91.5

Princeton

661

13.5

George Washington

587

53

St. John's, NY

516

91.5

Oberlin

660

15

Syracuse

583

54

Niagara

515

93

Cornell

657

16

Tulane

582

55

South Florida

514

94

Pennsylvania

655

17

St. Joseph's, Pa.

579

56

Toledo

513

95

Middlebury

650

18

CCNY

577

58

Louisville

512

97.5

Renss. Poly. Inst.

648

19

Massachusetts (Amherst)

577

58

Ohio

512

97.5

Johns Hopkins

646

20

Wisconsin

577

58

Oregon

512

97.5

Rochester

645

21

North Carolina

576

60

Tulsa

512

97

Air Force

640

23

Miami (Ohio)

575

61

Texas Christian

511

100.5

Davidson

640

23

Wake Forest

572

62

Wayne State

511

100.5

Lehigh

640

23

Pennsylvania State

570

63

Georgia

510

102

Tufts

635

25

Santa Clara

569

64

Missouri

509

103

Duke

629

26

Pittsburgh

562

65

Rhode Island

507

104

Georgetown

628

27.5

Northeastern

558

66.5

Indiana

505

105

Grinnell

628

27.5

Rutgers

558

66.5

Houston

504

106

Boston College

627

29.5

Maine

557

68

Arkansas

503

107.5

Colgate

627

29.5

Virginia Mil. Inst.

553

69

Duquesne

503

107.5

Antioch

626

31.5

Virginia Tech.

551

70

Temple

502

109

Vanderbilt

626

31.5

Connecticut

550

72

Oregon State

500

110

Naval Academy

621

33

Fairfield

550

72

South Carolina

498

111

Virginia

618

34.5

Villanova

550

72

Arizona

496

112

West Point

618

34.5

Texas (Austin)

547

74

Hawaii

495

113

SUNY (Bingh.)

615

36

Miami (Florida)

546

75

Idaho

483

114

Fordham

613

37

Southern California

544

76

Jacksonville

471

115

Emory

612

38.5

New Hampshire

543

77.5

Texas Tech

468

116

Washington & Lee

612

38.5

Purdue

543

77.5

22 ties

 

 

 

Table 5

Collection of All Rankings

School

Undergrad.

Graduate

Football

Basketball

School

Undergrad.

Graduate

Football

Basketball

Calif. I. Tech

1

3

 

 

Wisconsin

57

7

 

 

Mass. I. Tech

2

5

 

 

North Carolina

60

 

25

3

Harvard

3

1

 

 

Miami (Ohio)

61

 

 

 

Yale

4

8

 

 

Wake Forest

62

 

 

 

Rice

5

 

 

 

Penn. State

63

 

2

 

Brandeis

6

 

 

 

Santa Clara

64

 

 

21

Brown

7

28

 

 

Pittsburgh

65

 

 

 

Chicago

7

11

 

 

Northeastern

66

 

 

 

Reed

7

 

 

 

Rutgers

66

 

 

 

Carleton

10

 

 

 

Maine

68

 

 

 

Dartmouth

10

 

27

 

Va. Mil. Inst.

69

 

 

 

Williams

10

 

 

 

Virginia Tech

70

 

 

51

Columbia

13

19

 

 

Connecticut

71

 

 

 

Princeton

13

6

 

 

Fairfield

71

 

 

 

Oberlin

15

 

 

 

Villanova

71

 

 

31

Cornell

16

12

 

 

Texas (Austin)

74

10

1

 

Pennsylvania

17

18

 

6

Miami (Fl.)

75

 

 

 

Middlebury

18

 

 

 

Southern Calif.

76

 

11

24

Renss. Poly. Inst.

19

 

 

 

New Hampshire

77

 

 

 

Johns Hopkins

20

17

 

 

Purdue

77

19

23

30

Rochester

21

 

 

 

N. Carolina St.

79

 

32

10

Air Force

22

 

31

 

Delaware

80

 

 

 

Davidson

22

 

 

15

La Salle

80

 

 

16

Lehigh

22

 

 

 

Vermont

80

 

 

 

Tufts

25

 

 

 

Southern Meth.

83

 

27

 

Duke

26

 

 

 

Providence

84

 

 

28

Georgetown

27

 

 

 

St. Bonaventure

85

 

 

21

Grinnell

27

 

 

 

Auburn

86

 

12

 

Colgate

29

 

 

 

Mass. (Boston)

87

 

 

 

Boston College

29

 

 

 

Cincinnati

88

 

 

 

Antioch

31

 

 

 

Detroit

88

 

 

 

Vanderbilt

31

 

 

 

Texas A & M

88

 

 

 

Naval Acad.

33

 

 

 

St. John’s, NY

91

 

 

24

Virginia

34

 

 

42

San. Fran. State

91

 

 

50

West Point

34

 

 

 

Niagara

93

 

 

45

SUNY (Binghamton)

36

 

 

 

South Florida

94

 

 

 

Fordham

37

 

 

35

Toledo

95

 

21

 

Emory

38

 

 

 

Louisville

96

 

35

13

Wash. & Lee

38

 

 

 

Ohio

96

 

38

 

Wash. (St. Louis)

40

28

 

 

Oregon

96

 

 

 

Stevens I. Tech

41

 

 

 

Tulsa

96

 

 

 

Carnegie Mellon

42

24

 

 

Texas Christian

100

 

 

 

Case West. Res.

42

28

 

 

Wayne State

100

 

 

 

SUNY (Stoney Br.)

44

 

 

 

Georgia

102

 

18

 

William & Mary

45

 

 

 

Missouri

103

 

19

35

Northwestern

46

24

 

 

Rhode Island

104

 

 

 

Wabash

46

 

 

 

Indiana

105

22

 

34

Boston University

48

 

 

 

Houston

106

 

20

8

Michigan

48

9

6

 

Arkansas

107

 

10

 

SUNY (Buffalo)

50

 

 

 

Duquesne

107

 

 

21

Georgia Tech.

51

 

26

 

Temple

109

 

 

51

New York

52

 

 

 

Oregon State

110

 

30

 

George Washington

53

 

 

 

South Carolina

111

 

 

4

Syracuse

54

 

 

41

Arizona

112

 

 

 

Tulane

55

 

32

 

Hawaii

113

 

 

40

St. Joseph’s, PA

56

 

 

48

Idaho

114

 

 

 

CCNY

57

 

 

 

Jacksonville

115

 

 

8

Mass. (Amherst)

57

 

 

 

Texas Tech.

116

 

 

 

 

 

 

Table 5 (continued)

Collection of All Rankings

School

Undergrad.

Graduate

Football

Basketball

School

Undergrad.

Graduate

Football

Basketball

Alabama

 

 

14

 

Memphis State

 

 

 

28

Arizona State

 

 

13

 

Michigan State

 

26

 

 

Brigham Young

 

 

 

31

Minnesota

 

16

 

13

California (Berkeley)

 

2

 

 

Mississippi

 

 

15

 

California (Davis)

 

23

 

 

Nebraska

 

 

3

 

UCLA

 

14

22

1

New Mexico St.

 

 

 

11

California (San Diego)

 

27

 

 

Notre Dame

 

 

4

11

Colorado

 

 

16

48

Ohio State

 

 

5

37

Drake

 

 

 

16

Oklahoma

 

 

8

 

Florida

 

 

27

24

Oral Roberts

 

 

 

45

Illinois

 

13

 

51

Rockefeller

 

15

 

 

Iowa

 

 

 

31

Southwestern La.

 

 

 

16

Kansas

 

 

 

16

Stanford

 

4

16

 

Kansas State

 

 

24

39

Tennessee

 

 

7

45

Kentucky

 

 

 

5

Utah State

 

 

 

43

Long Beach State

 

 

 

7

Wash. (Seattle)

 

21

36

 

Louisiana State

 

 

9

 

Washington State

 

 

36

 

Marquette

 

 

 

2

Western Kentucky

 

 

 

24

Marshall

 

 

 

37

West Virginia

 

 

32

 

Maryland

 

 

 

16

 

 

 

 

 

 

 

 

 

 

Numbers ranked:

116

30

38

51

 

 

 

 

 

Number of ties:

22

3

5

14

 

IV. CORRELATION COEFFICIENT

 

We use the expression for the correlation coefficient for two different rankings derived in the book by Yule and Kendall[3]. This expression allows for the possibility of tied ranks. It is

where  is the total number of entries,  is the rank of the ith  entry in the first ranking;  is the rank of the ith entry in the second ranking;

 ,

where  is the number of ties in the first ranking,  is the number of ties in the second ranking and  is the number that are tied in the jth  tie for the ranking in question. The  for tied ranks are the average ranking for the particular tie in question; i.e., if  entries occupy the ranks  then

 .

These values of  are listed for the tied entries in Tables 2, 3 and 4.

 

But we have a further complication not discussed by Yule and Kendall; namely, we have entries that are ranked in only one of the two rankings to be compared. We handle this situation as follows: Let  be the total number of different entries in both rankings (as given above),  be the number of entries in the first ranking and  be the number of entries in the second ranking. Thus, there are  entries that are unranked in the first ranking and  entries that are unranked in the second ranking. We use a computer random generator to randomly fill all of the ranks from  to  for the first ranking and from  to  for the second ranking. Since surely some of these entries should be truly ranked larger than , this procedure should favor larger correlations.

 

We do this residual random ranking a large number of times (1000 times) and take the average correlation coefficient and the standard deviation as our correlation coefficient and its error. The results are listed in Table 6.

 

Table 6

Average Correlation Coefficients and Standard Deviations

Undergraduate

1.

 

 

 

Graduate

+0.033±0.053

1.

 

 

Football

-0.418±0.046

-0.540±0.032

1.

 

Basketball

-0.496±0.033

-0.556±0.038

-0.453±0.030

1.

 

Undergraduate

Graduate

Football

Basketball

Maximum and Minimum Correlation Coefficients Obtained in 1000 Residual Random Rankings

Undergraduate

1

 

 

 

Graduate

+0.192

-0.125

1

 

 

Football

-0.275

-0.580

-0.433

-0.635

1

 

Basketball

-0.382

-0.591

-0.441

-0.669

-0.354

-0.541

1

 

Undergraduate

Graduate

Football

Basketball

V. Conclusion and Criticism

 

Before discussing the results in Table 6, perhaps we should state what correlation coefficients indicate. A correlation coefficient of +1 for two rankings indicates that the two rankings are identical. A correlation coefficient of  -1 indicates that the two rankings are exactly opposite. A coefficient of 0 would indicate that the two rankings are totally random relative to each other. Thus, a large positive correlation coefficient indicates that the two rankings closely coincide and a large negative coefficient indicates that the two rankings are nearly anti­-coincident.

 

Table 6 clearly shows that, for the methods of ranking that we use, there are significant negative correlations between all pairs of ranking except undergraduate versus graduate. In this one exceptional comparison the correlation is effectively zero, although it should be pointed out that this correlation may be greater than zero for large schools and that we were not able to obtain freshman SAT scores for several highly ranked graduate schools that we suspect have high freshman SAT scores. A more careful study should be done on this correlation; it is not our main purpose here.

 

So it appears that the contentions that big‑time athletics (1) attracts good students and (2) enables programs of academic excellence are both false. It also appears that concentration on excellence in one big‑time sport usually excludes excellence in the other big‑time sport. However, concentration on excellence in either graduate or undergraduate education does not exclude excellence in the other. Have we possibly biased the result toward small correlations? As indicated above, at various stages, we have always tried to bias it toward large correlations when there was a choice.

 

1. Other methods of ranking could be used. For example, percentage of students who go on to graduate school could be used as a measure of undergraduate excellence. This would measure the product of the school rather than the “raw material” measure that we used.

2. We did not study rankings of small colleges with regard to athletic excellence. We believe that most of the small colleges with strong big-time athletic programs are ranked quite low on average SAT scores for incoming freshmen. If so, then our results stand. Further study is needed on this point.

3. Singletary's compendium2 did not give entering SAT scores for some schools that we know must be truly highly ranked according to SAT scores. We suspect that this correction would lower the correlation coefficients. Further study is desirable.

4. A further study should separate out schools of different student body sizes to see if large schools are able to simultaneously promote athletics and academic excellence more easily than can small schools.

5. A further study should separate out state‑supported schools from private schools to see if there are differences between the two types.

6. An interesting question to pursue is: Is the United States the only country where big‑time sports and education institutions are intimately connected?

 

If our conclusions remain after further study, one must ask the question: What is the actual connection between big‑time sports and educational institutions? We would offer an hypothesis: Societies from the “beginning” have depended upon physical prowess for their survival, and, thus, have come to savor physical combat; and the most likely combatants are young men. Now that societies are “suddenly” depending more on intellectual capacity, which must be constantly developed from an early age, it is understandable why these seemingly unrelated emphases are found together in institutions for development of the young.

 

But our newly acquired intellectual capacity compels us to ask: Is that the best way? Should we, instead, have separate institutions dedicated to these unrelated pursuits? Of course, we do have professional sports organizations and we have many educational institutions (our best, as this study shows) that do not emphasize big‑time sports. Would not our society better recognize its increasing dependence on intellectual capability over physical prowess if the institutions that promote the two were separate and distinct? And would not institutions supposedly dedicated to increasing our intellectual capability be better able to use their limited financial and sociological resources to that end if they were not diverted to the unrelated pursuit of physical prowess?

 

We want to make it clear that we believe that assurance of physical fitness for all students is a necessary part of any educational program. We would urge an expansion of athletic programs for all students coincident with curtailment of big-time athletics in our institutions of higher education.

 

One of the authors (LDR) would be glad to run the computer code used here on any reasonable set of measures for academic excellence ranking.

 

The authors wish to thank Mr. Michael Tarpley, Dr. Robert L. Shotwell, Dr. Richard A. Arndt and several other colleagues, who may wish that their names not be mentioned, for help they have given us.



[1] Roose, K. D. and Andersen, C. J., A Rating of Graduate Programs, American Council of Education, Washington DC, 1970.

[2] American Colleges and Universities, 10th Ed., Edited by Otis A. Singletary, American Council on Education, Washington DC, 1968.

[3] Yule, G. U. and Kendall, M. G., An Introduction to the Theory of Statistics, Hafner Pub. Co., New Your, 1968, pp. 258-267.