Introduction to Statistics: A Simulation-First Approach
Pilot edition · Spring 2027
Welcome
This is a free, open textbook for introductory statistics. You’ll learn statistics the way statisticians think about it: by asking what would happen if we collected the data again, and then finding out.
One idea
Most of statistics comes back to one question: what if we did it again? A new sample or a new random assignment would give a different result. Simulation shows how different. P-values, confidence intervals and standard errors are all ways of answering that question.
One habit
Finish every analysis by answering four questions:
- Could it be chance?
- How big is it?
- Who does it apply to?
- Did one thing cause the other?
A small p-value answers only the first. The other three are what make a conclusion worth reading. Each chapter opens with a real question and closes by answering these four.
How the book works
Unit 1 is about data: how it’s collected, graphed and summarized. Unit 2 builds the ideas of inference with simulation. You’ll shuffle and resample real data in your browser and see how much results vary. After that, each method shows up three ways:
- Simulate it. Run the simulation on the chapter’s data.
- Model it. Learn the formula, which is a shortcut for what you just simulated.
- Compare. Check that the two agree, and see when the shortcut breaks down.
Unit 5 collects the probability and calculation tools behind the methods.
What you’ll see in each chapter
StatLens boxes like this one link to a free simulation tool that opens in your browser, already loaded with the chapter’s data. Nothing to install. Many boxes ask you to predict before you run it. A quick guess first makes the result stick.
- Guided Practice questions appear throughout, with answers in the footnotes. Try them before you peek.
- Worked examples walk through a complete analysis, start to finish.
- Going deeper boxes are optional. Open them if you’re curious.
For homework and projects you’ll also use Jamovi, a free point-and-click program, or R if your instructor prefers. See Technology setup.
This edition is being piloted in Spring 2027, so your feedback matters. Click the < tab on the right edge of any page to open the annotation sidebar (Hypothesis, free). Then select any text and click Annotate to leave a comment pinned to that sentence. Unclear explanations, examples that fall flat and typos all help.
About this book
This book remixes two open textbooks from OpenIntro: Introduction to Modern Statistics and OpenIntro Statistics. Interactive simulations are powered by StatLens, developed at the University of Wisconsin–La Crosse. Instructors: the Preface explains how the book is built.
This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License. You may share and adapt it for any purpose, as long as you give credit and share your changes under the same license.