By Visruth Srimath Kandali (California Polytechnic State University, San Luis Obispo)
Information
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, but students often struggle with what does “not too skewed” mean. Our research seeks to clarify a guideline that incorporates measures of skewness along with sample size. Extensions include specification of different error rates and corrections for bias in the sample skewness statistic. We used simulation to explore the consequences of skewed populations with different sample sizes. We are currently testing versions of the new guidelines in introductory statistics classes at Cal Poly San Luis Obispo, a PUI, and we have found that it encourages students to consider their sample a little more holistically. We hope to provide students and practitioners with a more refined yet still viable guideline that encourages consideration of skewness.