Simulating the Central Limit Theorem

Abstract

Understanding the central limit theorem is crucial for comprehending parametric inferential statistics. Despite this, undergraduate and graduate students alike often struggle with grasping how the theorem works and why researchers rely on its properties to draw inferences from a single unbiased random sample. In this article, I outline a new command, sdist, that can be used to simulate the central limit theorem by generating a matrix of randomly generated normal or nonnormal variables and comparing the true sampling distribution standard deviation with the standard error from the first randomly generated sample. The user also has the option of plotting the empirical sampling distribution of sample means, the first random variable distribution, and a stacked visualization of the two distributions.