  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. We apply the methods to realistic simulations of the Fermi
Large Area Telescope data, in particular the search for dark matter
annihilation lines. Further, we discuss the counter-intutive scenario where the
look-elsewhere corrections are more conservative than much more computationally
efficient corrections for multiple hypothesis testing. Finally, we provide
general guidelines for navigating the tradeoffs between statistical and
computational efficiency when selecting a statistical procedure for signal
detection.
