Statistics

Basic Concepts

Introducing the concept of the probability of an event. Also covers set operations and the sample-point method.

Basic Concepts

A brief introduction to what we're going to discuss in later chapters.

Conditional Probability

Introducing conditional probability and independence of events. Bayes' rule comes in as well.

Fundamentals of Nonparametric Methods

Some basic tools such as the permutation test and the binomial test. We also introduce order statistics and ranks, which will come in handy in later chapters.

Definitions for Discrete Random Variables

The probability mass function, cumulative distribution function, expectation and variance for random variables.

Location Inference for Single Samples

The Wilcoxin signed rank test explained.

Common Discrete Random Variables

We introduce the binomial (Bernoulli), geometric and Poisson probability distributions and their properties. The properties include their expectations, variances and moment generating functions.

Other Single Sample Inferences

Explore whether the sample is consistent with a specified distribution at the population level. Kolmogorov's test, Lilliefors test and Shapiro-Wilk test are introduced, as well as tests for runs or trends.

Definitions for Continuous Random Variables

The probability density function, cumulative distribution function, expectation and variance for a continuous random variable.

Methods for Paired Samples

An obvious extension of the one-sample procedures.