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.

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