The inflation of significance that comes from searching many places at once; the reason local and global significance differ.The look-elsewhere effect is a statistical phenomenon that occurs when a researcher searches for a significant result across many different places — such as many energy ranges, many possible signal locations, or many candidate variables — and finds a 'significant' result purely by chance. The more places you look, the more likely you are to find a false positive. This effect is the reason why a local significance (e.g., a 3-sigma bump in one bin) is not the same as a global significance (the probability of seeing such a bump anywhere in the entire search space).
The concept has been known in statistics for decades, but it became widely prominent in high-energy physics during the search for the Higgs boson, where physicists had to correct for the fact that they were scanning a wide mass range.
When you perform many independent tests, the probability of at least one false positive increases dramatically. For example, if you test 100 independent hypotheses at the 5% significance level, you expect about 5 false positives by chance alone. The look-elsewhere effect quantifies this inflation and provides a correction: the global p-value is the probability of seeing a result as extreme as the observed one anywhere in the search space, not just at the specific location where it was found. This is often computed using Monte Carlo simulations or analytic approximations.
It is essential in particle physics (e.g., searching for new particles), in genomics (scanning the genome for disease associations), and in astronomy (searching the sky for signals).
In particle physics, a '5-sigma' discovery claim is often quoted with the look-elsewhere correction factored in — the famous Higgs boson discovery had a local significance of 5.9 sigma, but a global significance of about 5.1 sigma.
