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◒ Statistics

An interactive introduction, from the first chance experiment to inference, experiment design, and regression. A deeper OpenIntro reading guide follows the course.

Distribution of the number of heads in ten independent fair coin flips. Five heads is most likely; zero and ten are rare. 0 5 10 ten fair coins, one head count number of heads → a distribution

Statistics through experiments

Start here. Try an idea, give it a name, then arrive at the definition, formula, or theorem it helps you understand. These sixteen chapters need no statistics or programming background.

Chapter Question
1. Probability and Events Can you know the chance and still be surprised? ◒
2. Random Variables and Distributions What shape appears when you repeat a chance experiment? ◒
3. Center and Spread What can an average hide? ◒
4. Descriptive Statistics and Student Surveys What can a small student survey reveal? ◒
5. Populations and Samples What can a handful of observations tell us? ◒
6. Sampling Bias and Random Assignment Can more data still mislead us? ◒
7. Sampling Distributions and the Central Limit Theorem Why do estimates move between samples? ◒
8. Confidence Intervals How much uncertainty remains after sampling? ◒
9. Hypothesis Tests and p-Values Could chance explain this result? ◒
10. Experimental Design What makes a comparison fair? ◒
11. Comparing Proportions Did the new version help? ◒
12. Comparing Means with Student’s t How different are these averages? ◒
13. Errors, Power, and Multiple Testing What might our test miss? ◒
14. Chi-Square Tests and ANOVA What changes when there are more than two groups? ◒
15. Correlation and Linear Regression What does a fitted line tell us? ◒
16. Reading a Statistical Study What can this study actually claim? ◒

The OpenIntro reading guide

Go deeper with worked examples and runnable Scheme and Python in this guide to OpenIntro Statistics (CC BY-SA 3.0). For the mathematics behind chance, follow the companion Introduction to Probability.

Chapter Question
1. Introduction to Data What should we measure, and how should we choose who enters a study? ◒
2. Summarizing Data When do center and spread reveal a pattern, and when do they hide one? ◒
3. Probability How do events combine, and when does knowing one change another? ◒
4. Distributions Which probability model fits the outcomes we are counting? ◒
5. Foundations for Inference How can a sample speak about a population without pretending certainty? ◒
6. Inference for Proportions How can we compare percentages when every count is noisy? ◒
7. Inference for Means How can we compare averages when the spread is estimated too? ◒
8. Simple Linear Regression Which line best fits the data, and how should we read its misses? ◒
9. Multiple and Logistic Regression What changes when we use several predictors or predict a yes-or-no outcome? ◒

📺 StatQuest videos ↗

OpenIntro Statistics is by David Diez, Mine Çetinkaya-Rundel, and Christopher Barr. The introductory chapters include their own source credits and licensing.

Neighbors