Monday, August 8, 2016

Math versus verbal SAT Scores at private and public universities

Math versus verbal SAT Scores at private and public universities


Issue:   The table below has data on math and verbal SAT scores (at the 75th 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 75th 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 t-test and the Wilcoxon rank sum test are presented below. 



Test results for differences in math minus verbal SAT scores at private versus public schools
p-value
two-sample t-test 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 inter-quartile range of SAT scores.


http://dailymathproblem.blogspot.com/2016/08/the-interquartile-range-of-math-sat.html

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