SAT Comparisons Small Sample Example One
Question: Below are data on Verbal and Math SAT Scores
at the 25^{th} 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 pvalues.
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 ttest on means. Since I am agnostic about
whether math is lower or higher than verbal at the Big Ten I want to use a
twotailed 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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