Trialsworn: Look-Elsewhere Effect
Measurement, Noise & the Lab arc, page 128 of 193. Back to The Pixelated Physics Universe
Who they are
Trialsworn has one line, and says it often: “Local 3 sigma. global shrug.”
Trialsworn is a character of the Measurement, Noise & the Lab arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Look-elsewhere effect: a local significance must be corrected for the number of places you searched, lowering the global significance.
$$ \begin{gathered} p_{\text{global}} \approx p_{\text{local}} + \langle N(c_0) \rangle\, e^{-(c - c_0)/2} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $p_{\text{global}}$ | global p-value | — |
| $p_{\text{local}}$ | local p-value | — |
| $\langle N(c_0) \rangle$ | mean number of upcrossings of level c_0 | — |
| $c$ | observed test statistic (−2 ln likelihood ratio) | — |
| $c_0$ | low reference level | — |
Sources
Crossovers
Trialsworn meets Sigmarel (Five Sigma Discovery). Sigmarel's 5σ local bump may not survive Trialsworn: if you searched many places, the global significance is lower. That is why discovery claims report both.
Trialsworn meets Diphantom (750 GeV Diphoton Excess). Trialsworn always asks Diphantom how many mass bins were searched. The look-elsewhere effect cut the bump's global significance well below its local value.
Wear the lore
Concept keywords: Look-Elsewhere Effect, Trialsworn, Measurement, Noise & the Lab, physics lore, Pixelated Physics