Simulating and Visualizing the Central Limit Theorem: A Practical Exploration
This post explores the Central Limit Theorem (CLT) through simulation and visualization. The author, having previously avoided statistics, uses R to generate samples from various distributions (uniform, normal, binomial, beta, exponential, chi-squared) and calculates sample means. The results visually demonstrate how the distribution of sample means approaches a normal distribution as sample size increases, confirming the CLT. The post further investigates the practical implications of using the t-distribution instead of the normal distribution for confidence interval calculations when dealing with limited sample sizes and unknown population variance. Simulations highlight the difference in confidence interval coverage across various sample sizes. Finally, an animation showcases how the distribution of sample means converges to a normal distribution as the sample size grows, offering a compelling visual understanding of this fundamental statistical concept.
Read more