Looking for a Needle in a Haystack? Look Elsewhere! A statistical comparison of approximate global p-values

The search for new significant peaks over a energy spectrum often involves a statistical multiple hypothesis testing problem. Separate tests of hypothesis are conducted at different locations producing an ensemble of local p-values, the smallest of which is reported as evidence for the new resonance. Unfortunately, controlling the false detection rate (type I error rate) of such procedures may lead to excessively stringent acceptance criteria. In the recent physics literature, two promising statistical tools have been proposed to overcome these limitations. In 2005, a method to find needles in haystacks was introduced by Pilla et al. [1], and a second method was later proposed by Gross and Vitells [2] in the context of the look elsewhere effect and trial factors. We show that, for relatively small sample sizes, the former leads to an artificial inflation of statistical power that stems from an increase in the false detection rate, whereas the two methods exhibit similar performance for large sample sizes. Finally, we provide general guidelines to select between statistical procedures for signal detection with respect to the specifics of the physics problem under investigation.