Toward a robust and simple guideline for checking the Central Limit Theorem

Music City Center 

In statistical practice, many introductory statistical procedures require the sampling distribution of means to be approximately normal. Most students learn a simplified check of this condition as ``$n ≥ 30$'', which often becomes a black-and-white mantra replacing visual inspection of the data. A slightly more detailed version might be "n ≥ 30 as long as the population distribution is not too skewed." Our research seeks to clarify a guideline that incorporates measures of skewness along with sample size. We used simulation to explore the consequences of skewed populations with different sample sizes. We hope to provide students and practitioners with a slightly more refined rule that allows a way to operationalize the degree of skewness in statistical analysis.

Applied Statistics

Statistical Pedagogy

Simulation

Central Limit Theorem

Skewness

Normality Check 

Section on Statistics and Data Science Education