The Practical Scope of the Central Limit Theorem
Other Statistics
2021-11-25 v1 Statistics Theory
Applications
Methodology
Statistics Theory
Abstract
The \textit{Central Limit Theorem (CLT)} is at the heart of a great deal of applied problem-solving in statistics and data science, but the theorem is silent on an important implementation issue: \textit{how much data do you need for the CLT to give accurate answers to practical questions?} Here we examine several approaches to addressing this issue -- along the way reviewing the history of this problem over the last 290 years -- and we illustrate the calculations with case-studies from finite-population sampling and gambling. A variety of surprises emerge.
Cite
@article{arxiv.2111.12267,
title = {The Practical Scope of the Central Limit Theorem},
author = {David Draper and Erdong Guo},
journal= {arXiv preprint arXiv:2111.12267},
year = {2021}
}
Comments
47 pages, 17 figures