By Huda Saeed, Cassandra Pattanayak
Information
This Shiny application aims to increase understanding of the Central Limit Theorem (CLT) for advanced introductory or intermediate statistics students, as well as students taking a probability course. Unlike existing CLT applets, most of which end with a visualization of a sampling distribution, this application not only visualizes but also quantifies the similarity of the sampling distribution to a normal distribution via a Kolmogorov-Smirnov (K-S) statistic. The application aligns with a lesson plan, through which students internalize the intuition behind each step of the CLT and understand its limitations. Students learn about a variety of probability distributions and about the K-S statistic and then follow a series of guided questions to explore the relationship between population distribution, sample size, and K-S statistic that compares the sampling distribution to a normal. This project is motivated by experience guiding students through a CLT simulation and asking them to describe the extent to which the resulting sampling distribution is normal. Though there is value in descriptions like “somewhat normal” or “almost normal,” this application provides a more satisfying and concrete way for students to understand convergence to normality. This tool has been introduced in a class of 25-30 second-level statistics students.