A visual, example-led first course in probability and statistics for students who know calculus. Every chapter is one interactive page with worked examples, real data and R code with its output.

Start reading 25 lectures

Contents

1. Chapter 0Before We Start

   Reference material: what the course is about, the calculus you will use, and a first session with R.

2. Chapter 1Prediction, Inference and Data

   The two big ideas of the course, where data come from, and why the way we sample matters.

   1. Lecture 1 Prediction, inference and sampling
   2. Lecture 2 Variables, studies and independence
3. Chapter 2Describing Data

   Shape, centre and spread, boxplots, honest pictures, and Simpson's paradox.

   1. Lecture 3 Shape, centre and spread
   2. Lecture 4 Boxplots, honest pictures and Simpson's paradox
4. Chapter 3Probability

   What probability means, its rules, counting, conditioning, Bayes' theorem and simulation.

   1. Lecture 5 What probability means and its rules
   2. Lecture 6 Counting and equally likely outcomes
   3. Lecture 7 Conditional probability and independence
   4. Lecture 8 Bayes' theorem, simulation and random variables
5. Chapter 4Discrete Random Variables

   Expected value and variance, and the binomial, geometric, negative binomial, hypergeometric and Poisson models.

   1. Lecture 9 Distributions, expected value and variance
   2. Lecture 10 Binomial, geometric and hypergeometric models
   3. Lecture 11 The Poisson model and choosing a model
6. Chapter 5Continuous Random Variables

   Densities, the Gaussian distribution, waiting times and other shapes of chance.

   1. Lecture 12 Densities, expected value and the uniform
   2. Lecture 13 The Gaussian distribution
   3. Lecture 14 Exponential, gamma, beta and other shapes
7. Chapter 6Joint Distributions

   Two random variables at once: joint, marginal and conditional distributions, correlation and prediction.

   1. Lecture 15 Joint, marginal and conditional distributions
   2. Lecture 16 Prediction, covariance and sums
8. Chapter 7Sampling Distributions

   Why averages are predictable: the Law of Large Numbers, the Central Limit Theorem and the bootstrap.

   1. Lecture 17 Statistics as random variables and the Law of Large Numbers
   2. Lecture 18 The Central Limit Theorem and the bootstrap
9. Chapter 8Estimation

   Estimators and their errors, the method of moments, maximum likelihood and confidence intervals.

   1. Lecture 19 Estimators and the method of moments
   2. Lecture 20 Maximum likelihood
   3. Lecture 21 Confidence intervals for a mean
   4. Lecture 22 Intervals for proportions and what confidence means
10. Chapter 9Hypothesis Testing

    The logic of tests, p-values, errors and power, and what significance does and does not mean.

    1. Lecture 23 The logic of a test, p-values and tests for a mean
    2. Lecture 24 Tests for a proportion, errors and power
    3. Lecture 25 Significance, many tests and replication