History of "n = 30" Rule in Statistics

Voiceover

Presenter(s)

Hailey Johnson, Jewel Jemila

Abstract or Description

If you’ve taken an introductory statistics class, you’ve probably seen the “n > 30” rule--it has become so common that it has even been tested on the AP statistics exam. However, the “rule” is far from infallible, and it’s not derived from a calculation or proof. Consequently, our research question is: how did this rule come to the forefront of introductory statistics? What is the history of “n = 30”? Our dual approach included investigating samples of introductory statistics textbooks here at CSU for appearances of the rule, as well as online research of the history of the phenomenon. We had one hypothesis for the origin of “n=30” at first: in the original Student’s t-tables from 1917, Gosset wrote that “for ordinary purposes [Normal z-tables] may be used with n > 30.” From there, his work has been referenced for more than a century. However, what we were surprised to find through our research was that, as time went on, the “n>30” rule was referenced more and more in the context of the central limit theorem, rather than the t-distribution converging to the Normal distribution. This is particularly concerning as, for more skewed distributions, larger and larger sample sizes are needed, and “n>30” is insufficient. We believe it is hardly necessary to have n>30 as another rule for students to memorize in introductory statistics classes for little reason, and which must later be unlearned in more complex statistics.

Mentor

Ben Prytherch