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

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 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 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 75^th percentile of the variable minus the 25^th 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 75^th 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 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 inter-quartile range of math SAT scores.