%0 Journal Article %1 demortier2014testing %A Demortier, Luc %A Lyons, Louis %D 2014 %K maths review stats %T Testing Hypotheses in Particle Physics: Plots of $p_0$ Versus $p_1$ %U http://arxiv.org/abs/1408.6123 %X 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.

@article{demortier2014testing, abstract = {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.}, added-at = {2019-11-08T17:01:38.000+0100}, author = {Demortier, Luc and Lyons, Louis}, biburl = {https://www.bibsonomy.org/bibtex/209e8f7909be9cde143dc013f4f7bfb87/vindex10}, description = {Testing Hypotheses in Particle Physics: Plots of $p_{0}$ Versus $p_{1}$}, interhash = {02529f0438f41fd855dc4f0ce523798b}, intrahash = {09e8f7909be9cde143dc013f4f7bfb87}, keywords = {maths review stats}, note = {cite arxiv:1408.6123Comment: 46 pages, 19 figures}, timestamp = {2019-11-08T17:01:38.000+0100}, title = {Testing Hypotheses in Particle Physics: Plots of $p_{0}$ Versus $p_{1}$}, url = {http://arxiv.org/abs/1408.6123}, year = 2014 }