Comparing a cross section of inter-quartile 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 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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