## 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