Testing Hypotheses in Particle Physics: Plots of p₀ Versus p₁

August 26, 2014

For situations where we are trying to decide which of two hypotheses ​$H_{0}$ and ​$H_{1}$ provides a better description of some data, we discuss the usefulness of plots of ​$p_{0}$ versus ​$p_{1}$, where ​$p_{i}$ is the p-value for testing ​$H_{i}$. They provide an interesting way of understanding the difference between the standard way of excluding ​$H_{1}$ and the ​$CL_{S}$ approach; the “Punzi” definition of sensitivity; the relationship between p-values and likelihood ratios; and the probability of observing misleading evidence. They also help illustrate the Law of the Iterated Logarithm and the Jeffreys-Lindley paradox.

This paper, written in collaboration with Louis Lyons, is available on the arXiv at arxiv.org/abs/1408.6123