Technology Tips: A Fathom Activity for the Central Limit Theorem

2008 ◽  
Vol 102 (2) ◽  
pp. 151-153
Author(s):  
Todd O. Moyer ◽  
Edward Gambler
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Hypothesis Testing ◽  
Confidence Intervals ◽  
Central Limit ◽  
Skewed Distribution ◽  
Sampling Distribution ◽  
Sample Sizes ◽  
The Central Limit Theorem ◽  
Lecture Method

The central limit theorem, the basis for confidence intervals and hypothesis testing, is a critical theorem in statistics. Instructors can approach this topic through lecture or activity. In the lecture method, the instructor tells students about the central limit theorem. Typically, students are informed that a sampling distribution of means for even an obviously skewed distribution will approach normality as the sample sizes used approach 30. Consequently, students may be able to use the theorem, but they may not necessarily understand the theorem.

Statistical Simulation with Web-Based Apps

2018 ◽  
Vol 111 (6) ◽  
pp. 466-469
Author(s):  
Anne Quinn
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Confidence Intervals ◽  
Central Limit ◽  
Web Application ◽  
Original Data ◽  
Statistical Simulation ◽  
Web Based ◽  
The Central Limit Theorem

While looking for an inexpensive Web application to illustrate the Central Limit theorem, I found the Rossman/Chance Applet Collection, a group of free Web-based statistics apps. In addition to illustrating the Central Limit theorem, the apps could be used to cover many classic statistics concepts, including confidence intervals, regression, and a virtual version of the popular Reese's® Pieces problem. The apps allow users to investigate concepts using either preprogrammed or original data.

Statistical Inference and Simulation with StatKey

2016 ◽  
Vol 109 (9) ◽  
pp. 708-711 ◽  
Author(s):  
Anne Quinn
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Statistical Inference ◽  
Confidence Intervals ◽  
Central Limit ◽  
Real Data ◽  
Web Based ◽  
The Central Limit Theorem

StatKey, a free Web-based app, supplies real data to help with the central limit theorem, confidence intervals, and much more.

scholarly journals Statistical Approximating Distributions Under Differential Privacy

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Yue Wang ◽  
Daniel Kifer ◽  
Jaewoo Lee ◽  
Vishesh Karwa
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Confidence Intervals ◽  
Central Limit ◽  
Differential Privacy ◽  
Prior Work ◽  
Finite Sample ◽  
The Central Limit Theorem ◽  
Approximating Distributions

Statistics computed from data are viewed as random variables. When they are used for tasks like hypothesis testing and confidence intervals, their true finite sample distributions are often replaced by approximating distributions that are easier to work with (for example, the Gaussian, which results from using approximations justified by the Central Limit Theorem). When data are perturbed by differential privacy, the approximating distributions also need to be modified. Prior work provided various competing methods for creating such approximating distributions with little formal justification beyond the fact that they worked well empirically. In this paper, we study the question of how to generate statistical approximating distributions for differentially private statistics, provide finite sample guarantees for the quality of the approximations.

scholarly journals Estimating the Ratio of Means

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Confidence Intervals ◽  
Central Limit ◽  
Infinite Variance ◽  
Finite Variance ◽  
The Central Limit Theorem

Confidence intervals for ratio of means for large paired and unpaired samples with finite variance,obtained by applying the central limit theorem and Cramér-Wold device, are given. Also, these intervals for ratiosare obtained under infinite variance and when considering independent populations, by using stable distributions.Numerical illustrations by considering problems typically presented in practice are given

scholarly journals Simulating the Central Limit Theorem

2018 ◽  
Vol 18 (2) ◽  
pp. 345-356
Author(s):  
Marshall A. Taylor
Keyword(s):  
Standard Deviation ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Graduate Students ◽  
Central Limit ◽  
Standard Error ◽  
Random Variable ◽  
Sampling Distribution ◽  
The Central Limit Theorem ◽  
Variable Distribution

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.

scholarly journals Simulating the Central Limit Theorem

2018 ◽  
Author(s):  
Marshall A. Taylor
Keyword(s):  
Standard Deviation ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Graduate Students ◽  
Central Limit ◽  
Standard Error ◽  
Random Variable ◽  
Sampling Distribution ◽  
The Central Limit Theorem ◽  
Variable Distribution

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 paper, I outline a new Stata package, sdist, which can be used to simulate the central limit theorem by generating a matrix of randomly generated normal or non-normal variables and comparing the true sampling distribution standard deviation to 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.

Publication Bias: A Computer-Assisted Demonstration of excluding Nonsignificant Results from Research Interpretation

1997 ◽  
Vol 24 (4) ◽  
pp. 279-282 ◽  
Author(s):  
Todd C. Riniolo
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Publication Bias ◽  
Central Limit ◽  
Full Range ◽  
Computer Assisted ◽  
Sample Sizes ◽  
The Central Limit Theorem

This article describes a computer-assisted classroom demonstration illustrating the consequences of excluding nonsignificant findings from interpreting published literature. This demonstration, based on tenets of the Central Limit Theorem, simulates research interpretation when the full range of results are available compared with the subsample of significant results only. Results demonstrated that (a) exclusion of nonsignificant findings positively biases research interpretation and (b) smaller sample sizes are prone to greater bias when nonsignificant results are excluded from research interpretation.

Sign in / Sign up

Export Citation Format

Share Document