Sunday, August 7, 2016

The Interquartile Range of Math SAT Scores in Public and Private Colleges in California


The Interquartile Range of Math SAT Scores in Public and Private Colleges in California

Issue:  Below are the 25th percentile and 75th percentile of Math SAT scores for 31 public universities and 20 private universities in the state of California.   Describe differences between the Inter-quartile range of the Math SAT scores for public and private universities in the state of California.   Are the differences between Inter-quartile 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
25th  
Pctl Math SAT Score
75th 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 inter-quartile range of a variable is the 75th percentile of the variable minus the 25th percentile of the variable.

Below are descriptive statistics for the inter-quartile ranges of the Math SAT scores for 31 public universities and 20 private universities in the state of California.







Descriptive Statistics on Inter-Quartile 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 75th percentile of the inter-quartile range of math SAT scores for public colleges appear notably higher than the inter-quartile range for private universities. 


Are these differences statistically significant?

I conducted two tests on differences in the public and private college inter-quartile range of the math SATs.   The first test is the standard t-test 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
P-value
T-test Unequal Variances
0.0063
Two Sample Wilcoxon Rank-Sum Test
0.0012



Both tests reveal that differences in public and private school inter-quartile math SAT scores are significantly different than zero.




Conclusion:   It seems as though that the gap between highest scoring students (as measured by the 75th percentile of math SAT scores) and lower scoring students (as measured by the 25th 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 inter-quartile range of math SAT scores. 

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