Statistics 101, 201, and 202: Three Shiny Apps for Teaching Probability Distributions, Inferential Statistics, and Simple Linear Regression

TL;DR

The paper presents three open-source interactive web apps built with R and Shiny to facilitate teaching fundamental statistics concepts like probability distributions, confidence intervals, hypothesis testing, and linear regression.

Contribution

It introduces a suite of freely accessible, user-friendly apps that support statistical education without requiring programming knowledge, integrating computation and reasoning visually.

Findings

Apps enable students to perform statistical computations easily.

Visualizations and derivations support understanding of core concepts.

Source code is openly available under a permissive license.

Abstract

Statistics 101, 201, and 202 are three open-source interactive web applications built with R \citep{R} and Shiny \citep{shiny} to support the teaching of introductory statistics and probability. The apps help students carry out common statistical computations -- computing probabilities from standard probability distributions, constructing confidence intervals, conducting hypothesis tests, and fitting simple linear regression models -- without requiring prior knowledge of R or any other programming language. Each app provides numerical results, plots rendered with \texttt{ggplot2} \citep{ggplot2}, and inline mathematical derivations typeset with MathJax \citep{cervone2012mathjax}, so that computation and statistical reasoning appear side by side in a single interface. The suite is organised around a broad pedagogical progression: Statistics~101 introduces probability distributions and their properties; Statistics~201 addresses confidence intervals and hypothesis tests; and Statistics~202 covers the simple linear model. All three apps are freely accessible online and their source code is released under a CC-BY-4.0 license.