sdist: A Stata Module for Simulating the Central Limit Theorem

A sound understanding of 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 actually works and why researchers rely on its properties to draw inferences from a single unbiased random sample.

This package, sdist, offers a tool for teaching and learning the central limit theorem via easy-to-generate simulations. Specifically, sdist can be used to simulate the central limit theorem by (1) generating a matrix of randomly-generated normal or non-normal variables, (2) plotting the associated empirical sampling distribution of sample means, (3) comparing the true sampling distribution standard deviation to the standard error from the first randomly-generated sample, and (4) automatically producing a side-by-side comparison of the two distributions.