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Figures Don’t Lie #4: % of Less Than 20-Students Classes

Small Class.jpgThe ever-evolving Dartblog Style Book restrains writers from referring to a subject as a “textbook case” unless the textbook itself is to hand. Fortunately for this writer, I have the book! As we examine the administration’s oft-made (and previously criticized here and here) boast that “…over the past decade… we also have offered more classes with fewer than 20 students, going from 57 percent to 64 percent of our classes,” we can can legitimately deem this figure a textbook example of a misleading statistic and refer to Professor Joel Levine’s Introduction to Data Analysis: The Rules of Evidence, the book he has employed for more than a decade in the Mathematics and Social Science 15 course of the same name.

Introduction to Data Analysis devotes ten full pages to laying out how the percentage of <20-student classes measurement confuses rather than enlightens students about the quality of a university. For a summary of why this statistic is yet another example of legerdemain on the part of the administration, examine the following two universities:

University A
Total # of Classes: 30
# of Classes with 19 Students: 20
# of Classes with 101 Students: 10
% of classes with <20 students: 67%

University B
Total # of Classes: 30
# of Classes with 19 Students: 20
# of Classes with 30 Students: 10
% of classes with <20 students: 67%

Which school would you rather attend? After all, both universities have the same percentage of classes with <20 students.

It does not take much reflection to see that the percentage of classes with <20 students statistic isn’t much help to you in making this decision. It rates both schools equally. As such, the percentage of small classes measure meets the test of a bad statistic: it rates two quite different situations equally. (Another banal example: the average height of professors at Dartmouth and at the University of New Hamsphire is equal, therefore…)

Here’s a better way of analyzing the same two schools:

University A
# of Students in Classes with <20 Students: 380 (20 classes of 19 students equals...)
# of Students in Classes with 20-80 Students: 0
# of Students in Classes with >100 or more Students: 1,010
% of Students in Classes with <20 Students: 27%

University B
# of Students in Classes with <20 Students: 380
# of Students in Classes with 20-80 Students: 300
# of Students in Classes with >100 or more Students: 0
% of Students in Classes with <20 Students: 56%

At University A, your chances as a student of being in a small class are 27%; at University B, your odds of being in a small class are 56%. Again, which school would you rather attend? This statistic is more helpful, don’t you think?

Here is the exact breakdown of the student experience at Dartmouth for the 2008-2009 year as drawn from the ever-helpful Dartmouth Fact Book:

Student Enrollments by Class Size
2-19 students: 34%
20-29 students: 15%
30-39 students: 14%
40-49 students: 10%
50+ students: 28%

Despite the administration’s assertion that almost two thirds of Dartmouth classes have <20 students, in fact, only a third of Dartmouth students found themselves in classes with <20 students last year. From a student’s perceptive, that is a more honest statistic.

Tomorrow: We’ll look briefly at where those classes are to be found (and where they aren’t).

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