statistics

trials factor

The number of independent chances a search had to produce a fluctuation, by which local significance must be corrected.
7 related articles

Description

The trials factor (also known as the look-elsewhere effect) quantifies how much the statistical significance of a claimed signal is inflated when you search for it in many places at once. If you roll a die 100 times, you expect to see a six about 17 times; seeing one six is not remarkable. Similarly, if you scan a wide range of particle masses or energy ranges for a bump, a random fluctuation somewhere is likely. The trials factor is the number of independent chances your search had to produce such a fluctuation, and it tells you how much to penalize your initial 'local' significance to get the true 'global' significance.

History

The concept emerged in the 1970s in the context of high-energy physics searches, though its precise origin is diffuse. Louis Lyons and colleagues popularized the term 'look-elsewhere effect' in the 1980s, and the trials factor is the quantitative expression of that effect.

How it works

When you search for a signal, you compute a local p-value — the probability that a fluctuation at one specific location would look as extreme as what you saw. But because you tried many locations, the chance that at least one of them fluctuates is much higher. The trials factor is the ratio of the global p-value (probability of seeing such a fluctuation anywhere) to the local p-value. Roughly, if you have N independent search locations, the global significance is about the local significance multiplied by N (for small p-values). The correction becomes crucial when claiming discoveries in high-energy physics, where scanning over many possible new particle masses is routine.

In practice

Used in particle physics to set correct significance levels for new particle searches (e.g., the Higgs boson discovery) and in cosmology for scanning over many possible signals in cosmic microwave background data.

Fun fact

The trials factor can be as large as millions in a typical search for a new particle over a wide mass range, turning a 5-sigma local fluctuation into a mere 2-sigma global significance.

Concept graph →

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