Math versus verbal SAT Scores at private and public
universities
Issue: The table below has data on math and verbal
SAT scores (at the 75^{th} percentile) for 31 public schools and 20
private schools in California. Does the
gap between math and verbal SAT scores differ between private and public
schools? Is this gap statistically
significant?
Data on Math and Verbal SAT at the 75h Percentile


School Number

Verbal SAT 75th Percentile

Math SAT 75th Percentile

Difference Math  Verbal Scores

Dummy equal to 1 if the University is private 0 otherwise

1

650

690

40

0

2

720

770

50

0

3

680

760

80

0

4

660

730

70

0

5

550

600

50

0

6

640

680

40

0

7

600

670

70

0

8

590

610

20

0

9

570

620

50

0

10

520

540

20

0

11

650

690

40

0

12

550

560

10

0

13

550

570

20

0

14

550

590

40

0

15

550

580

30

0

16

480

510

30

0

17

580

630

50

0

18

510

530

20

0

19

490

510

20

0

20

510

530

20

0

21

610

620

10

0

22

500

520

20

0

23

530

540

10

0

24

550

560

10

0

25

530

530

0

0

26

500

520

20

0

27

470

470

0

0

28

540

540

0

0

29

510

520

10

0

30

580

560

20

0

31

550

590

40

0

32

720

760

40

1

33

780

790

10

1

34

660

680

20

1

35

680

700

20

1

36

640

680

40

1

37

630

640

10

1

38

510

520

10

1

39

650

670

20

1

40

640

650

10

1

41

600

610

10

1

42

640

660

20

1

43

550

580

30

1

44

590

613

23

1

45

610

620

10

1

46

630

630

0

1

47

600

610

10

1

48

700

700

0

1

49

550

520

30

1

50

620

620

0

1

51

550

560

10

1

The descriptive statistics for Math SAT – Verbal SAT at 75^{th}
percentile for the two groups of schools are listed below.
Descriptive Statistics
for difference between math and verbal SAT Scores at the 75th Percentile for
Public and Private Schools In California


Public Universities

Private Universities


Mean

28.1

13.2

Median

20

10

STD

22.8

15.3

N

31

20

Min

20

10

Max

80

40

The results of the standard ttest and the Wilcoxon rank sum
test are presented below.
Test results for differences in math minus verbal SAT scores at
private versus public schools


pvalue


twosample ttest with equal variances

0.014

Wilcoxon Rank Sum Test

0.018

Concluding Remark:
In California, the gap between math and verbal SAT scores
tends to be higher in public universities the private ones.
These results are statistically significant.
You are probably also interested in how public and private universities differ with regard to the interquartile range of SAT scores.
http://dailymathproblem.blogspot.com/2016/08/theinterquartilerangeofmathsat.html
You are probably also interested in how public and private universities differ with regard to the interquartile range of SAT scores.
http://dailymathproblem.blogspot.com/2016/08/theinterquartilerangeofmathsat.html
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