Introduction to Statistics: A Simulation-First Approach

An Open Educational Resource

Welcome

This is an open educational resource (OER) for introductory statistics, built on a simulation-first pedagogy. Students develop statistical reasoning through hands-on simulation before encountering formal mathematical theory.

📝 Help improve this book — leave feedback in the margin

This textbook is a work in progress, and your feedback makes it better. You can comment right on the page — nothing to install.

1. Click the < tab on the right edge of any page to open the annotation sidebar (powered by a free tool called Hypothesis). The first time, create a free account.
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Anything helps — unclear explanations, notation you’d change, examples that fall flat, or plain typos.

Why simulation first?

Traditional introductory statistics courses begin with probability rules and distribution theory, then use those tools to build confidence intervals and hypothesis tests. Students memorize formulas without understanding why they work.

This textbook reverses that order:

1. Explore data — See patterns, describe distributions, visualize relationships.
2. Simulate inference — Use resampling (bootstrap, permutation) to understand what inference is and why it works.
3. Approximate with theory — Learn that the normal and \(t\)-distributions are mathematical shortcuts for what simulation does directly.
4. Formalize probability — Study probability rules and random variables after students already have deep intuition about randomness.
5. Model relationships — Apply all inference tools to regression and categorical data.

By the time students encounter the Central Limit Theorem, they have already built sampling distributions hundreds of times. The theorem becomes an elegant confirmation of what they’ve seen, not an abstract declaration to accept on faith.

How to use this book

Throughout this text, StatLens activities invite you to explore statistical concepts interactively. Look for boxes like this one. Each activity links to a browser-based simulation tool — no software installation required.

Launch StatLens to explore all available tools.

Guided Practice exercises appear throughout each chapter with solutions in footnotes — try them before peeking.

Worked Examples walk through complete analyses step by step.

Definitions highlight key statistical vocabulary.

About this book

This textbook remixes material from two outstanding open-source statistics textbooks:

• Introduction to Modern Statistics (2nd edition) by Mine Çetinkaya-Rundel and Johanna Hardin
• OpenIntro Statistics by David Diez, Mine Çetinkaya-Rundel, and Christopher Barr

Both are licensed under Creative Commons BY-SA 3.0, and this remix is shared under the same license.

Interactive simulations are powered by StatLens, an open-source statistics visualization toolkit developed at the University of Wisconsin-La Crosse.

License

This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.

You are free to share and adapt this material for any purpose, even commercially, as long as you give appropriate credit and distribute your contributions under the same license.