Mathematical background

This book assumes a basic acquaintance with introductory probability and descriptive statistics. Specifically, it will help to have met:

• basic probability rules and notation;
• random variables and their probability distributions;
• probability mass functions, probability density functions and cumulative distribution functions.

Everything else the book relies on is built up within it. Measures of central tendency and dispersion are reviewed in Unit 1 before they are used, and random variables, expected values and variances are developed there from first principles rather than assumed. If those terms are unfamiliar, that is where they are introduced.

The focus throughout is statistical inference and data analysis rather than probability theory itself. Where an idea from probability is needed, it is recalled briefly at the point of use.

A word to readers who are uncertain whether they have enough mathematics for this. Almost everything in the list above is notation and vocabulary rather than technique, and the difficulty of statistics lies elsewhere — in understanding what a question is asking and what the data can answer. If you can follow an argument carefully and are willing to work through the derivations rather than skip them, you have what this book requires. Begin at Unit 1 and consult a probability text only if something there genuinely does not yield.