The Essentials of Hypothesis Testing for Risk Managers

Nigel Da Costa Lewis

Hypothesis testing has perhaps found its greatest use in medical science. New treatments for cancer, heart disease and diabetes are frequently subject to randomised trials where medical efficacy is assessed partly through statistical tests. Risk managers are also increasingly conducting formal statistical tests when building their models. In this chapter, we will introduce a straightforward approach to hypothesis testing. We begin by outlining the role of the normal distribution, before discussing the central limit theorem. This is followed by a step-by-step procedure for conducting a hypothesis test. We illustrate many of the ideas surrounding hypothesis testing with code samples written in R.

At the historical heart of hypothesis test procedures lies normal distribution, discovered by the Huguenot refugee, Abraham de Moivre, in 1733. However, it was Carl Friedrich Gauss, in his Theoria Motus Corporum of 1809, who derived it. In his honour, mathematicians and physicists refer to it as Gaussian distribution, and considerable importance was placed on it by early statisticians. In 1899, Francis Galton called it the “law of frequency of error”:

I know scarcely anything so apt to