## Friday, May 27, 2016

### SAT Comparisons Small Sample Example One

SAT Comparisons Small Sample Example One

Question:   Below are data on Verbal and Math SAT Scores at the 25th percentile for the 14 Big Ten Schools.   Using Excel commands calculate the average and the standard deviation of these two SAT scores for the Big Ten schools and test for whether differences in mean and dispersion between the two SAT scores are significant at standard p-values.

Data:

The data used in the analysis is presented below.

 Big Ten Verbal and Math SAT Averages School Verbal SAT 25th Percentile Math SAT 25th Percentile Ohio State 540 610 University of Michigan 620 660 Michigan State 420 550 University of Minnesota 550 620 University of Iowa 540 620 Purdue 520 560 Indiana University 520 540 Rutgers 520 570 University of Maryland 580 620 Northwestern 690 700 University of Illinois 560 700 Penn State 530 560 University of Wisconsin 530 630 University of Nebraska 490 520

Notes:

Use F.test to find out whether the standard deviations of the two SAT scores are identical or different and T.Test to determine whether means are statistically significant.

Since F.test reveals standard deviations do not differ assume identical variances in the t-test on means. Since I am agnostic about whether math is lower or higher than verbal at the Big Ten I want to use a two-tailed test.

Results:

 Comparison of Big Ten SAT Verbal and Math Scores School Verbal SAT 25th Percentile Math SAT 25th Percentile Average 543.6 604.3 Std 61.5 56.9 F.test for  equal variances 0.7865 T test for equal means 0.0117

The results confirm that Big Ten schools tend to do much better on the math SAT than the verbal SAT.  The difference in means is highly significant.

I wonder if this is true for private schools.

Statistic students might want to calculate the test statistic from the formulas in their text book rather than rely on the Excel functions.   This would be a useful learning exercise.