Look-Elsewhere Effect¶

Discount an exciting best-of-many find by the size of the search that produced it — converting a local p-value at one scanned peak into a global p-value asking whether any peak this extreme would occur anywhere, via the trials factor.

Core Idea¶

The look-elsewhere effect is the inflation of apparent significance that occurs when a search scans many locations or parameter values for a signal and reports the most extreme result without correcting for the size of the search space. A local p-value — is this peak improbable at this location — must be converted to a global p-value — would any peak this extreme occur anywhere in the window under the null — and the conversion, via the trials factor (the number of effectively independent looks), shrinks significance sharply. A 3-sigma local excess may become 1.5–2 sigma globally.

Scope of Application¶

Because it is a correction, not a mechanism, it applies wherever its precondition holds: a search scanning many positions and reporting the extremum, with a local significance and a countable number of effectively independent looks.

Particle physics — the original coinage: peak-fitting in mass spectra (Gross & Vitells 2010).
Astronomy and gravitational-wave detection — template-bank and sky-position trials factors.
Genome-wide association studies — the same problem under Bonferroni/FDR across millions of SNPs.
A/B testing platforms — many metrics across many segments inflating apparent winners.
Anomaly detection — scanning many time-series for spikes.

Clarity¶

Naming the effect makes visible the difference between two significances an isolated bump conflates: the local p-value (improbable at this location?) and the global p-value (would any excess this extreme appear anywhere?). Its load-bearing service is making the trials factor an explicit, estimable quantity rather than a silent feature of the pipeline, localizing where significance leaked — the freedom of the procedure to flag any of many candidate positions — and telling the experimenter which design choices inflate it.

Manages Complexity¶

An open-ended, per-pipeline anxiety about scanning collapses onto a single scalar: the trials factor. The analyst tracks two numbers — local significance and trials factor — and the honest global significance reads off. A clean discrete-versus-continuous fork fixes how the factor is computed (multiplicative Bonferroni-type versus expected-upcrossings approximation), and because the factor is tied to design choices, pre-specifying the window or blinding shrinks it before unblinding.

Abstract Reasoning¶

The effect licenses a deflationary-discounting move from a striking local result and search size down to honest global significance, a boundary move distinguishing the local from the global p-value, a diagnostic-on-the-procedure move locating the leak in the trials factor, an interventionist move shrinking the factor by design before unblinding, and a computation-routing move selecting the counting method by the discrete-versus-continuous shape of the search.

Knowledge Transfer¶

As an instrument, the correction transfers literally wherever its precondition holds — the identical trials-factor logic serves particle physics, astronomy, GWAS, A/B testing, and anomaly detection, with the discrete/continuous fork selected by the search shape. The boundary is instrument-reach versus over-reading: it applies only where genuine local p-values and a countable look-count exist. The portable correction belongs to the parent multiple_comparisons_correction (with Bonferroni and Benjamini–Hochberg as siblings); the portable intuition into non-statistical settings belongs to selection_bias and data_leakage, not this named effect.

Relationships to Other Abstractions¶

Current abstraction Look-Elsewhere Effect Domain-specific

Parents (1) — more general patterns this builds on

Look-Elsewhere Effect is a kind of Multiple Comparisons Correction Prime

The Look-Elsewhere Effect is multiple-comparisons correction specialized to a scanned or continuous search space, where a local extremum is converted to global significance through an effective trials factor.

Hierarchy paths (6) — routes to 6 parentless roots

Look-Elsewhere Effect → Multiple Comparisons Correction → Type I & Type II Errors → Hypothesis Testing (Null vs. Alternative) → Statistical Inference → Inductive Reasoning

Show alternative paths (5)

Neighborhood in Abstraction Space¶

Look-Elsewhere Effect sits in a sparse region of the domain-specific corpus (93^rd percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Statistical Bias & Sampling Artifacts (6 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-07-12