Further reading

Because of its obvious importance, inferential statistics is covered in many statistics books. Chapter 10 of Spiegel (1992) provides a clear introduction to statistical hypothesis testing with many examples. A more in-depth discussion is given in Chapter 5 of Wilks (1995). Chapter 3 of Emery and Thomson (1997) has a concise summary of hypothesis testing.

The whole of this chapter is based on classical statistical inference, which assumes that the population parameters are fixed constants with no uncertainty. Bayesian statisticians relax this assumption and treat both variables and population parameters as random variables. The extra uncertainty in the population parameters can sometimes lead to different Bayesian inferences to those found using classical inference. A clear non-mathematical introduction to Bayesian statistics can be found in Berry (1996).

Many wise and amusing words on the difficult art of inference and its potential pitfalls can be found in the stories of Sherlock Holmes by Sir Arthur Conan Doyle.