Comparing a cross section of interquartile ranges for college test scores in California.
The Interquartile Range of Math SAT Scores in Public and Private Colleges in California
Issue: Below are the 25^{th} percentile and
75^{th} percentile of Math SAT scores for 31 public universities and 20
private universities in the state of California. Describe differences between the
Interquartile range of the Math SAT scores for public and private universities
in the state of California. Are the
differences between Interquartile range of public and private university Math
SAT scores statistically significant?
MATH SAT DATA for 51
Universities in California:
SAT Scores for 51 Schools
In California


School Number

School

25^{th}
Pctl Math SAT Score

75^{th}
Percentile
Math SAT
Score

DUM
Private
is 1.0

1

Cal Poly

590

690

0

2

UC Berkleuy

630

770

0

3

UCLA

600

760

0

4

UCSD

620

730

0

5

San Jose State

470

600

0

6

UC Davis

560

680

0

7

UC Irvine

530

670

0

8

SDSU

500

610

0

9

Cal State Poly

490

620

0

10

Cal State Sacramento

430

540

0

11

UCSB

560

690

0

12

San Francisco State
University

450

560

0

13

Cal state Chico

460

570

0

14

Cal State Long Branch

460

590

0

15

Cal State Fullerton

470

480

0

16

Cal State Los Angeles

390

510

0

17

University of California
Riverside

500

630

0

18

Cal State Northridge

400

530

0

19

Cal State San Bernadino

400

510

0

20

Cal State Fresno

410

530

0

21

UCAl Santa Cruz

490

620

0

22

Cal State East Bay

400

520

0

23

Cal State San Marcos

430

540

0

24

Sonoma State University

450

560

0

25

Cal State Channel Islands

420

530

0

26

Cal State Bakersfield

400

520

0

27

Cal State Dominquez Hill

380

470

0

28

Cal State Monterey Bay

430

540

0

29

Cal State Stanislaus

410

520

0

30

Humboltd State University

440

560

0

31

University of California
Merced

460

590

0

32

University of Souther
California

660

760

1

33

Stanford

700

790

1

34

Pepperdine

570

680

1

35

Santa Clara

610

700

1

36

University of Pacific

530

680

1

37

University of San
Francisco

540

640

1

38

Mount Saint Marys

420

520

1

39

University of San Diego

570

670

1

40

Loyola Marymount
University

550

650

1

41

Saint Mary’s College of
California

510

610

1

42

Chapman University

570

660

1

43

University of La Verne

470

580

1

44

California Lutheran
University

510

613

1

45

University of Redlands

520

620

1

46

Point Loma Nazarene
University

520

630

1

47

Azusa Pacific University

490

610

1

48

Occidental College

610

700

1

49

Vanguard University of
Southern California

400

520

1

50

Biola University

503

620

1

51

California Baptist
University

420

560

1

Descriptive Statistics:
The interquartile range of a variable is the 75^{th}
percentile of the variable minus the 25^{th} percentile of the
variable.
Below are descriptive statistics for the interquartile
ranges of the Math SAT scores for 31 public universities and 20 private
universities in the state of California.
Descriptive Statistics on
InterQuartile Range of Math SAT Scores at Public and Private Colleges in
California


Public Colleges

Private Colleges


Mean

119.7

107.0

Median

120.0

100.0

STD

13.8

16.1

N

31.0

20.0

Min

90.0

90.0

25th

110.0

100.0

75th

130.0

111.8

Max

160.0

150.0

The mean, median, and 75^{th} percentile of the
interquartile range of math SAT scores for public colleges appear notably higher
than the interquartile range for private universities.
Are these differences
statistically significant?
I conducted two tests on differences in the public and
private college interquartile range of the math SATs. The first test is the standard ttest on the
difference in two means when the variances are unequal. The second test is the Wilcoxon Rank sum test. This test calculates the ranks from the two
populations when the two samples are combined and compares the rank sums of the
two observations.
Test Results for
Difference in Interquartile Range of Math SAT Scores for Private and Public
Universities In California


Test

Pvalue

Ttest Unequal Variances

0.0063

Two Sample Wilcoxon
RankSum Test

0.0012

Both tests reveal that differences in public and private
school interquartile math SAT scores are significantly different than zero.
Conclusion: It seems as though that the gap between
highest scoring students (as measured by the 75^{th} percentile of math
SAT scores) and lower scoring students (as measured by the 25^{th}
percentile of math SAT scores) is larger in public universities than in private
universities. This result pertains to
schools in California. It would be
interesting to see if the results hold for other states and whether other
factors impact the interquartile range of math SAT scores.
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